ADVANCED CORPORATE FINANCE -...

ADVANCED CORPORATE FINANCE

Dr. Marta [email protected]

Introduction

Module Outline

Literature

Grading

The purpose of this course is to give a

solid foundation in principles of corporate

finance in order to understand and analyze

the major issues affecting the financial

policies of corporations.

This course deals with

(1)investment,

(2)financing,

(3)payout and

(4)corporate governance decisions

from the point of view of maximizing shareholder

value.

Introduction Course Outline Literature Grading


Corporate Finance: Bigger Picture

Maximize shareholder

wealth/firm’s value

Investment decision

Financial decision Dividend decisionInvestment decision

Dividend decisionFinancial decision

What projects? Debt or equity? Active role?What projects? Debt or equity? Active role?

OBJECTIVE



These decisions are highly inter-related

Suppose a firm wishes to invest in a new project…

The project needs financing…

This can be paid with retained earnings (cash), by borrowing more (debt) or by a share issue (equity)

Cash: the investment decision affects the Dividend decision

Debt/Equity: the investment decision affects the Financial decision

Day Time Topic Book

16.09 (1) Goal of the firm(2) Present value calculations(3) Capital budgeting BM 1-6

17.09(1) Risk and return(2) Market efficiency(3) Valuing stocks and bonds

BM 7-15

7.10 (1) Dividend policy(2) Capital structure(3) Options

BM 16-21

4.11 (1) Leasing(2) Mergers(3) Corporate control and corporate

governance

BM 25, 31-33

5.11 Presentation

Test






Investment decision




OBJECTIVE

LECTURE 3LECTURE 1&2

LECTURE 1&4

Brealey, Richard A. and Myers, Stewart C. (2013),

Principles of Corporate Finance

11th edition (or older), McGrawHill


Additional articles can be provided during the course

http://www.google.co.uk/url?sa=i&rct=j&q=principles+of+corporate+finance+11th+edition&source=images&cd=&cad=rja&docid=9BDdw5NUd9PMVM&tbnid=q4xz_NCegDqJ1M:&ved=0CAUQjRw&url=http://shop.mcgraw-hill.com/mhshop/productDetails?isbn=0078034760&category=3657&ei=b7PQUav-EoLYPcnQgegF&bvm=bv.48572450,d.bGE&psig=AFQjCNEKaVNeznveUIa9m4tcddOyLHqx7A&ust=1372718314318800

http://www.google.co.uk/url?sa=i&rct=j&q=principles+of+corporate+finance+11th+edition&source=images&cd=&cad=rja&docid=9BDdw5NUd9PMVM&tbnid=q4xz_NCegDqJ1M:&ved=0CAUQjRw&url=http://shop.mcgraw-hill.com/mhshop/productDetails?isbn=0078034760&category=3657&ei=b7PQUav-EoLYPcnQgegF&bvm=bv.48572450,d.bGE&psig=AFQjCNEKaVNeznveUIa9m4tcddOyLHqx7A&ust=1372718314318800

www.witor.biz/acf


BOOK

Lecture NOTES

Seminar Solutions (REMIND ME 7th OCT!)

(1)Group (of 2) Presentation*:

Business Plan Project

due 5th Nov (word file, via email)

to be presented 5th Nov

30%

*obligatory

(2) TEST:

70%


Business Plan

should include the following:

1. Cover page & Executive summary & Company overview

2. Industry analysis & Customer analysis &

Competitive analysis

3. Operations Plan & Management team

4. Financial Analysis incl. Cash flow prediction

(solid grounds)

5. Sensitivity analysis

http://www.startupdonut.co.uk/startup/business-planning/writing-a-business-plan

http://www.entrepreneur.com/formnet/form/451

It is not a task who gets the best business idea

It is a task of how to implement the tools you learn at the module in order to prepare

investment decision


see examples

http://www.startupdonut.co.uk/startup/business-planning/writing-a-business-plan

http://www.entrepreneur.com/formnet/form/451

TEST

1. 90 min test

2. closed books test

3. 2 sections:

Section 1

Calculation question

5 questions

All questions obligatory

Section 2

Essay questions

Choose 2 out of 3 questions

Each question worth 20% of the mark


see 2015 exam paper

Questions?


(1)Goal of the firm

(2)Present value calculations

(3)Capital budgeting

Lecture 1:

Goal of the firm

What is a Corporation?

The Role of The Financial Manager

Maximizing Shareholders’ Value

Goal of the firm

Sole Proprietorships

Partnerships

Corporations

Unlimited LiabilityPersonal tax on profits (US)

Limited LiabilityCorporate tax on profits + personal tax on

dividends (US)

Separation of ownership and

management

What Is A Corporation?

A corporation is a legal entity (technically, a juristic person) which has a legal personality distinct from those of its members

Corporate Finance vs Managerial FinanceCorporations vs All companies

Goal of the firm

Firm’s

operations Financial

marketsFinancial

manager

cash invested in

firm

cash generated by

operations

cash raised from

investors

cash returned to

investors

cash

reinvest

ed

What real assets should the firm invest in? => investment, capital

budgeting decision

How should the cash for investment be raised? => financing decision

Goal of the firm

The Role of Financial Manager

Fundamental financial objective of a firm:Maximize the value of cash invested in thefirm by shareholders





Investment decision




OBJECTIVE

Goal of the firm

Maximizing shareholders wealth

Maximizing firm’s value

Maximizing share price

The strength of the stock price maximization objective function is its internal self correction mechanism.

Choose an Objective Function


Firms can always focus on a different objective function. Examples would include maximizing revenues maximizing firm size maximizing market share …

The key thing to remember is that these are intermediate objective functions. To the degree that they are correlated with the long term

health and value of the company, they work well. To the degree that they do not, the firm can end up with a

disaster

Goal of the firm


Choose a Different Objective Function

Is maximizing shareholders’ value

easy to achieve?

NO

Managers

STOCKHOLDERS

Maximize

stockholder

wealth

Hire & fire

managers

- Board

- Annual Meeting

BONDHOLDERS/

LENDERS

Lend Money

Protect

bondholder

Interests

FINANCIAL MARKETS

SOCIETY

Reveal

information

honestly and

on time

Markets are

efficient and

assess effect on

value

No Social Costs

All costs can be

traced to firm

Corporation: separation of ownership and management=> AGENCY COSTS &problems

Goal of the firm


Difference in Information

Difference in Objectives

Managers

23

STOCKHOLDERS

Managers put

their interests

above

stockholders

Have little control

over managers

BONDHOLDERS/

LENDERS

Lend Money

Bondholders can

get ripped off

FINANCIAL MARKETS

SOCIETY

Delay bad news

or provide

misleading

information

Markets make

mistakes and

can over react

Significant Social Costs

Some costs cannot be

traced to firm

What can go wrong?


Goal of the firm

Goal of the firm

In theory: The stockholders have significant control over management.

The two mechanisms for disciplining management are (a) the annual meeting and (b) the board of directors. Specifically, we assume that Stockholders who are dissatisfied with managers can not only express

their disapproval at the annual meeting, but can use their voting power at the meeting to keep managers in check.

The board of directors plays its true role of representing stockholders and acting as a check on management.

In Practice: Neither mechanism is as effective in disciplining management.


I. Managers and Shareholders

Goal of the firm

The power of stockholders to act at annual meetings is diluted: Most small stockholders do not go to meetings because the cost of going

to the meeting exceeds the value of their holdings. For large stockholders, the path of least resistance, when confronted by

managers that they do not like, is to vote with their feet (buy other company stocks).

Annual meetings are also tightly scripted and controlled events, making it difficult for outsiders and rebels to bring up issues that are not to the management’s liking.



In 2010, the median board member at a Fortune 500 company was paid $212,512, with 54% coming in stock and the remaining 46% in cash. If a board member is a non-executive chair, he or she receives about $150,000 more in compensation.

A board member works, on average, about 227.5 hours a year (and that is being generous), or 4.4 hours a week, according to the National Associate of Corporate Directors. Of this, about 24 hours a year are for board meetings.

Many directors serve on three or more boards, and some are full time chief executives of other companies.

Goal of the firm

Board of Directors as a disciplinary mechanism



A 1992 survey by Korn/Ferry revealed that 74% of companies relied on recommendations from the CEO to come up with new directors; Only 16% used an outside search firm. While that number has changed in recent years, CEOs still determine who sits on their boards. While more companies have outsiders involved in picking directors now, CEOs still exercise significant influence over the process.

Directors often hold only token stakes in their companies. The Korn/Ferry survey found that 5% of all directors in 1992 owned less than five shares in their firms. Most directors in companies today still receive more compensation as directors than they gain from their stockholdings. While share ownership is up among directors today, they usually get these shares from the firm (rather than buy them).

Many directors are themselves CEOs of other firms. Worse still, there are cases where CEOs sit on each other’s boards.

Goal of the firm



The CEO often hand-picks directors

Board of Directors as a disciplinary mechanism

Calpers, the California Employees Pension fund, suggested three tests in 1997 of an independent board

Are a majority of the directors outside directors?

Is the chairman of the board independent of the company (and not the CEO of the company)?

Are the compensation and audit committees composed entirely of outsiders?

Disney (1997) was the only S&P 500 company to fail all three tests.


Goal of the firm


Goal of the firm

Who’s on Board? The Disney Experience - 1997

S&P500

Goal of the firm

Application Test: Who owns/runs your firm?

Who are the top stockholders in your firm?

What are the potential conflicts of interests that you see emerging from this stockholding structure?

Control of the firm

Government

LendersEmployees

Managers-length of tenue-links to insiders

Inside stockholders-% of stock held

-voting & non voting shares

-control structure

Outside Stockholders-size of holding

-active or passive-short or long term


Goal of the firm


Disney’s top stockholders in 2003


Goal of the firm


Things change.. Disney’s top stockholders in 2009


Goal of the firm


When managers do not fear stockholders, they will often put their interests over stockholder interests

Maximizing the size of the company (prestige)

Increasing managerial power

Making their jobs more secure

Increasing personal remuneration

Personal projects


Goal of the firm


In theory: there is no conflict of interests between stockholders and bondholders.

In practice: Stockholder and bondholders have different objectives. Bondholders are concerned most about safety and ensuring that they

get paid their claims.

Stockholders are more likely to think about upside potential

II. Shareholders’ objectives vs. Bondholders’ objectives

Goal of the firm


Examples of the conflict…

Increasing dividends significantly: When firms pay cash out as dividends, lenders to the firm are hurt and stockholders

may be helped. This is because the firm becomes riskier without the cash.

Taking riskier projects than those agreed to at the outset: Lenders base interest rates on their perceptions of how risky a firm’s investments are.

If stockholders then take on riskier investments, lenders will be hurt.

Borrowing more on the same assets: If lenders do not protect themselves, a firm can borrow more money and make all

existing lenders worse off.


Goal of the firm


An Extreme Example: Unprotected Lenders?


Goal of the firm


In theory: Financial markets are efficient. Managers convey information honestly and in a timely manner to financial markets, and financial markets make reasoned judgments of the effects of this information on 'true value'. As a consequence-

A company that invests in good long term projects will be rewarded.

Short term accounting gimmicks will not lead to increases in market value.

Stock price performance is a good measure of company performance.

In practice: There are some holes in the 'Efficient Markets' assumption.

III. Firms and Financial Markets

Goal of the firm


Managers control the release of information to the general public

Information (especially negative) is sometimes suppressed or delayed by managers seeking a better time to release it.

In some cases, firms release intentionally misleading information about their current conditions and future prospects to financial markets.


Goal of the firm


Evidence that managers delay bad news?


Goal of the firm


Some critiques of market efficiency...

Investors are irrational and prices often move for no reason at all. As a consequence, prices are much more volatile than justified by the underlying fundamentals. Earnings and dividends are much less volatile than stock prices.

Investors overreact to news, both good and bad.

Financial markets are manipulated by insiders; Prices do not have any relationship to value.

Investors are short-sighted, and do not consider the long-term implications of actions taken by the firm


Goal of the firm


In theory: All costs and benefits associated with a firm’s decisions can be traced back to the firm.

In practice: Financial decisions can create social costs and benefits. A social cost or benefit is a cost or benefit that accrues to society

as a whole and not to the firm making the decision. Environmental costs (pollution, health costs, etc..)Quality of Life' costs (traffic, housing, safety, etc.)

Examples of social benefits include:creating employment in areas with high unemploymentsupporting development in inner cities creating access to goods in areas where such access does not

exist

IV. Firms and the Society

Goal of the firm


Social Costs and Benefits are difficult to quantify because ...

They might not be known at the time of the decision. In other words, a firm may think that it is delivering a product that enhances society, at the time it delivers the product but discover afterwards that there are very large costs.

(Asbestos was a wonderful product, when it was devised, light and easy to work with… It is only after decades that the health consequences came to light)

They are ‘person-specific’, since different decision makers can look at the same social cost and weight them very differently.

They can be paralyzing if carried to extremes.


Goal of the firm


A test of your social consciousness: Put your money where you mouth is…

Assume that you work for Disney and that you have an opportunity to open a store in an inner-city neighborhood. The store is expected to lose about a million dollars a year, but it will create much-needed employment in the area, and may help revitalize it.

Would you open the store?

Yes

No

If yes, would you tell your stockholders and let them vote on the issue?

Yes

No

If no, how would you respond to a stockholder query on why you were not living up to your social responsibilities?


Goal of the firm


Goal of the firm

Conclusions

In the context of our discussion:

managers taking advantage of stockholders has led to a much more active market for corporate control.

stockholders taking advantage of bondholders has led to bondholders protecting themselves at the time of the issue.

firms revealing incorrect or delayed information to markets has led to markets becoming more “skeptical” and “punitive”

firms creating social costs has led to more regulations, as well as investor and customer backlashes.


What is a Corporation?

The Role of The Financial Manager


Goal of the firm

Present Value Calculations

Time Value of Money

Type of Interest / Compounding

Present Value Simple Cash flows Perpetuity Growing Perpetuity Annuity Growing Annuity

Asset


Time Value of Money

Which would you prefer:

(a) $ 10 000 today

or

(b) $ 10 000 in 5 years time?

Time Value of Money


Reasons why a cash flow in the future is worth less than a

similar cash flow today:

Individuals prefer present consumption to future consumption.

People would have to be offered more in the future to give up present

consumption.

When there is monetary inflation, the value of currency decreases

over time. The greater the inflation, the greater the difference in value between a cash flow today

and the same cash flow in the future.

Any uncertainty (risk) associated with the cash flow in the future

reduces the value of the cashflow.A promised cash flow might not be delivered for a number of reasons: the promisor might

default on the payment, the promisee might not be around to receive payment; or some

other contingency might intervene to prevent the promised payment or to reduce it.


Time Value of Money

The process by which future cash flows are

adjusted to reflect these factors is called

discounting,

and the magnitude of these factors is

reflected in the discount rate.

Present value (PV) Future value (FV)

$10 000

t=5t=0

?

< $10 000


Time Value of Money

Cash flows at different points in time cannot be compared and

aggregated.

All cash flows have to be brought to the same

point in time before comparisons and aggregations

can be made.


Time Value of Money

Compound Interest

Interest paid (earned) on any previous interest

earned, as well as on the principal borrowed

(lent).

Simple Interest

Interest paid (earned) on only the original

amount, or principal, borrowed (lent).

Types of Interest


If P = principal,

r = annual interest rate,

and t = time (in years),

then the simple interest I is given by

I = Prt

Simple Interest

Types of Interest


I = P(r)(t)

= $4,800(.07)(6/12)

= $168

Assume that you deposit $4,800 in an account

earning 7% simple interest for 6 months.

What is the interest at the end of the 6th

month?

Types of Interest

Simple Interest


FV = P + I

= $4,800 + $168

= $4,968

Future Value is the value at some future time of a

present amount of money, or a series of payments,

evaluated at a given interest rate.

What is the Future Value (FV) of the deposit?

Types of Interest

Simple Interest


The Present Value is simply the

$4,800 you originally deposited.

That is the value today!

Present Value is the current value of a future

amount of money, or a series of payments,

evaluated at a given interest rate.

What is the Present Value (PV) of the

previous problem?

Types of Interest

Simple Interest


If P = principal

Rm = annual interest rate compounded m times a year

and n = number of periods of time

then the FVn is given by

𝐹𝑉𝑛 = 𝑃 1 +𝑅𝑚

𝑚

𝑚𝑛

Types of Interest

Compound Interest


Compound Interest

Types of Interest


Continuous compounding

As m → ∞ :

where:

Rc is the annual interest rate

n is time period (expressed as a fraction of year)

𝐹𝑉𝑛 = 𝑃 𝑒𝑅𝑐𝑛

Compound Interest

Types of Interest


Value of 1 GBP

years annual semi quarter month continous

5% interest rate

0.05 0.050625 0.050945 0.051162 0.051271

1 1.05 1.050625 1.050945 1.051162 1.051271

5 1.276282 1.280085 1.282037 1.283359 1.284025

10 1.628895 1.638616 1.643619 1.647009 1.648721

15 2.078928 2.097568 2.107181 2.113704 2.117

20 2.653298 2.685064 2.701485 2.71264 2.718282

25 3.386355 3.437109 3.463404 3.48129 3.490343

30 4.321942 4.39979 4.440213 4.467744 4.481689

10% interest rate

0.1 0.1025 0.103813 0.104713 0.105171

1 1.1 1.1025 1.103813 1.104713 1.105171

5 1.61051 1.628895 1.638616 1.645309 1.648721

10 2.593742 2.653298 2.685064 2.707041 2.718282

15 4.177248 4.321942 4.39979 4.45392 4.481689

20 6.7275 7.039989 7.209568 7.328074 7.389056

25 10.83471 11.4674 11.81372 12.05695 12.18249

30 17.4494 18.67919 19.35815 19.8374 20.08554

Types of Interest



Types of Interest

Simple cash flows

Perpetuities

Growing perpetuities

Annuities

Growing annuities

Present ValueTypes of Cash Flows


A simple cash flow is a single cash flow in a specified

future time period; it can be depicted on a time line:

where CFt= the cash flow at time t.

This cash flow can be discounted back to the present using a discount rate

that reflects the uncertainty of the cash flow.

Concurrently, cash flows in the present can be compounded to arrive at an

expected future cash flow.

Present ValueSimple Cash Flow


0 t

CFt

The present value (PV) of a cash flow (CFt):

Compounding m times a year:

𝑷𝑽 =𝑪𝑭𝒕

𝟏 +𝑹𝒎𝒎

𝒎𝒏 = 𝑪𝑭𝒕 𝟏 +𝑹𝒎

𝒎

−𝒎𝒏

Continuous compounding:

𝑷𝑽 = 𝑪𝑭𝒕𝒆−𝒓𝒏

where

CFt= Cash Flow at the end of time period t

Other things remaining equal, the present value of a cash flow will

decrease as the discount rate increases and continue to decrease the

further into the future the cash flow occurs.


Present ValueSimple Cash Flow

A perpetuity is a constant cash flow (CF) at regular

intervals forever.

The present value of a perpetuity can be written as

𝑷𝑽 𝒐𝒇 𝑷𝒆𝒓𝒑𝒆𝒕𝒖𝒊𝒕𝒚 =𝑪𝑭

𝒓


Present ValuePerpetuity

Example: Valuing a Console Bond

A console bond is a bond that has no maturity and pays a fixed

coupon. Assume that you have a 6% coupon console bond.

The value of this bond, if the interest rate is 9%, is as

follows:

Value of Console Bond = $60 / .09 = $667

The value of a console bond will be equal to its face value

(which is usually $1000) only if the coupon rate is equal to

the interest rate.


Present ValuePerpetuity

A growing perpetuity is a cash flow that is expected to grow

at a constant rate forever.

The present value of a growing perpetuity can be written as:

𝑃𝑉 𝑜𝑓 𝐺𝑟𝑜𝑤𝑖𝑛𝑔 𝑃𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦 =𝐶𝐹1

𝑟−𝑔

where CF1 is the expected cash flow next year, g is the constant growth rate

and r is the discount rate.

The fact that a growing perpetuity lasts forever puts constraints on

the growth rate. It has to be less than the discount rate for this

formula to work.


Present ValueGrowing Perpetuity

Example: Valuing a Stock with Stable Growth in Dividends

In 1992, Southwestern Bell paid dividends per share of $2.73. Its earnings and dividends had

grown at 6% a year between 1988 and 1992 and were expected to grow at the same rate in the

long term. The rate of return required by investors on stocks of equivalent risk was 12.23%.

Current Dividends per share = $2.73

Expected Growth Rate in Earnings and Dividends = 6%

Discount Rate = 12.23%

Value of Stock = $2.73 *1.06 / (.1223 -.06) = $46.45

As an interesting aside, the stock was actually trading at $70 per share. This price could be

justified by using a higher growth rate. The value of the stock is graphed in figure 3.7 as a function

of the expected growth rate.

The growth rate would have to be approximately 8% to justify a price of $70.

This growth rate is often referred to as an implied growth rate.


Present ValueGrowing Perpetuity

An annuity is a constant cash flow that occurs at

regular intervals for a fixed period of time.

Defining A to be the annuity, the time line for an

annuity may be drawn as follows:

An annuity can occur at the end of each period, as in

this time line, or at the beginning of each period.

Present ValueAnnuity


0 1 2 3 4 5

$10 $10 $10 $10 $10

The present value of an annuity can be calculated by taking

each cash flow and discounting it back to the present and

then adding up the present values.

Alternatively, a formula can be used in the calculation. In

the case of annuities that occur at the end of each period,

this formula can be written as:

𝑃𝑉 𝑜𝑓 𝑎𝑛 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 = 𝑃𝑉 𝐴, 𝑟, 𝑛 =𝐴

𝑟1 −

1

1 + 𝑟 𝑛

where

A = Annuity

r = Discount Rate

n = Number of years

the present value of an annuity will be PV(A,r,n).



An annuity vs. a difference between 2 perpetuities

Since the cash flows are the same, the values must be the same



0 1 2 3 4 5

$10 $10 $10 $10 $10

0 1 2 3 4 5 6 7

$10 $10 $10 $10 $10 $10 $10

$10 $10

0 1 2 3 4 5 6 7

𝐶𝐹

𝑟

𝐶𝐹

𝑟

1

1 + 𝑟 𝑛

𝐶𝐹

𝑟1 −

1

1 + 𝑟 𝑛

Example: Estimating the Present Value of Annuities

Assume that you are the owner of Compnay X, and that you have a

choice of buying a copier for $10,000 cash down or paying $ 3,000

a year for 5 years for the same copier.

If the opportunity cost is 12%, which would you rather do?

𝑃𝑉 𝑜𝑓 $3000 𝑒𝑎𝑐ℎ 𝑜𝑓𝑟 𝑛𝑒𝑥𝑡 5 𝑦𝑒𝑎𝑟 =$3000

0.121 −

1

1 + 0.12 5= $10,814

The present value of the installment payments exceeds the cash-

down price; therefore, you would want to pay the $10,000 in cash

now.



Alternatively, the present value could have been estimated

by discounting each of the cash flows back to the present

and aggregating the present values as illustrated below:



Example : Present Value of Multiple Annuities

Suppose you are the pension fund consultant and that you are trying to estimate the present

value of the expected pension obligations, which amount in nominal terms to the following:

Years Annual Cash Flow

1 - 5 $ 200.0 million

6 - 10 $ 300.0 million

11 - 20 $ 400.0 million

If the discount rate is 10%, the present value of these three annuities can be estimated as

follows:

Present Value of 1st annuity = $ 200 million * PV (A, 10%, 5) = $ 758 million

Present Value of 2nd annuity = $ 300 million * PV (A,10%,5) / 1.105 = $ 706 million

Present Value of 3rd annuity = $ 400 million * PV (A,10%,10) / 1.1010 = $ 948 million

The present values of the second and third annuities can be estimated

in two steps:

First, the standard present value of the annuity is computed over the

period that the annuity is received.

Second, that present value is brought back to the present.

Thus, for the second annuity, the present value of $ 300 million each year for 5

years is computed to be $1,137 million; this present value is really as of the end

of the fifth year. It is discounted back 5 more years to arrive at today’s present

value which is $ 706 million.

Cumulated Present Value = $ 758 million+$706 million+$948 million = $2,412 million



In some cases, the present value of the cash flows is known and

the annuity needs to be estimated.

This is often the case with home and automobile loans, for

example, where the borrower receives the loan today and pays it

back in equal monthly installments over an extended period of

time.

This process of finding an annuity when the present value is

known is examined below

𝐴𝑛𝑛𝑢𝑖𝑡𝑦 𝑔𝑖𝑣𝑒𝑛 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒 = 𝑃𝑉𝑟

1 −1

1 + 𝑟 𝑛



Example: Calculating The Monthly Payment On A House Loan

Suppose you are trying to borrow $200,000 to buy a house on a conventional 30-year mortgage

with monthly payments. The annual percentage rate on the loan is 8%. The monthly payments on

this loan can be estimated using the annuity due formula:

Monthly interest rate on loan = APR/ 12 = 0.08/12 = 0.0067

𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 𝑜𝑛 𝑀𝑜𝑟𝑡𝑔𝑎𝑔𝑒 = $200,0000.0067

1 −1

1 + 0.0067 360

= $1473.11

This monthly payment is an increasing function of interest rates.

When interest rates drop, homeowners usually have a choice of refinancing, though

there is an up-front cost to doing so.



A growing annuity is a cash flow that grows at a constant rate for a

specified period of time.

If A is the current cash flow, and g is the expected growth rate,

the time line for a growing annuity appears as follows:

Note that, to qualify as a growing annuity, the growth rate in each period has

to be the same as the growth rate in the prior period.


Present ValueGrowing Annuity

In most cases, the present value of a growing annuity can

be estimated by using the following formula:

𝑃𝑉 𝑜𝑓 𝑎 𝐺𝑟𝑜𝑤𝑖𝑛𝑔 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 =𝐴 1 + 𝑔

𝑟 − 𝑔1 −

1 + 𝑔 𝑛

1 + 𝑟 𝑛

The present value of a growing annuity can be estimated in all cases, but

one - where the growth rate is equal to the discount rate. In that case, the

present value is equal to the nominal sums of the annuities over the period,

without the growth effect:

PV of a Growing Annuity for n years (when r=g) = n A

Note also that this formulation works even when the growth rate is greater

than the discount rate.



Example: The Value Of A Gold Mine

Suppose you have the rights to a gold mine for the next 20 years, over which period you plan

to extract 5,000 ounces of gold every year. The current price per ounce is $300, but it is

expected to increase 3% a year. The appropriate discount rate is 10%. The present value of

the gold that will be extracted from this mine can be estimated as follows:

𝑃𝑉 𝑜𝑓 𝑒𝑥𝑡𝑟𝑎𝑐𝑡𝑒𝑑 𝑔𝑜𝑙𝑑 = $300 ∗ 5000 ∗(1 + 0.03)

(0.1 − 0.03)1 −

(1 + 0.03)20

(1 + 0.1)20

The present value of the gold expected to be extracted from this mine is

$16.146 million; it is an increasing function of the expected growth rate in

gold prices.



Price of an asset (or a value of a project)

= PV of future cash flows generated by the asset and

discounted at the appropriate rate (opportunity cost

of capital)

Present ValueAsset


PV depends on:

i) Future cash flows

ii)Discount rate

iii)Number of periods

Price = PV

Time Value of Money

Type of Interest / Compounding

Present Value Simple Cash flows Perpetuity Growing Perpetuity Annuity Growing Annuity

Asset


Capital Budgeting

Introduction to Capital Budgeting

Investment appraisal methods Payback Period ROCE NPV IRR

Investment appraisal applications & risk

Taxation Inflation Sensitivity analysis

Capital Budgeting

Shareholders invest in companies to

make money.

We are interested in how to chose which project to invest in?

Capital Budgeting

Investment decision = Capital Budgeting

Introduction

Investment is an important component of GDP

Y = C + I + G

Why do firms invest?

How do they decide what to invest in?

Capital Budgeting

Introduction

Cash

Firm Shareholder

Investment Opportunity(real asset)

Investment Opportunities

(financial assets)

Invest Alternative:Pay divident to shareholders

Sharehoderscan invest for themselves

Capital Budgeting

Introduction

Shareholders invest in companies to make money.

Replacement projects (no need for very careful analysis)

Expansion projects, i.e. increasing the size of the firm (involves

more uncertainty)

New products or services (probably even riskier)

Regulatory, safety and environmental projects (often imposed by

regulatory agencies, so must be undertaken)

Pet projects (CEO getting a new aircraft!)

Capital Budgeting

IntroductionTypes of projects

Projects vary in level on analysis needed to take the decision

Independent projects

- undertaking one does not necessarily exclude the others

(provided that there is sufficient capital)

Mutually exclusive projects

- only one of the potential candidates may be undertaken

e.g. planning to buy a new machine, and there are two

which meet the requirements

In reality, company has a limited amount of capital to fund

potentially many recommended projects

→ Capital rationing

Capital Budgeting

IntroductionTypes of projects by compatibility

Managers undertake valuations to allocate capital (i.e. money

tied up in the form of equity / debt) between investment projects:

• Is Project A better than doing nothing?

• Is A better than B?

• Although A is better than B, should we still carry on B?

Appraisal methods help us in decision making. They take into

account:

• Cash flows – measure of value creation

• Time – opportunity cost of investing

Capital Budgeting

Introduction

Traditional techniques

(1) Payback Period

(2) Return on Capital Employed (ROCE)

Discounted cash flows methods

(3) Net Present Value (NPV)

(4) Internal Rate of Return (IRR)

Capital Budgeting

Investment Appraisal Methods

Capital Budgeting

Investment Appraisal MethodsPayback Period

How long does it take the project to “payback” its initial investment?

The payback rule says only accept projects that “payback” in the desired time frame.

A modified version that takes time value of money into account:

Discounted Payback Period = number of years required for the future cumulative discounted cash flows to match the initial outlay

Payback Period = number of years required for the future

cumulative cash flows to match the initial outlay

Capital Budgeting


Example

Payback Period = between 3 and 4 years Payback Period ~ 3.5 years Ranking criterion: Select the project with the lowest payback period

Year Cash flow ($) Cumulative cash flow ($)

0 (450) (450)

1 100 (350)

2 200 (150)

3 100 (50)

4 100 50

5 80 130

‘Zero’ (payback period) is

between 3&4 years

A conventional cash flow: A cash investment initially, followed by a series of cash inflows

over the life of a project

Advantages

Easy to understand, calculate, and communicate

In fact so straightforward that it is frequently used (but should really only be

used to get an initial indication)

Useful for companies that face cash flow constraints (e.g. small

companies) since it is biased toward liquidity

Arguably takes account of risk (since it assumes that a shorter

payback period is better than a longer one) – and assuming that

more distant cash flows are less certain (i.e. more risky)

Capital Budgeting


Disadvantages

Ignores cash flows after the payback period Income after the payback period is not considered, e.g. increasing the cash flow in

yr5 in our example must make the project better?

Biased against long-term projects

Ignores the time value of money Think back to our example: a cash flow of [£0, £0, £400] is considered equal to a

cash flow of [£400, £0, £0]

Arbitrary acceptance criterion (i.e. when there is a single project to consider) Why pick 3.5yrs over, say, 3yrs, or 4yrs?

Accepted projects may not actually add value to the company (or the shareholders’ wealth) All the Payback method really tells us is whether the company has the liquidity to

finance the project (although this can be important, particularly to small companies)

Capital Budgeting


Also known as return on investment (ROI) and accounting rate of return (ARR)

All definitions relate accounting profit to some measure of the capital employed

We will follow this formula:

𝑅𝑂𝐶𝐸 =𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑎𝑛𝑛𝑢𝑎𝑙 𝑎𝑐𝑐𝑜𝑢𝑛𝑖𝑡𝑛𝑔 𝑝𝑟𝑜𝑓𝑖𝑡

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡× 100

Accounting profits = before-tax operating cash flows adjusted to take account of depreciation

Average investment must take account of scrap value:

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑚𝑛𝑡 =𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑚𝑛𝑡 + 𝑆𝑐𝑟𝑎𝑝 𝑣𝑎𝑙𝑢𝑒

2

Capital Budgeting

Investment Appraisal MethodsReturn on Capital Employed (ROCE)

Project A generates annual cash flows (receipts less payments) of

$210,000 for 5 years

The initial cost of machinery is $500,000; no scrap value

Total cash profit = 210,000 × 5 = 1,050,000

Total accounting profit (after depreciation) = 550,000

Average accounting profit = 550,000/5 = 110,000

Average investment = (500,000 + 0)/2 = 250,000

ROCE =110 000

250 000= 44%

Ranking criterion: Select the project with the highest ROCE first

Capital Budgeting

Investment Appraisal MethodsReturn on Capital Employed (ROCE)

Example

Capital Budgeting

Return on Capital Employed (ROCE)Investment Appraisal Methods

Advantages

Percentage returns are familiar, and can be compared with the

ROCE of the company to determine if a new project is acceptable

Accounting information readily available

Reasonably simple to apply and can be used to compare mutually

exclusive projects

Unlike the payback method, ROCE considers all cash flows

Capital Budgeting

Return on Capital Employed (ROCE)Investment Appraisal Methods

Disadvantages

Accounting profits are not cash flows, since depreciation is an

accounting adjustment

Ignores time value of money

Arbitrary acceptance criterion: Compare ROCE to some ‘target’

rate of return

→ Is 44% ROCE high enough?

Accounting profits are not linked directly to maximising shareholder

wealth

Because average profits are used, the timing of profits is not taken

fully into consideration

𝑁𝑃𝑉 = −𝐼0 +𝐶1

(1 + 𝑟)+

𝐶2

1 + 𝑟 2+

𝐶3

1 + 𝑟 3+ ⋯ +

𝐶𝑛

1 + 𝑟 𝑛

where: I0 is the initial investment

C1, C2, C3 … are the cash flows expected in time 1, 2, 3,…

r is the cost of capital or required rate of return

Minimum acceptance criterion: Accept if NPV > 0

A positive NPV indicates that the investment offers a return in excess of the cost of capital

Ranking criterion: Select the project with the highest NPV first

Capital Budgeting

Investment Appraisal MethodsNet Present Value (NPV)

NPV is based in solid theory

• It makes use of the time value of money

• And the PV concept we considered earlier in the module

NPV measures actual wealth creation because

• It uses cash flows

• It uses ALL cash flows during the project life

• It discounts ALL cash flows during the project life, using the

cost of capital (or the required rate of return)

Capital Budgeting


Can be done very easily in a spreadsheet using Excel

Notice that NPV has an inverse relationship with r

As r increases the NPV of a given project falls

This makes sense; the higher the rate of return we require the fewer projects

we would expect to be profitable

Capital Budgeting


Example

Capital Budgeting


NPV in EXCEL calculates PV

=NPV(0.1, C3:C6)C8

To estimate NPV we need to:

Estimate the initial cost

→ Usually this is known for certain

Estimate future cash flows

→ “Expected” future cash flows, so subject to errors

→ Risk of appraisal methods in general, not only NPV

Estimate discount rate

→ Required rate of return

→ CAPM

Capital Budgeting


We will do that at the next lecture

Capital Budgeting


Advantages

Takes account of the time value of money

Uses cash flows rather than accounting profit

Uses all relevant cash flows

Academically(!) preferred method:

grounded in consumption theory

If capital is available NPV gives good investment advice

Net Present Value (NPV)

Capital Budgeting


Disadvantages

Hard to forecast future cash flows

But this is true of all investment appraisal techniques!

Cost of capital may change over the lifetime of the project

Net Present Value (NPV)

It is defined implicitly as the discount rate at which NPV is equal to zero

𝐶1

1 + 𝑟∗+

𝐶2

1 + 𝑟∗ 2+

𝐶3

1 + 𝑟∗ 3+ ⋯ +

𝐶𝑛

1 + 𝑟∗ 𝑛− 𝐼0 = 0

where r* is the Internal Rate of Return

Capital Budgeting

Investment Appraisal MethodsInternal Rate of Return (IRR)

Minimum acceptance criterion: Accept a project if its IRR exceeds

the cost of capital (or required rate of return)

Ranking criterion: Select the project with the highest IRR first

Example: You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?

0)1(

000,4

)1(

000,2000,4

21

IRRIRRNPV %08.28IRR

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

10 20 30 40 50 60 70 80 90100

Discount rate (%)

NP

V (

,000

s)

IRR= 28%

Capital Budgeting

Internal Rate of Return (IRR)Investment Appraisal Methods

𝐶1

1 + 𝑟∗+

𝐶2

1 + 𝑟∗ 2+

𝐶3

1 + 𝑟∗ 3+ ⋯ +

𝐶𝑛

1 + 𝑟∗ 4− 𝐼0 = 0

Equation (1) is not easy to solve (even if C = C1 = C2 = C3 = … = Cn)

𝐼0 =𝐶

𝑟∗1 −

1

1 + 𝑟∗ 𝑛

We would need to solve equation (2) to find r*

Before we had Excel the solution was basically to guess...

Capital Budgeting


(2)

(1)

PV of Annuity

Of course mathematicians don’t guess!

Instead they use Numerical Analysis...

…and in this case Linear Interpolation

Which sounds far more sophisticated than ‘guessing’

Let’s see how it works…

Capital Budgeting


Suppose we know the two end points

[x0, y0],[x1,y1]

Substituting for y and x in the standard

formula for a straight line, y = ax+b, gives:

𝑎 =𝑦1 − 𝑦0

𝑥1 − 𝑥0

and 𝑏 = 𝑦0 −𝑦1−𝑦0

𝑥1−𝑥0𝑥0

Capital Budgeting


This means the formula for a straight line becomes:

𝑦 =𝑦1 − 𝑦0

𝑥1 − 𝑥0𝑥 + 𝑦0 −

𝑦1 − 𝑦0

𝑥1 − 𝑥0𝑥0

Capital Budgeting


To find the approximation of a true IRR, i.e. IRR*

is equivalent with solving the below for x:

𝑦 =𝑦1 − 𝑦0

𝑥1 − 𝑥0𝑥 + 𝑦0 −

𝑦1 − 𝑦0

𝑥1 − 𝑥0𝑥0

we obtain:

𝑥 = 𝑥0 − 𝑦0

𝑥1 − 𝑥0

𝑦1 − 𝑦0

which can be written in terms of points A and B as:

𝐼𝑅𝑅∗ = 𝑅1 − 𝑁𝑃𝑉1

𝑅2 − 𝑅1

𝑁𝑃𝑉2 − 𝑁𝑃𝑉1

NPV

+

0

-

Discount rateIRR

B(R2,NPV2)

A(R1,NPV1)

(IRR*, 0)

Capital Budgeting


NPV

+

0

-

Discount rateIRR

B(R2,NPV2)

A(R1,NPV1)

(IRR*, 0)

To finding the IRR*, which is an

approximation is called Linear Interpolation.

Of course the closer the NPV1 and NPV2

are to zero (from above and below) the

closer the approximation

Since the relationship between NPV and

the discount rate of a conventional cash

flow is negatively sloped and convex the

estimate will always be an over-estimate

Generally, very computationally challenging, i.e. no formula, not

as straightforward as NPV

Trial & error – keep trying different discount rates untill NPV=0

Capital Budgeting

Use Solver in Excel


Pitfall 1 - Lending or Borrowing?With some cash flows (as noted below) the NPV of the project increases as the discount rate increases. This is contrary to the normal relationship between NPV and discount rates.

75.%20728,1320,4600,3000,1

%10@NPVIRRCCCC 3210

Discount Rate

NPV

Pitfall 2 - Multiple Rates of ReturnCertain cash flows can generate NPV=0 at two different discount rates.The following cash flow generates NPV=0 at both (-50%) and 15.2%.

150150150150150800000,1

CCCCCCC 6543210

NPV

Discount RateIRR=-50%

IRR=15.2%

Capital Budgeting

Internal Rate of Return (IRR)Investment Appraisal Methods

Pitfall 3 - Mutually Exclusive ProjectsIRR sometimes ignores the magnitude of the project. The following two projects illustrate that problem.

Pitfall 4 - Term Structure AssumptionWe assume that discount rates are stable during the term of the project. This assumption implies that all funds are reinvested at the IRR. This is a false assumption. NPV allows for change in discount rate.

Capital Budgeting


At 10% IRRA=19.5% while IRRB= 17%.

As the discount rate decreases, and before the lines cross, NPV suggests B, while IRR suggests A .

There is no conflict between these two methods when a singleproject with conventional cash flows is being considered

But for non-conventional (strange cash flows) mutually exclusive

projects, a conflict might arise

NPV is academically preferred because it measures the absolute

increase in value of the company

In all cases where there is no constraint on capital, the NPV

decision rule offers sound investment advice

Capital Budgeting

Investment Appraisal MethodsNPV vs. IRR

There are a number of issues that we need to take into account when applying NPV in practice (i.e. how do we come up with the cash flows and what considerations do we need to make?):

Relevant project cash flows – Ask whether a cash flow occurs as a result of undertaking a project (Incremental cash flows)

Taxation – what effect does taxation have on the cash flow from the project

Inflation – reduces the real value of future cash flows

Investment risk – when things don’t go as you expect

Capital Budgeting

Investment Appraisal ApplicationNPV vs. IRR

Capital Budgeting

Include:

• Cash in- and outflows resulting from the project, including

additional investment or working capital

• Opportunity costs / benefits foregone

• Side effects: Erosion or synergy

e.g. by launching Coke Zero, demand for Diet Coke will drop; by

launching iPhone, demand for Mac will increase

Ignore:

• Sunk costs(e.g. market research takes place whether the project goes ahead or not)

• Apportioned fixed costs – unless incremental / additional

• Any interest expenditure, even if debt financing

→ Adjustments for cost of debt reflected in r

Incremental Cash FlowsInvestment Appraisal Application

Opportunity Cost- Example

Project A requires 500 kg of material A

Suppose we have 1,000 kg of material A in inventory, which cost $2,000 when purchased 6 months ago

The supplier now quotes a price of $2.2 per kg, and the material can be resold at $1.9 per kg

What is the relevant cost of material A?

a) $1,000

b) $1,100

c) $950

(no, a sunk cost since the company has bought material A

already)

(yes, but only if the company has other projects that could

use material A)

(yes, but only if there is no other use for material A, which

would have to be resold if the project were not undertaken)

Capital Budgeting

Investment Appraisal ApplicationIncremental Cash Flows

Companies pay corporate tax

Estimate after-tax incremental cash flows for NPV

The amount and timing of tax payments affect NPV

Corporate tax is based on taxable profit which is not the same as

cash flow (see next slide)

For taxation purposes, capital expenditure is written off against

taxable profits by means of annual capital allowances

Capital Budgeting

Investment Appraisal ApplicationEffects of taxation

Timing of tax liabilities and benefits : UK

Tax liabilities taken as being paid one year after the originating

taxable profits

Tax benefits also received one year in arrears

Small UK companies (taxable profit < £1.5 m) pay tax nine

months after the end of the relevant accounting year

Large UK companies pay most of their tax close to the end of the

relevant accounting year

→ Tax liabilities & benefits treated as occurring in the same year

Capital Budgeting

Investment Appraisal ApplicationEffects of taxation

Inflation can have a serious effect on investment decisions by

reducing the real value of future cash flows

Deflate nominal cash flows by the general rate of inflation to obtain

real cash flows

Relationship between real and nominal costs of capital

1 + 𝑅𝑒𝑎𝑙 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 =1 + 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑐𝑜𝑠𝑡 𝑓𝑜 𝑐𝑎𝑝𝑖𝑡𝑎𝑙

1 + 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒

Golden rule of discounting:

Use real rates to discount real cash flows

Use nominal rates to discount nominal cash flows

Capital Budgeting

Investment Appraisal ApplicationEffects of inflation

Capital Budgeting

Investment Appraisal ApplicationEffects of inflation

Nominal discount rate = 10%

Expected inflation = 4%

Real discount rate = 1.10/1.04 – 1 = 5.8%

Next year’s sales = £100 in today’s prices

PV using real cash flow = 100/1.058 ~ £94.50

PV using nominal cash flow = 100×1.04/1.10 ~ £94.50

This example illustrates how NPV obtained by discounting real

cash flows with a real cost of capital is identical to NPV obtained

by discounting nominal cash flows with a nominal cost of capital

Example:

Capital Budgeting

Investment Appraisal ApplicationSensitivity Analysis

Sensitivity Analysis is a method of assessing an investment

project by evaluating how responsive the outcome of the project

appraisal is to changes in relevant variables…

Conventional approaches:

• Change each project variable by a set amount and

recalculate NPV

• Change each project variable such that NPV = 0, and

evaluate the magnitude of change required

Some rules: Change one variable at a time, and change it in the

direction that adversely affects NPV

Equation 1


Example:

Capital Budgeting

Using Equation 1, we can show that𝜕𝑁𝑃𝑉

𝜕𝑆= 𝑁 × 𝐶𝑃𝑉𝐹12,4 = 800,000 × 3.037 = 2,429,600

So, a one $ drop in sales price leads to a $2.4 m drop in NPV

(which will make it negative)

This implies that a percent drop in price (=$0.092) will lead to a

$223,523 drop in NPV = 29% drop

A similar analysis shows that if the initial cost increases by a

percent, NPV drops by 9% only

Sales price is therefore a key variable


Example cont.:

Capital Budgeting

Capital Budgeting


A similar process could be carried out for changes to any other

of the variables (for example, how low would volume of sales

need to get for NPV to be zero, and so forth)

The hard part is interpreting the interaction between all these

uncertainties!...but if you look at impact of 1% change on the

NPV you should be quick to identify the main risk factors

USE IN YOUR BUSINESS PLAN

Capital Budgeting

Investment Appraisal in Practise

Companies don’t always make use all of the sorts of analysis we

have looked at today

In part this almost certainly reflects the large amount of

uncertainty associated with predicting the future!

The payback method is most common (although often

accompanied by some sort of discounted cash flow method)

Capital Budgeting

Investment Appraisal in Practise

It is surprising how few companies formally adjust calculations

for inflation

Drury et al, 1993, suggest only some 27%

The use of more advanced sensitivity or probability analysis

also appears to be relatively rare

Although surely in part because managers see it as being of

relatively little practical benefit

Traditional techniques

(1) Payback Period

(2) Return on Capital Employed (ROCE)

Discounted cash flows methods

(3) Net Present Value (NPV)

(4) Internal Rate of Return (IRR)

Main conclusions:

(3) & (4) preferred to (1) & (2)

(3) preferred to (4)

Capital Budgeting

Conclusions

Introduction to Capital Budgeting

Investment appraisal methods

Payback Period

ROCE

NPV

IRR

Investment appraisal applications & risk

Taxation

Inflation

Sensitivity analysis

Capital Budgeting

EXERCISES

Profitability Index

When resources are limited, the profitability index (PI) provides a tool for selecting among

various project combinations and alternativesA set of limited resources and projects can yield various combinations. The highest weighted average PI can indicate which projects to select.

Investment

NPVIndexity Profitabil

Example

We only have $300,000 to invest. Which do we select?

Project NPV Investment PI

A 230 000 200 000 1.15

B 141 250 125 000 1.13

C 194 250 175 000 1.11

D 162 000 150 000 1.08Select projects with highest Weighted Avg PI

01.1300

)25(*0

300

)150(*08.1

300

)125(*13.1)( BDWAPI

WAPI (A) = 0.77 WAPI (BC) = 1.12

Capital Budgeting

Equivalent Annual Cost

Equivalent Annual Cost (EAC)The cost per period with the same present value as the cost of buying and operating a machine.

Equivalent annual cost =present value of costs

annuity factor

Example

Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method.

Machine Year 1 Year 2 Year 3 Year 4 PV@6% EAC

A 15 5 5 5 28.37 10.61

B 10 6 6 21 11.45

EAC is the annual cash flow sufficient to recover a capital investment, including the cost of capital for that investment, over the investment’s economic life.

Capital Budgeting

Solution

TimingEven projects with positive NPV may be more valuable if deferred.The actual NPV is then the current value of some future value of the deferred project.

tr

t

)1(

date of as valuefutureNet NPVCurrent

9.411.915.420.328.8 valuein change %

109.410089.477.564.450($1000s) Net FV

543210

YearHarvest

5.581.10

64.41 year in harvested if NPV

67.968.367.264.058.550($1000s) NPV

543210

YearHarvest

Example

You may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV?

Capital Budgeting

Question 1

Question 2

Question 3

Show by a simple graph-theoretic procedure how linear interpolation can

be used to determine the internal rate of return of a project.

Question 4

ABC plc is comparing two investment projects. The expected cash flows

are given below. Assume the cost of capital is 10 per cent.

(a) Calculate the payback period, net present value, internal rate of return,

and return on capital employed on each project.

(b) Show the rankings of the projects by each of the four methods.

Comment on your findings.

Question 5

XYZ plc is evaluating the purchase of a new machine and has the following

information:

Initial investment: 350 000

Residual value: nil

Expected life: 10 years

Sales volume: 20 000 units per year

Sales price: £ 8.50 per unit

Variable cost: £ 3.50 per unit

Fixed costs: £ 24 875 per year

Cost of capital: 15%

(a) Calculate the IRR of the project.

(b) Assess the sensitivity of the purchase evaluation to a change in project life.

(c) Assess the sensitivity of the purchase evaluation to a change in sales price.

Question 6

(1)Risk, Return and Portfolio

Theory

(2)Market efficiency

(3)Valuating stocks and bonds

Lecture 2:

Risk, Return and Portfolio Theory

For NPV we need discount rate.

The opportunity cost of capital.

Rate of return that you would earn on capital market for investing in something of equivalent level of risk

Risk , Return...

Financial Markets

Measuring Risk and Return

Diversification

Optimal Portfolio

Capital Asset Pricing Model

Risk , Return...

Financial Markets

Risk , Return...

Purpose of Financial Markets

Price discovery: Trading on secondary markets provides public

information on asset prices (market price = last traded price of an

asset)

Lower search costs: Since all trading parties converge to the same

location, matching is made easier

Provides liquidity: investors can sell assets prior to maturity on

secondary markets to satisfy their time preference for consumption and

diversification needs.

To facilitate the transfer of funds between borrowers

and lenders

To trade time & risk

Risk , Return...

Financial Markets

time to maturity

1 year

Money Market

for short-term debt securitieswith maturities shorter than1 year

Capital Market

for long-term debt or equitysecurities with maturities greaterthan 1 year

Financial Markets

Risk , Return...

Primary Market

Markets that

involve the issue

of new securities

Capital formation

occurs

Secondary Market

Markets that involve

buyers and sellers

of existing

securities

No capital formation

occurs

Risk , Return...

Financial Markets

Types of Secondary Markets

Exchanges or Auction Markets

Secondary markets that involve a bidding process that takes place in specific location

For example TSX, NYSE

Dealer or Over-the-counter (OTC) Markets

Secondary markets that do not have a physical location and consist of a network of dealers who trade directly with one another.

For example FX market

Risk , Return...

Financial Markets

What are securities?

Definition: a legal representation

of the right to received

prospective future benefits under

stated conditions.

Financial Markets

Risk , Return...

Debt Instruments Commercial paper

Bankers’ acceptances

Treasury bills

Mortgage loans

Bonds

Debentures

Equity Instruments

Common stock

Preferred stock

There are two major categories of financial securities:

Risk , Return...

Financial Markets

Non-marketable securities

Cannot be traded between or among investors

May be redeemable (a reverse transaction between the borrower and the lender)

Examples:

Savings accounts

Term Deposits

Guaranteed Investment Certificates

Marketable securities

Can be traded between or among investors after their original issue in public markets and before they mature or expire

Risk , Return...

Financial Markets

Securities categorized by the time to maturity:

time to maturity

1 year

Money Market Securities

short-term debt securitieswith maturities shorter than1 year Bankers’ acceptances Commercial Paper Treasury Bills

Capital Market Securities

long-term debt or equitysecurities with maturities greaterthan 1 year Bonds Debentures Common Stock Preferred Stock

Financial Markets

Risk , Return...

Marketable Securities

0,1

10

1000

1925 1940 1955 1970 1985 2000

S&P

Small Cap

Corp Bonds

Long Bond

T Bill

Ind

ex

Year End

Source: Ibbotson Associates

Measuring Risk and ReturnThe Value of an Investment of $1 in 1926

Risk , Return...

0,1

10

1000

1925 1940 1955 1970 1985 2000

S&P

Small Cap

Corp Bonds

Long Bond

T Bill

Real returns

Ind

ex

Year EndSource: Ibbotson Associates

Measuring Risk and ReturnThe Value of an Investment of $1 in 1926

Risk , Return...

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 95

2000

Common Stocks

Long T-Bonds

T-Bills

Source: Ibbotson Associates

Year

Perc

enta

ge R

etu

rnMeasuring Risk and Return

Rates of return 1926-2000

Risk , Return...


Risk , Return...

What investors care about when making the investments?

Return

Risk


Risk , Return...

What is return (R)?

Income received on an investment plus any

change in market price, usually expressed

as a percent of the beginning market price

of the investment.

Dt + (Pt - Pt-1 )

Pt-1

R =

𝑜𝑟 𝑅 = ln𝐷𝑡 + 𝑃𝑡

𝑃𝑡−1

logarithmic return

simple return


Risk , Return...

additive properties

What is risk?

Risk, in traditional terms, is viewed as something ‘negative’. Webster’s dictionary, for instance, defines risk as “exposing to danger or hazard”.

The Chinese symbols for risk, reproduced below, give a much better description of risk

危機

The first symbol is the symbol for danger, while the second is the symbol for opportunity, making risk a mix of danger and opportunity.

You cannot have one, without the other


Risk , Return...

What is risk?

In finance it is something different than

expected.

It is measured by standard deviation of

returns.

In finance, we call this measure ‘volatility’

𝜎 =

𝑖=1

𝑛

𝑅𝑖 − 𝑅 2𝑝𝑖


Risk , Return...

The variance on any investment return measures the disparity between actual and expected (mean) returns.

Expected Return

High Variance Investment

Low Variance Investment

Probability

NO RISK

Risk , Return...


(1) (2) (3)

Percent Rate of Return Deviation from Mean Squared Deviation

+ 40 + 30 900

+ 10 0 0

+ 10 0 0

- 20 - 30 900

Variance = average of squared deviations = 1800 / 4 = 450

Standard deviation = square of root variance = 450 = 21.2%

Example: Coin Toss Game-calculating variance and standard deviation


Risk , Return...

Mean-variance framework

expected returns measured by mean of returns

and risk measured by standard deviation of returns

Mean-variance approach holds when:

investors maximize the expected utility,

prefer more to less,

are risk averse,

and when either security returns are normally distributed or utility function is quadratic

Risk , Return...


Basis for Portfolio Theory

If volatility V[A] is a correct measure of risk, then in theory

V[A] > V[B] → E[A] > E[B]

Otherwise, there won’t be any incentive to take risk

The underlying assumption is: Investors are risk-averse

Expected return is liked – variance is disliked

This is the essence of the so-called mean-variance analysis

Measuring Risk and ReturnRisk-return trade off

Risk , Return...

Sometimes, historical estimates don’t conform to the theoretical

risk-return tradeoff

Clearly, GM is preferable

Is it better to hold IBM too?

i.e. a portfolio of two stocks

STOCK MEAN (%) VARIANCE

IBM 2.95 51.12

GM 5.16 46.65

Risk , Return...


𝑅𝑝 =

𝑖=1

𝑛

𝑅𝑖𝑤𝑖

Portfolio return:

)wR()w(R Return Portfolio Expected 2211

2 asset portfolio:


Risk , Return...

Portfolio risk:

)σσρww(2σwσwVariance Portfolio 211221

2

2

2

2

2

1

2

1

2 asset portfolio:

The variance of a two stock portfolio is

the sum of these four boxes

2

2

2

2

211221

1221

211221

12212

1

2

1

σwσσρw w

covww2Stock

σσρw w

covwwσw1Stock

2Stock 1Stock


Risk , Return...

1

2

3

4

5

6

N

1 2 3 4 5 6 N

To calculate

portfolio

variance add up

the boxes

The shaded boxes contain variance terms;

the remainder contain covariance terms.

STOCK

STOCK


Risk , Return...

Example

Suppose you invest 65% of your portfolio in

Coca-Cola and 35% in Reebok. The expected

dollar return on your CC is 10% x 65% = 6.5% and

on Reebok it is 20% x 35% = 7.0%. The expected

return on your portfolio is 6.5 + 7.0 = 13.50%.

Assume a correlation coefficient of 1.

222

2

2

2

211221

211221222

1

2

1

)5.58()35(.σw5.585.311

35.65.σσρwwReebok

5.585.311

35.65.σσρww)5.31()65(.σwCola-Coca

ReebokCola-Coca

% 31.7 1,006.1 Deviation Standard

1.006,15)1x31.5x58.2(.65x.35x

]x(58.5)[(.35)

]x(31.5)[(.65) Valriance Portfolio

22

22


Risk , Return...

If we hold half IBM and half GM:

Expected return = 4%

Volatility = 5%

Compared with holding GM alone, this portfolio achieves 1% less

expected return, but about 2% lower risk!

But is it better? Depends on investors risk preferences

STOCK MEAN (%) Variance Corr.

IBM 2.95 51.12 -0.48

GM 5.16 46.65

Back to Risk-return trade off ExampleMeasuring Risk and Return

Risk , Return...

Expected Return (%)

Standard Deviation

Which portfolio is the best and why?

A

B

C

Risk , Return...


Expected Returns and Standard Deviations of Portfolio vary given

different weighted combinations of the stocks

Expected Return (%)

Standard Deviation

Coca-Cola

35% in Reebok

Reebok

Portfolio possibility curve

Efficient frontier

(higher return for the same risk)

Minimum

Variance

Portfolio

(MVP)


Risk , Return...

Short sale allowed

Example

Correlation Coefficient = .4

Stocks s % of Portfolio Avg Return

ABC Corp 28 60% 15%

Big Corp 42 40% 21%

Standard Deviation = weighted avg = 33.6

Standard Deviation = Portfolio = 28.1

Return = weighted avg = Portfolio = 17.4%

Let’s add New Corp to the portfolio

Correlation Coefficient = .3

Stocks s % of Portfolio Avg Return

Portfolio 28.1 50% 17.4%

New Corp 30 50% 19%

NEW Standard Deviation = weighted avg = 31.80

NEW Standard Deviation = Portfolio = 23.43

NEW Return = weighted avg = Portfolio = 18.20%

NOTE: Higher return & Lower risk

How did we do that? DIVERSIFICATION

Strategy designed to reduce risk by spreading the portfolio across many investments.

Diversification

Risk , Return...

Expected Return (%)

Standard Deviation

The shape of the portfolio possibility curve depends on the

correlation coefficient (ρ) between the returns of the assets

The lower the correlation, the higher risk reduction

ρ=0.2

ρ=1

ρ=-1

−1 ≤ ρ ≤ 1

Diversification

Risk , Return...

Total Risk = Systematic Risk + Unsystematic Risk

Total

Risk

Unsystematic

risk (Unique risk)

Systematic risk(Market risk)

ST

D D

EV

OF

PO

RT

FO

LIO

RE

TU

RN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors such as

changes in nation’s

economy, tax reform

by the Congress,

or a change in the

world situation.

Factors unique to a particular company

or industry. For example, the death of a

key executive or loss of a governmental

defense contract.

Diversification

Risk , Return...

“Optimal” exposure to risky assets with respect to their risk-

return tradeoff

Generally, a well-diversified portfolio has lower volatility than

more concentrated portfolios of similar levels of expected returns

Smaller random noise due to errors in data

Unsystematic risks are neutralised

Diversification

Risk , Return...

Benefits of a well-diversified portfolio

A theoretic approach is to try to maximise the investor’s utility

subject to the risk-return tradeoff (constraints)

→ We will consider the investor’s indifference curve on the risk-

return plane

A more practical approach is to come up with a target expected

return, and then find the weights that minimise portfolio risk

→ This approach is due to Markowitz (1952) who was awarded a

Nobel Prize in 1990

Risk , Return...

Optimal Portfolio Selection

Investors utility curvesOptimal Portfolio Selection

Risk , Return...

Degree of risk aversionOptimal Portfolio Selection

Risk , Return...

Modern portfolio theory

Investors do (or should) consider:

Expected return as a desirable thing and

Variance of return as an undesirable thing

So, either

• Min variance s.t. the required rate of return

• Maximising the expected return s.t. the acceptable risk

Intuitive and can be easily handled in Excel

Risk , Return...

Markowitz PortfoliosOptimal Portfolio Selection

Basic Markowitz problem:

min𝑤𝑖

𝑉 𝑅𝑝 =

𝑖=1

𝑁

𝑤 𝑖2𝑉 𝑅𝑖 + 2

𝑖=1

𝑁

𝑗>1

𝑁

𝑤𝑖𝑤𝑗𝐶 𝑅𝑖 , 𝑅𝑗

𝑠. 𝑡. 𝐸 𝑅𝑝 =

𝑖=1

𝑁

𝑤𝑖 𝐸 𝑅𝑖 = 𝑥%

𝑖=1

𝑁

𝑤𝑖 = 1

Optional constraints:

𝑤𝑖 ≥ 0𝑤𝑖 < 𝑘%

Optimal Portfolio SelectionMarkowitz Programming

Risk , Return...

Optimal Portfolio SelectionMarkowitz Programming

Risk , Return...

Expected Return (%)

Standard Deviation

Coca-Cola

Tangency Portfolio (TG)

Reebok

Portfolio possibility curve

Efficient frontier

(higher return for the same risk)

Minimum

Variance

Portfolio

(MVP)

Risk , Return...

Short sale allowed

rf


Sharpe ratio is a measure of portfolio performance and can bedefined as

The portfolio that has the highest Sharpe ratio optimally balancereturns against risk

Thus the optimal risky assets portfolio (the Tangency Portfolio) isthe one that maximize Sharpe ratio.

P

FP rRratioSharpe

.

Risk , Return...


Portfolio theory = Normative theory

Given the portfolio inputs, what should investors do?

If we are willing to assume that everyone acts similarly, then it

might be possible to draw some implication about aggregate

behaviour of investors

That is, if demand & supply (the portfolio weights) are known,

then we may be able to determine the clearing (market) price or

return ← Equilibrium concept

Asset pricing models = Positive theory

From Markowitz to equilibrium modelsCapital Asset Pricing Model

Risk , Return...

Rational investors with mean-variance preferences (i.e. they

don’t care about higher moments)

No transaction costs (otherwise, buyers and sellers may face

different prices)

No tax, in particular personal income tax

No price impact (price taking behaviour)

Unlimited short sales allowed

** Unlimited borrowing / lending at the risk-free rate **

AssumptionsCapital Asset Pricing Model

Risk , Return...

Homogenous expectations

◊ About portfolio inputs

◊ About the relevant period of investment

Can be interpreted as all information being freely available

All assets are marketable, i.e. can be bought and sold including

all stocks and bonds, real estate, commodities and even human

capital!

More AssumptionsCapital Asset Pricing Model

Risk , Return...

By definition, this is an asset whose return is known with

certainty, i.e. with probability one (Levy & Post, 2005)

As a result, the expected return is constant

The variance of the risk-free asset is zero

The covariance with other assets is zero

(Can you prove these?)

It is common among practitioners to use the rate of return on

short-term Treasury bills as a proxy for the risk-free interest rate

Risk free assetCapital Asset Pricing Model

Risk , Return...

All investors, regardless of their risk preferences, will choose a

portfolio from the CML

Separation of investment process into two stages:

1) Locate the tangency portfolio TG

2) All investors maximise their utility by choosing the “right”

mix of TG and the risk-free asset

Tobin’s separation theorem (1958)

Since we assume that all investors

face the same risk-free rate, and

the same efficient set, all investors

will face the same CML

Capital Market Line (CML)


Risk , Return...

From Separation Theorem to CAPM

CML is merely a tool, but not particularly useful in practice

Separation theorem gives a rather boring (and probably

erroneous) yet very strong implication on portfolio allocation

It implies the information for aggregate investment

behaviour ← Equilibrium concept

This is the basis for CAPM


Risk , Return...

𝐸 𝑅𝑖 = 𝑟𝐹 + 𝛽𝑖(𝐸 𝑅𝑀 − 𝑟𝐹)

Return on asset i, Ri

Market return, RM

Risk-free rate, rF

Risk measure βi, rather than volatility of i

𝛽𝑖 =𝐶[𝑅𝑖 , 𝑅𝑀]

𝑉[𝑅𝑀]


Risk , Return...

Betathe slope

Expected

return

Expectedmarketreturn

10%10%- +

-10%+10%

stock

-10%

Total risk = diversifiable risk + market risk

Market risk is measured by beta, the sensitivity to market changes

2

m

imi

where

Covariance of asset i returns with the market returns

Variance of the market returns

im

2

m

𝜎𝑖𝑚 = 𝑎=1

𝑛 𝐼𝑎 − 𝐼 𝑀𝑎 − 𝑀

𝑛 − 1


Risk , Return...

http://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=-g6JV9WexSFi5M&tbnid=Vyfu76ebWGxHPM:&ved=&url=http://education.howthemarketworks.com/glossary/covariance-analysis/&ei=DVwAVNeuN9Lkau2igLAO&bvm=bv.74115972,d.d2s&psig=AFQjCNFW0-vXisvSYphdBJydH70NqrNOwQ&ust=1409396110310693

http://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=-g6JV9WexSFi5M&tbnid=Vyfu76ebWGxHPM:&ved=&url=http://education.howthemarketworks.com/glossary/covariance-analysis/&ei=DVwAVNeuN9Lkau2igLAO&bvm=bv.74115972,d.d2s&psig=AFQjCNFW0-vXisvSYphdBJydH70NqrNOwQ&ust=1409396110310693

An average stock (or the market portfolio) has a beta = 1.0.

Beta shows how risky a stock is if the stock is held in a well-diversified

portfolio.

β=1 → stock has average risk.

β>1 → stock is riskier than average.

β<1 → stock is less risky than average.

β=0 → risk free assets (e.g., Treasury bills)


Risk , Return...

The beta of a portfolio (βP) is the weighted average of the betas from its

constituent securities.

Example:

You have $6,000 invested in IBM, $4,000 in GM. You estimate that IBM

has a beta of 0.95 and GM has a beta of 1.15.

What is the beta of your portfolio?

βP = 0.6*0.95 + 0.4*1.15 = 1.03


Risk , Return...

Beta estimates:

Betas are sometimes as large as 2-3 for highly volatile stocks

Low beta: Stable stocks, less affected by business cycles, e.g.

consumer products, and utilities

High beta: ‘Tech’ stocks, financial sector

Negative beta: precious metals and precious-metal-related

stocks, e.g. gold and gold exchange-traded funds (ETF)

Risk , Return...


Source: Levy & Post (2005)

Portfolio Mean Volatility Alpha Beta

Beer & Liquor 0.89 4.63 0.81 0.17

Utilities 0.20 4.56 0.08 0.27

Food products 0.55 4.81 0.36 0.44

Petroleum & Gas 0.55 4.98 0.31 0.56

Helthcare 0.77 4.80 0.50 0.61

Consumer goods 0.82 4.55 0.52 0.70

Financial sector 0.83 4.99 0.47 0.82

Automobiles 0.31 6.76 -0.10 0.93

Machinery 0.51 6.34 0.01 1.13

Services 0.69 8.52 -0.01 1.62

Market portfolio 0.44 4.55 0.00 1.00


Risk , Return...

Industry estimates (US: Jan93-Dec02)

Applications

Investors use CAPM to calculate the expected rate of return on a

security – asset valuation (pricing)

Let’s look a the following data:

Beta of British Airways plc = 1.17

Yield of short-dated Treasury bills = 3.1%

Market risk premium = 4.2%

The expected return on BA = 3.1% + (1.17 × 4.2%) = 8%

This is also the cost of equity for BA!


Risk , Return...

𝐸 𝑅𝑖 = 𝑅𝐹 + 𝛽𝑖 × (𝐸 𝑅𝑀 − 𝑅𝐹)

Return to time Size of risk Return to risk

Some special cases

◊ Risk-free asset: βi = 0

Return is due solely to time value of money

◊ Market: βi > 0

Return comes from the risk component

◊ Counter-cyclical stock: βi < 0

Expected return below the market! Why?

Capital Asset Pricing ModelDecomposition of return

Risk , Return...

𝑅𝑖 − 𝑅𝐹 = 𝛽𝑖 𝑅𝑀 − 𝑅𝐹 + 𝑒𝑖

idiosyncracy

𝑒𝑖~𝑖𝑖𝑑(0, 𝜎𝑒2)

We have introduced a random error term to account for the

difference between the expected and the actual return on asset I

This reflects the idiosyncratic component, which is not priced in

equilibrium

Capital Asset Pricing ModelEx post CAPM specification

Risk , Return...

Return

Beta

Risk Free

Return = rf

Security Market Line

(SML)

SML Equation = rf + B ( rm - rf )

Security Market Line

A

A

C

Risk , Return...


𝛼𝑖 = 𝑅𝑖 − [𝑅𝑓 + 𝛽𝑖 𝑅𝑀 − 𝑅𝑓 ]

Alpha measures the “abnormal” return above (or below) the level

explained by the market return

Risk-adjusted performance index

If i represents a portfolio, then positive alpha could signify the

investment skills of the fund managers

- Asset allocation / stock selection

- Market timing

Jensen’s Alpha (1968)Capital Asset Pricing Model

Risk , Return...

𝑉 𝑅𝑖 = 𝛽𝑖2𝑉 𝑅𝑀 + 𝑉 𝑒𝑖

systematic risk idiosyncratic risk

High risk, high return’ is correct …

provided that you know the correct measure of risk

In theory, beta (economic concept) is preferred to volatility

(statistical concept)

Stocks with high volatilities may not always be highly valued


Risk , Return...

Decomposition of risk

Checking if idiosyncratic risk is relevant

Checking if the relationship is not linear

Testing CAPMCapital Asset Pricing Model

Risk , Return...

. regress rbar beta sig, robust

Linear regression Number of obs = 101

F( 2, 98) = 2.54

Prob > F = 0.0838

R-squared = 0.1040

Root MSE = .00047

------------------------------------------------------------------------------

| Robust

rbar | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

beta | -.0005175 .0002296 -2.25 0.026 -.0009732 -.0000618

sig | .0327825 .0169871 1.93 0.057 -.000928 .0664929

_cons | .0002485 .0001712 1.45 0.150 -.0000912 .0005881

------------------------------------------------------------------------------

Testing CAPM

no idiosyncratic risk


Risk , Return...

. regress rbar beta beta2, robust

Linear regression Number of obs = 101

F( 2, 98) = 2.28

Prob > F = 0.1081

R-squared = 0.0763

Root MSE = .00048

------------------------------------------------------------------------------

| Robust

rbar | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

beta | .0009477 .0004908 1.93 0.056 -.0000264 .0019217

beta2 | -.0004873 .0002336 -2.09 0.040 -.0009509 -.0000236

_cons | .0000256 .0002206 0.12 0.908 -.0004122 .0004634

------------------------------------------------------------------------------

Testing CAPM

quadratic relation


Risk , Return...

The betas discussed so far are equity betas

The company’s asset beta is the weighted average of its liability betas: equity and debt

𝛽𝑎 = 𝛽𝑒 ×𝐸

𝐸 + 𝐷(1 − 𝐶𝑇)+ 𝛽𝑑 ×

𝐷(1 − 𝐶𝑇)

𝐸 + 𝐷(1 − 𝐶𝑇)

where: βa = asset beta or ungeared beta

βe = equity beta ot geared beta

E = market value of equity

D = market value of debt

CT = corporate tax rate

βd = debt rate

CAPM in Investment Appraisal: Asset betaCapital Asset Pricing Model

Risk , Return...

The asset beta is always lower than the equity beta, unless a

company is all-equity financed

If we assume that companies do not default on their interest

payments we can take the debt beta to be zero, and hence

𝛽𝑎 = 𝛽𝑒 ×𝐸

𝐸 + 𝐷(1 − 𝐶𝑇)

We can use this formula to determine the new equity beta when

there is a change in capital structure

𝛽𝑒 = 𝛽𝑎 ×𝐸 + 𝐷(1 − 𝐶𝑇)

𝐸

CAPM in Investment Appraisal: Asset beta with no default riskCapital Asset Pricing Model

Risk , Return...

Example:

Company X which owns and operates grocery stores across the United States, currently has $50 million in debt and $100 million in equity outstanding. Its stock has a beta of 1.2. It is planning a leveraged buyout , where it will increase its debt/equity ratio of 8. If the tax rate is 40%, what will the beta of the equity in the firm be after the LBO?

• Unlevered Beta = 1.20 / (1 + (1-0.4) (50/100)) = 0.923076923

• New Beta = 0.923 (1 + (1-0.4) (8)) = 5.35

Unlevered Beta = levered beta / (1+(1-tax rate)(D/E))

Levered Beta = Unlevered Beta (1+(1-tax rate)(D/E))

CAPM in Investment Appraisal: (Un)Leveraged BetaCapital Asset Pricing Model

Risk , Return...

Arbitrage Pricing Model (Arbitrage Pricing Theory APT)

𝐸(𝑅𝑖) = 𝑅𝐹 + 𝛽1𝑖𝐼1 + 𝛽2𝑖𝐼2 + 𝛽3𝑖𝐼3 …

where I is the risk premium on the factor

Estimated risk premiums

for taking on risk factors

(1978-1990)

6.36Mrket

.83-Inflation

.49GNP Real

.59-rate Exchange

.61-rateInterest

5.10%spread Yield

)(r

PremiumRisk EstimatedFactor

factor fr

CAPM AlternativeCapital Asset Pricing Model

Risk , Return...

0

5

10

15

20

251928

1933

1938

1943

1948

1953

1958

1963

1968

1973

1978

1983

1988

1993

1998

High-minus low book-to-market

Return vs. Book-to-MarketDollars

Low minus big

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

CAPM in Investment Appraisal: Asset betaCapital Asset Pricing Model

Risk , Return...

Financial Markets


Diversification

Optimal Portfolio


Risk , Return...

Market Efficiency

Market Efficiency

Tests of EMH: Empirical investigation

Market Efficiency

A perfect market has the following characteristics:

No taxes or transaction costs to inhibit buying or

selling

Similar expectations amongst participants regarding

asset prices, interest rates and other economic factors

Free entry and exit to and from the market

All information available freely to everyone

Many buyers and sellers (perfect competition)

Market Efficiency

Market Efficiency

Since no capital market can possibly meet these

requirements it is normally said to be enough for

capital markets to offer fair prices & to be efficient in

order to allow reasoned investment and financial

decisions

In practice an efficient capital market should satisfy:

Operational efficiency: fast trading at low cost

Pricing efficiency: prices should reflect all available information

Allocational efficiency: efficient pricing leads to optimal

allocation of investment funds)

Market Efficiency

Market Efficiency

This is a hypothesis originated by Fama (1965), ‘The Behaviour

of Stock Market Prices’, Journal of Business

How efficiently do markets process information?

EMH: Security prices fully reflect all relevant

information

If a financial market is efficient, the best estimate of the true

value of a security is its current market price

Market Efficiency

Market Efficiency

Relationship with allocation efficiency:

Assumptions:

◊ No transaction costs

◊ Information acquisition incurs no cost

If the information suggests that a share is undervalued, i.e.P* > Pt, then some investors will buy it, and the price will rise

Similarly, when the stock is overvalued

If every investor shares the same set of information, themarket will be in equilibrium at any time: P* = Pt

Market Efficiency

Market Efficiency

Relationship with allocation efficiency:

Assumptions:

◊ No transaction costs

◊ Information acquisition incurs no cost

Very strong assumptions

More realistic EMH: Prices reflect information untill the

marginal cost of obtaining information and traiding no

longer exceed the marginal benefit.

Market Efficiency

Market Efficiency

Three forms of market efficiency

Weak form

~ Historical prices

Investors could not use historical stock price information

to make (abnormal) profit

Semi-strong form

~ Publicly available information

Neither stock price nor firms’ financial statements or

supplementary information

Strong from

~ ALL available information

Not even insider trading

Strong Form

Semi-Strong

Weak Form

Market Efficiency

Market Efficiency

Three forms of market efficiency

Weak form ~ Historical prices

test whether all information contained in historical prices is

fully reflected in current prices

tests of return predictability

Semi-strong form ~ Publicly available information

test whether publicly available information is fully reflected in

current prices

event studies or studies of announcements

Strong from ~ ALL available information

test whether all information, public or private, is fully reflected

in current prices

Market Efficiency

Market Efficiency

Can investors ‘beat the market’?

If prices reflect all relevant information, any changes must be

due to an arrival of new information – which seems to be random

EMH rules out any possibilities of investors making sustained abnormal profit

EMH does not rule out the possibility of obtaining profit from the

arrival of new information

If there is actually some opportunity to make extra money, it

should disappear very quickly (thanks to the quick dissemination

of information)

Market Efficiency

Market Efficiency

An Efficient Market Hypothesis (EMH) joke

What would you do if you found a 1 PLN coin on the street?

Answer: it should not have been there in the first place!

Market Efficiency

Market Efficiency

Investment strategies

◊ Active

- Fundamental analysis, e.g. ratio analysis

- Technical “Chartism” analysis

◊ Global macro

◊ Momentum: Long winners & short losers

◊ Market timing / rotational strategies

◊ Multiple strategies

If market is efficient non of them should work

Market Efficiency

Market Efficiency

http://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=iVoKaEgoMjD4KM&tbnid=KCdqJsHa8kBwmM:&ved=0CAUQjRw&url=http://sprawdzian.net.pl/ile_wazy_100_zl.html&ei=56wIVLoBhOlo-seCkAo&bvm=bv.74649129,d.ZGU&psig=AFQjCNGq7GxWipz1vHrjrHlXTOSsBlzK7Q&ust=1409941092742278

http://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=iVoKaEgoMjD4KM&tbnid=KCdqJsHa8kBwmM:&ved=0CAUQjRw&url=http://sprawdzian.net.pl/ile_wazy_100_zl.html&ei=56wIVLoBhOlo-seCkAo&bvm=bv.74649129,d.ZGU&psig=AFQjCNGq7GxWipz1vHrjrHlXTOSsBlzK7Q&ust=1409941092742278

Any changes in price are random

What would be your best estimate of Pt+1?

Answer: Pt because you don’t know what the “news term” is

going to be

We say that price is a martingale:

𝐸[𝑝𝑡+1 Ω𝑡] = 𝑝𝑡

where the expectation is conditional on all available

information at t (Ω𝑡)

Market Efficiency

Market Efficiency

A simple example:

𝑝𝑡+1 = 𝑝𝑡 + 𝜀𝑡+1, 𝑤𝑖𝑡ℎ 𝐸[𝜀𝑡+1 Ω𝑡] = 0

Random term = noise term = “news” term

We can then study the property of return

∆𝑝𝑡+1 = 𝜀𝑡+1

𝐸∆𝑝𝑡+1

𝑝𝑡 Ω𝑡 = 𝐸

𝜀𝑡+1

𝑝𝑡 Ω𝑡 =

1

𝑝𝑡𝐸 𝜀𝑡+1 Ω𝑡 = 0

Market Efficiency

Market Efficiency

The movement of stock prices from day to day DOES NOT reflect any pattern.

Statistically speaking, the movement of stock prices is random (skewed positive over the long term).

Market Efficiency

Market Efficiency

$103.00

$100.00

$106.09

$100.43

$97.50

$100.43

$95.06

Coin Toss Game

Heads

Heads

Heads

Tails

Tails

Tails

Market Efficiency

Is FTSE 100 a martingale?

Market Efficiency

If price is a martingale, then return is a martingale difference:

𝐸 𝑅𝑡+1 Ω𝑡 = 0

By the law of iterated expectation, it follows that

𝐸 𝑅𝑡+1 = 0

But this barely makes any senses economically.

Dividend is an important part of total return

𝐸 𝑅𝑡+1 + 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑 > 0

Market Efficiency

Market Efficiency

This random walk model assumes that the “news term” is

identically and independently distributed:

𝜀𝑡~𝐼𝐼𝐷(0, 𝜎2)

A “step” from Pt to Pt+1 is random, thus the terminology

Return will also be iid since ∆𝑝𝑡+1 = 𝜀𝑡+1

This implies that return shows no autocorrelation, i.e. return at

time t+1 must not show any correlation with return at time t

Market Efficiency

Market Efficiency

Louis Bachelier is a pioneer in the study of financial mathematics

His model assumes further that

𝜀𝑡~𝑁𝐼𝐷(0, 𝜎2)

i.e. “news” is normally and independently distributed with mean

zero and constant variance

Normality is convenient (two-parameter distribution), but also

highly controversial

This has been a building block of modern finance

Market Efficiency

Market Efficiency

Price simulation – Anything goes!

log 𝑝𝑡 = log 𝑝𝑡−1 + 𝜀𝑡

𝑝0 = 1𝜀𝑡~𝑁𝐼𝐷(0, 0.12)

Market Efficiency

Market Efficiency

Trending

Market Efficiency

Market Efficiency

Cyclical movements

Market Efficiency

Market Efficiency

nid returns

Market Efficiency

Market Efficiency

Estimated distribution of returns

Market Efficiency

Market Efficiency

Market Efficiency

Market Efficiency

Estimated distribution of prices

Predictability as an evidence of inefficiency

The random walk model implies that returns must not be

predictable

If returns are predictable, then it might be possible to

systematically generate excess returns

→ Long positive return / short negative return

Unpredictability is sufficient, but not necessary, for

market efficiency

→ Small average excess returns might not generate net gains once

costs have been taken into account

Market Efficiency

Market Efficiency

Testing for return predictability

Examine whether one can forecast Rt+1 with a certain degree of

accuracy

One may use all sorts of predictors e.g. past returns, macroeconomic

variables, some dummy variable associated with certain events (calendar

effects), stock characteristics

Most of the time, the relevant techniques are very simple!

Linear regression

Market Efficiency

Market Efficiency

Testing for return predictability: Examples

Day-of-the-week effects

𝑅𝑡 = 𝑐0 + 𝑐1𝐷1𝑡 + 𝑐2𝐷2𝑡 + 𝑐3𝐷3𝑡 + 𝑐4𝐷4𝑡 + 𝜀𝑡

Autoregressive time-series model

𝑅𝑡 = 𝛼 + 𝛾𝑅𝑡−𝑘 + 𝜀𝑡

Factor model

𝑅𝑡 = 𝛽1𝑥1𝑡 + 𝛽2𝑥2𝑡 + ⋯ 𝛽𝑘𝑥𝑘𝑡 + 𝜀𝑡

Then, we can conduct simple hypothesis tests (t or F)

Market Efficiency

Market Efficiency

Tests of return predictability

Time paterns in security returns

Predicting returns from the past

Returns and firm characteristics

Announcement and price return

Investment funds performance

Market Efficiency


Time patterns in security returns

Intraday and day of the week paterns

Returns on Monday are much lower than on other days

Some evidence of large possitive returns on Wednesday and Friday (Gibbons and Hess, 1981)

Monthly paterns

January higher returns than in other months, especially for small stocks

Explanation: market microstructure (bid- ask spread), tax-selling hypothesis

Turn of the callender effect

Bulk of the return comes form last trading day of the month and the first few of the following month

Market Efficiency

Tests of EMH: Empirical investigationTesting for return predictability

Comparison of Returns on the S&P 500, and the Smallest Quintile of CRSP Stocks:1941–81 and 1982–91

Source: Elton, Gruber, Brown, and Goetzman (2011)

Market Efficiency


Predicting returns from the past

Short term predictability

Correlation tests

𝑟𝑡 = 𝑎 + 𝑏𝑟𝑡−1−𝑇 + 𝑒𝑡

(returns are log returns)

Run tests

If we denote price increase as + and price decrease as – (no changeas 0), then a sequence of the same signs is called run

Compare the numer of actual runs with the number attributed to chance

Trading rules (eg. Filter rule)

Formulate trading rule appropriate to particular patern and checkwhat will happen if the rule is followed

Filter rule example: Purchase if incerwased by X% from previouslow, sell if decreased by Y% from subsequent high

Relative strength

Current price/average price

Market Efficiency


Daily Correlation Coefficients (from Fama [78]), (1/2)


Small number

Market Efficiency


Daily Correlation Coefficients (from Fama [78]), (2/2)


Market Efficiency


Correlation of Return with Returns in Prior Periods for Various Countries (1/2)


Market Efficiency


Correlation of Return with Returns in Prior Periods for Various Countries (2/2)


Market Efficiency


Total Actual and Expected Numbers of Runs for One-, Four-, Nine-, and Sixteen-Day Differencing Intervals (from Fama [75]), (1/2)


Fewer runs than we expected: evidence of

small possitiverelationship between

returns

Market Efficiency


Total Actual and Expected Numbers of Runs for One-, Four-, Nine-, and Sixteen-Day Differencing Intervals (from Fama [75]), (2/2)


Market Efficiency


Security Price and Time, Implementation of Filter Rule


Market Efficiency


Comparison of rates of Return, before Commissions, under the Filter

Technique and under a Buy and Hold Policy, (1/2)


Market Efficiency


Comparison of rates of Return, before Commissions, under the Filter

Technique and under a Buy and Hold Policy, (2/2)


Market Efficiency


Returns and firm characteristics

The size effect

Excess returns would be earned if hold small cap stocks (Branz, 1981)

Additional variable in APT

Market to book

Hight book to market stock returns higher than low book to market

Earnings price

Once size and market to book are coounted for E/P ratio doenst matter?

Stocks with low PE ratios provide higher returns than stock with higher

PE

Market Efficiency


Announcement and price return (abnormal return)

e.g. stock splits, cash dividends, stock dividend

Excess return around announcement day.


Market Efficiency


stock prices will

respond to

announcements only

when the information

being announced is

new and unexpected

Announcements and returns

Cumulative excess return around split date.


Market Efficiency

Tests of EMH: Empirical investigationAnnouncements and returns

Cumulative excess return around announcement date.


Market Efficiency


Excess return around publication date


Market Efficiency


At 10AM EST, the U.S. Supreme Court refused to hear

an appeal from MSFT regarding its anti-trust case.

The stock immediately dropped. This example, one of

hundreds available every day, illustrates that prices

adjust extremely rapidly to new information.

But, did the price adjust correctly? Only time will tell,

but it does seem that over the next hour the market is

searching for the correct level.

Market Efficiency


Average Annual Return on 1493 Mutual Funds and the Market Index

Source: Brealey and Myers (2006)

-40

-30

-20

-10

0

10

20

30

40

1962

1977

1992

Retu

rn (

%)

Funds

Market

Market Efficiency

Tests of EMH: Empirical investigationInvestment funds performance

Source: Barber, and Odean

(2000)

Market Efficiency


Market Efficiency


Testing for random walk (prieces behave as random with a drift as we

have inflation)

𝑃𝑡 = 𝛽1 + 𝛽2𝑃𝑡−1 + 𝑢𝑡 (1)

H0: β2=1 (EMH holds)

𝑃𝑡 = 𝛽1 + 𝛽2𝑃𝑡−1 + 𝛽3𝑃𝑡−2 + 𝛽4𝑃𝑡−3 + 𝑢𝑡 (2)

H0: β3=0 and β4=0 (EMH holds)

Testing for serial correlation in error term

durbina test: H0: no serial correlation (EMH holds)

Testing for day of the day of the week effect

Serching for patterns in residuals: ARCH and GARCH

Market Efficiency


Testing procedure

Aviva Example

23

45

67

AV

IVA

01jul2007 01jul2008 01jul2009 01jul2010 01jul2011 01jul2012date

Market Efficiency

Tests of EMH: Empirical investigationAviva Example

. regress x10 l.x10 day1-day4

Source | SS df MS Number of obs = 1305

-------------+------------------------------ F( 5, 1299) =17357.07

Model | 1390.05463 5 278.010925 Prob > F = 0.0000

Residual | 20.8062875 1299 .016017157 R-squared = 0.9853

-------------+------------------------------ Adj R-squared = 0.9852

Total | 1410.86091 1304 1.08194855 Root MSE = .12656

------------------------------------------------------------------------------

x10 | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

x10 |

L1. | .9898067 .00336 294.59 0.000 .9832152 .9963982

|

day1 | -.0200002 .0110787 -1.81 0.071 -.0417343 .0017338

day2 | .0046152 .0110787 0.42 0.677 -.017119 .0263494

day3 | -.0099373 .0110787 -0.90 0.370 -.0316714 .0117967

day4 | -.0096329 .0110787 -0.87 0.385 -.031367 .0121011

_cons | .0449657 .0155495 2.89 0.004 .0144608 .0754706

------------------------------------------------------------------------------

. test l.x10=1

( 1) L.x10 = 1

F( 1, 1299) = 9.20

Prob > F = 0.0025

. durbina

Durbin's alternative test for autocorrelation

---------------------------------------------------------------------------

lags(p) | chi2 df Prob > chi2

-------------+-------------------------------------------------------------

1 | 0.243 1 0.6217

---------------------------------------------------------------------------

H0: no serial correlation

. test day1 day2 day3 day4

( 1) day1 = 0

( 2) day2 = 0

( 3) day3 = 0

( 4) day4 = 0

F( 4, 1295) = 1.56

Prob > F = 0.1821

Market Efficiency

Market Efficiency


Market Efficiency

Valuating Stocks and Bonds

Valuing Stocks and Bonds

Bond Valuation

Stock Valuation:

DCF valuation

Relative Valuation


Bond Valuation

Bonds have a par value or principal(which is typically 100 units of currency)

Bonds pay interest payments (the coupon) based on

the par value

Zero coupon bond pay no coupon

Yield (YTM) of a bond is a discount rate that makes

the PV of bond payments equal to todays price

Example:

If today is October 2002, what is the value of the following bond?

An IBM Bond pays $115 every Sept for 5 years. In Sept 2007 it pays an additional$1000 and retires the bond.The bond is rated AAA (WSJ AAA YTM is 7.5%)

84.161,1$

075.1

115,1

075.1

115

075.1

115

075.1

115

075.1

1155432PV

Cash flows:

Sept 03 04 05 06 07

115 115 115 115 1115


Bond Valuation

Present value of the Cash Flows the instrument is generating


Fair value of Financial Instrument:

Bond Valuation

→ DCF Valuation

Discounted Cashflow (DCF) valuation:Relates the value of an asset to the present value of expected future

cashflows on that asset.

Relative valuation:Estimates the value of an asset by looking at the pricing of 'comparable'

assets relative to a common variable like earnings, cashflows, book value

or sales.

Contingent claim valuation:Uses option pricing models to measure the value of assets that share

option characteristics.

Stock Valuation


Valuing a Business

The value of a business is usually computed as the discounted value of FCF out to a valuation horizon (H).The valuation horizon is sometimes called the terminal value and is calculated likePVGO.

H

H

H

H

r

PV

r

FCF

r

FCF

r

FCFPV

)1()1(...

)1()1( 2

2

1

1

PV (free cash flows) PV (horizon value)


CASH FLOW:The difference between money received and money paid.

Often confused with accounting profits. 2 issues: 1. Profits are shown as they are earned, not when the cash is paid2. The cash outflows are divided into: current expenses and capital expenses. Current

expenses are deducted when calculating profit. Capital expenses are not (they are deducted over number of years).

Thus profits include some cash flows and excludes others, they are reduced by depreciation charges (which are not cash flows at all)

Always estimate cash flows on after tax basis.

Cash flows are recorded when they occure and not when work is undertaken or liability is incured.


Stock ValuationDCF valuation

Example: Given the cash flows for Company X calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6%

66613132020202020(%) growth .EPS

1.891.791.681.59.23-.20-1.39-1.15-.96-.80- FlowCash Free

1.891.781.681.593.042.693.462.882.402.00Investment

3.783.573.363.182.812.492.071.731.441.20Earnings

51.3173.2905.2847.2643.2374.2028.1740.1400.1200.10ValueAsset

10987654321

Year

4.22

06.10.

59.1

1.1

1 value)PV(horizon

6

6.3

1.1

23.

1.1

20.

1.1

39.1

1.1

15.1

1.1

96.

1.1

.80-PV(FCF)

65432

$18.822.4-3.6 value)PV(horizonPV(FCF)s)PV(busines


Stock Valuation

To use discounted cash flow valuation, you need:

to estimate the life of the asset

to estimate the cash flows during the life of the asset

to estimate the discount rate to apply to these cash flows to

get present value


Stock ValuationDCF valuation

Dividend Discount Model Computation of today’s stock price which states that share value equals the present value of all expected future dividends.

PDiv

r

Div

r

Div P

r

H H

H01

1

2

21 1 1

( ) ( )...

( )

H – investment time horizon

Stock Valuation


Example: Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?

PV

PV

300

1 12

324

1 12

350 94 48

1 12

00

1 2 3

.

( . )

.

( . )

. .

( . )

$75.

Stock Valuation


If we forecast no growth, and plan to hold out stock indefinitely,

we will then value the stock as a PERPETUITY.

Perpetuity PDiv

ror

EPS

r 0

1 1

Assumes all earnings are paid to shareholders.

Constant Growth DDM A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model).

Stock Valuation


Example - continued: If the same stock is selling for $100 in the stock market, what might the market be assuming about the growth in dividends?

09.gg

12.

00.3$100$

Answer: The market is assuming the dividend will grow at 9% per year, indefinitely.

If a firm elects to pay a lower dividend, and reinvest the funds, the stockprice may increase because future dividends may be higher.

Payout RatioFraction of earnings paid out as dividents.

PlowbackRatioFraction of earnings retained by the firm.

Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations.

g = return on equity * plowback ratio

Stock Valuation


Example: Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?

P0

5

1267

.$41. 08.40.20. g

No growth

00.75$08.12.

30

P

With growth

If the company did not plowback some earnings, the stock price would remain at $41.67. With the plowback, the price rose to $75.00.

The difference between these two numbers (75.00-41.67=33.33) is called the Present Value of Growth Opportunities (PVGO).

Present Value of Growth Opportunities (PVGO) Net present value of a firm’s future investments.

Sustainable Growth Rate Steady rate at which a firm can grow: plowback ratio X return on equity.

Stock Valuation



Bond Valuation

Stock Valuation:

DCF valuation

Relative Valuation

EXERCISES

Question 1

A company is financed by bonds and ordinary shares.

The 12% bonds are redeemable in 5 years’ time at par. Annual interest has

just been paid. The current ex-interest market price of the bond is £114.

Corporation tax is 28%.

The ex-dividend ordinary share price is £3.14 and the most recent dividend

was 35 pence per share. Both dividend and share price are expected to

increase by 7% per year for the foreseeable future.

The company has 5,000 redeemable bonds (par value £100) and 225,000

ordinary shares (par value £1).

(a) Calculate the cost of debt. [Hint: remember the ‘tax-shield’.]

(b) Calculate the cost of equity.

(c) Calculate the company’s WACC.

Question 2

At January 2012 a company’s sources of debt and equity finance are

summarised as follows:

7% (DP) preference shares (£1) £400,000

8% bonds (redeemable January 2021, par [ ] £100) £600,000

9% bank loan £500,000

Ordinary shares (£1) £400,000

By making use of this and the following information calculate the

company’s WACC at market prices.

[Hint: remember the ‘tax-shield’.]

Question 3

Explain the term diversification in finance, and give a few examples.

Question 4

You are considering investing in two securities, X and Y, and have the

following information.

a) Draw the probability distribution for X, and for Y. Comment on their

shape.

b) Calculate the expected return for each security.

c) Calculate the expected risk of each security.

Question 5

You are considering investing in two securities, X and Y, and have the

following information.

a) Do the above data conform to the risk-return trade-off?

b) Calculate the expected return and standard deviation for the following

portfolios:

i. 100 per cent X;

ii. 75 per cent X and 25 per cent Y;

iii. 50 per cent X and 50 per cent Y;

iv. 25 per cent X and 75 per cent Y;

v. 100 per cent Y.

c) Plot your answers on the risk-return plane, and comment on the benefit

of diversification.

Question 6

Stock A has a beta of 1.0, and very high idiosyncratic risk. If the expected

return on the market is 20%, what will be the expected return on Stock A

according to the CAPM?

Question 7

Suppose you estimate the CAPM model for Stock B. Your result shows that

this stock has beta of 1.4, and the standard deviation of the error term of

7%. Assume that the standard deviation of the market is 12%. What is the

total standard deviation of Stock B?

Question 8

Suppose you invested £600 in Stock C, and £400 in Stock D. Stock C’s beta

is 1.2, and Stock D’s beta is 0.9. What is the beta of your portfolio?

Question 9

You formed a portfolio by combining the risk-free asset and Stock Z. The

risk-free rate is 6%, while the expected return of Stock Z is 22%. The

volatility of Stock Z is 40%. If your portfolio shows the standard deviation

of 30%, what is the expected return on your portfolio?

Question 10

A firm has an equity beta of 1.3, and is currently financed by 25% debt and

75% equity. What will be the company’s new equity beta if the company

changes its financing to 33% debt and 67% equity? Assume corporate tax

is 30%.

Question 11

A company has in issue bonds which are convertible in 3 years’ time into

25 ordinary shares per bond. If not converted, they will be redeemed in 6

years’ time at par. The bonds pay 9% interest per year and currently have a

market price of £90.01. The current ordinary share price is £3.24. If holders

of ordinary bonds of a similar risk class require a return of 13% per

annum:

(a) Are bond holders likely to convert?

(b) What is the expected annual growth rate of the ordinary share price?

(c) Calculate the minimum growth rate in the ordinary share price

necessary to make conversion an attractive option.

(d) Calculate the implicit conversion premium

(1) Capital Structure

(2) Dividend policy

(3) Options

Lecture 3:

Capital Structure

Does it matter which source of capital company chooses?

If some forms of capital costs less than others this suggests there could be a capital structure that maximizes shareholder wealth

Capital Structure

Capital Structure

WACC

Gearing, risk and required rate of return

Theories of capital structure:

Traditional approach

MM

Conflicts of interest

Pecking order theory

Valuations/ WACC cont.

EDA r

V

Er

V

DrWACC

Weighted Average Cost of Capital (WACC) combines the individual costs of capital with the weights each source of financing takes in forming the company's capital structure

Capital Structure

WACC

Simple debt/equity example:

After tax WACC:

ETDA r

V

ECr

V

DrWACC )1(

We can extend the formula for

as many source of finance as

the company has

.10=rD

.20=rE

.15=rA

BEBABD

Risk

Expected Return

Equity

All assets

Debt

Capital Structure

WACC

Example - A firm has $2 mil of debt and 100,000 of outstanding shares at $30 each. If they can borrow at 8% and the stockholders require 15% return what is the firm’s WACC?

D = $2 million

E = 100,000 shares X $30 per share = $3 million

V = D + E = 2 + 3 = $5 million

12.2%or 122.

15.5

308.

5

2

ED r

V

Er

V

DWACC

Capital Structure

WACC

When WACC can be used as the discount rate in investment appraisal?

The business risk of the investment project needs to be the same as the company’s overall risk profile

Finance is raised such that capital structure is preserved

The marginal investment project must preserve the risk/return relationship

Capital Structure

WACC

Risk (a summary)

Business risk – the risk associated with profits and earnings changing due to the sector the company operates in (systematic risk)

Financial risk – the risk associated with increased gearing due to uncertainty over interest payments on debt capital

Bankruptcy risk – the risk of a company becoming insolvent due to an inability to meet interest payments on debt capital

Risk-free rate – the return that can be achieved for certain (on say government bonds)

Capital Structure


Gearing and required rate of return

Capital Structure


The diagram illustrates how investors’ required rates of return on equity increase with a company’s gearing:

i. The risk-free rate remains constant

ii. Business risk remains constant, the level reflecting the company’s sector

iii. Financial risk increases with gearing, reflecting the increasing effect of interest rate changes as the company’s debt levels

increase (potentially adversely affecting profits)

iv. Bankruptcy risk is shown for high levels of gearing as investors start to face risks of the company entering liquidation (and

potentially losing everything)

That was for equity holders

For holders of debt the only risk is that of bankruptcy, since interest payments on debt are guaranteed

Even then, debt holders face less bankruptcy risk than equity holders because they are higher in the hierarchy of creditors if the company were to be liquidated

Capital Structure


Traditional approach is often referred to as ‘trade-off theory’

Some simplifying assumptions:

No taxation

Finance is either perpetual debt (interest payments only) or ordinary shares

Companies can change their financial structure costlessly

All earnings paid as dividends

Constant risk over time

Earnings and dividends do not grow

Capital Structure

Theories of Capital StructureTraditional approach

Cost of capital

D

V

rD

rE

WACC

Theories of Capital StructureTraditional approach

Capital Structure

With no gearing the WACC is equal to the

cost of equity

As gearing increases the WACC decreases to reflect the cheaper cost

of finance

At some point the increased financial risk

(interest rate) associated with ever higher gearing starts

to increase WACC

At very high levels of gearing bankruptcy risk further increases WACC

optimal capital structure exists

(min WACC)

Miller & Modigliani (M&M) (1958) proposed a model that suggested that WACC remains constant for all levels of gearing

By adding the additional assumption of perfect capital markets to the previous model (which means firms can always borrow more) M&M assumed away bankruptcy risk…

Since M&M(i) implies a constant WACC it is often referred to as their “irrelevance” theory, i.e. the choice of capital structure doesn’t matter

Capital Structure

Theories of Capital StructureMiller and Modigliani (i)

Cost of capital

D

V

rD

rE

WACC

Theories of Capital Structure

Capital Structure

With no bankruptcy risk the cost of debt remains

constant. The cost of debt is independent of the level

of gearing

As gearing increases the cost of equity increases

linearly to reflect increased financial risk

The WACC remains constant. The reduced cost of debt finance is exactly offset by the

increased financial risk associated with higher

gearing levels

WACC is independent of capital structure

(capital structure is irrelevant)

Miller and Modigliani (i)

Assumptions

By issuing 1 security rather than 2, company diminishes investor choice. This does not reduce value if:

– Investors do not need choice, OR

– There are sufficient alternative securities

Capital structure does not affect cash flows e.g...

– No taxes

– No bankruptcy costs

– No effect on management incentives

Capital Structure


Example - Macbeth Spot Removers - All Equity Financed

201510% 5(%) shares on Return

2.001.501.00$.50shareper Earnings

2,0001,5001,000$500Income Operating

D C BA

Outcomes

10,000 $Shares of ValueMarket

$10shareper Price

1,000shares ofNumber

Data

M&M (Debt Policy Doesn’t Matter)

Expected outcome

Capital Structure


Example

cont.

50% debt

M&M (Debt Policy Doesn’t Matter)

3020100%(%) shares on Return

321$0shareper Earnings

500,11,000500$0earningsEquity

500500500$500Interest

000,21,5001,000$500Income Operating

CBA

Outcomes

5,000 $debt of ueMarket val

5,000 $Shares of ValueMarket

$10shareper Price

500shares ofNumber

Data

D

Capital Structure


Example - Macbeth’s - All Equity Financed

- Debt replicated by investors

3020100%(%) investment$10 on Return

3.002.001.000 $investment on earningsNet

1.001.001.00$1.0010% @Interest :LESS

4.003.002.00$1.00shares twoon Earnings

DCBA

Outcomes

M&M (Debt Policy Doesn’t Matter)Capital Structure


Since investors can replicate what company does, why

would they pay more for firm with leverage?

The many assumptions of M&M(i) are clearly implausible

In their paper Miller & Modigliani acknowledge that the simplifications are implausible, yet necessary in order to start developing formal models of capital structure

Their second capital structure paper, Miller & Modigliani (ii) (1963), considers the tax shield associated with debt finance

Capital Structure


All Equity 1/2 Debt

EBIT 1,000 1,000

Interest Pmt 0 100

Pretax Income 1,000 900

Taxes @ 40% 400 360

Net Cash Flow $600 $540

Example - You own all the equity of Space Babies Diaper Co. The company has no debt. The company’s annual cash flow is $1,000, before interest and taxes. The corporate tax rate is 40%. You have the option to exchange 1/2 of your equity position for 10% bonds with a face value of $1,000.

Should you do this and why?

Total Cash Flow

All Equity = 600

*1/2 Debt = 640

(540 + 100)

Interest Tax Shield- Tax savings resulting from deductibility of interest payments.

Capital Structure

Theories of Capital StructureMiller and Modigliani (ii)

PV of Tax Shield =

(assume perpetuity)

D x rD x Tc

rD

= D x Tc

Example:

Tax benefit = 1000 x (.10) x (.40) = $40

PV of 40 perpetuity = 40 / .10 = $400

PV Tax Shield = D x Tc = 1000 x .4 = $400

Capital Structure


Firm Value =

Value of All Equity Firm + PV Tax Shield

Example

All Equity Value = 600 / .10 = 6,000

PV Tax Shield = 400

Firm Value with 1/2 Debt = $6,400

Capital Structure


Cost of capital

D

V

rD

rE

WACC


Capital Structure

The tax shield reduces the cost of debt

Holding everything else equal that leads to downward

slopping WACC.The tax advantage of debt finance means that WACC

decreases as gearing increases.

The implications of MM(ii) is that

companies should be financed entirely by

debt

Miller and Modigliani (ii)

rD(1-CT)

Since we don’t see all-debt companies presumably all-debt is not optimal (and in fact taxpayers & banks recently learnt the hard way what can happen if companies are too highly geared)

The final model adds bankruptcy risk to M&M(ii)

Capital Structure

Theories of Capital StructureMiller and Modigliani (ii) with bankruptcy

D/V

Mar

ket

Val

ue

of

The

Firm


Capital Structure

Market value of an all equity company

As the company increases debt levels the value of the

company increases reflecting the benefits of

the tax-shield

At high level of gearing bankruptcy risk starts to reduce

the value of the company

At some point increased bankruptcy risk more than off-set the tax advantage of debt. Again there is (theoretically) an optimal

capital structure

Market Value = Value if all Equity Financed

+ PV Tax Shield

- PV Costs of Financial Distress

Capital Structure


D/V

Mar

ket

Val

ue

of

The

Firm

Value ofunlevered

firm

PV of interesttax shields

Costs offinancial distress

Value of levered firm

Optimal amount of debt

Maximum value of firm


Capital Structure

How much leverage?

In principle, yes be as highly geared as is feasible in order to maximise the value

However, a company needs to make enough profits to fully benefit from the tax-shield advantages of debt (this is tax exhaustion)

Agency costs: if shareholders hold too small a part of a company they may start to prefer higher risk projects

Capital Structure


Company X has $50 of 1-year debt.

Company X (Book Values)

Net W.C. 20 50 Bonds outstanding

Fixed assets 80 50 Common stock

Total assets 100 100 Total liabilities

Theories of Capital StructureConflicts of interest

Capital Structure

Company X has $50 of 1-year debt.

Why does the equity have any value ? Shareholders have an option: they can obtain the rights to the

assets by paying off the $50 debt.

Company X (Market Values)




Capital Structure


Company X may invest $10 as follows.

y)probabilit (90% $0

$10Invest

y)probabilit (10% $120

Next Year PayoffsPossibleNow

Assume the NPV of the project is (-$2).

What is the effect on the market values?

Capital Structure


Company X value (post project)

Firm value falls by $2, but equity holder gains $3





Capital Structure


Company X value (assumes a safe project with NPV = $5)

While firm value rises, the lack of a high potential payoff for shareholders causes a decrease in equity value.





Capital Structure


Consider the following story:

The announcement of a stock issue drives down the stock price because investors believe managers are more likely to issue when shares are overpriced.

Therefore firms prefer internal finance since funds can be raised without sending adverse signals.

If external finance is required, firms issue debt first and equity as a last resort.

The most profitable firms borrow less not because they have lower target debt ratios but because they don't need external finance.

Capital Structure

Theories of Capital StructurePecking order theory

Some Implications:

Internal equity may be better than external equity.

Financial slack is valuable.

If external capital is required, debt is better. (There is less room for difference in opinions about what debt is worth).


Capital Structure


WACC: How are costs of financing determined?

Return on equity can be derived from market data

Cost of debt is set by the market given the specific rating

of a firm’s debt

Preferred stock often has a preset dividend rate

…

Capital Structure

Valuations

If you discount at WACC, cash flows have to be projected

just as you would for a capital investment project. Do not

deduct interest.

Calculate taxes as if the company were all equity financed.

The value of interest tax shields is picked up in the WACC

formula.

Capital Structure

Valuations

Discounting at WACC values the assets and

operations of the company.

If the object is to value the company's equity, that

is, its common stock, don't forget to subtract the

value of the company's outstanding debt.

Capital Structure

Valuations

Cost of equity depends on financial leverage, if

financial lavarage change significantly, discounting

cash flows at today’s cost of equity capital will not

give the right answer

Capital Structure

Valuations

What if project is finance at different D/E than the whole company?

Step 1 : Unlevering the WACC:

calculate r (opportunity cost of capital) at current debt rate

r=rD *(D/V) +rE(E/V)

Step 2 – calculate new rE after the change in capital structure, use new D/V (use new rD)

rE=r+(r-rD)(D/E)

Step 3 – Calculate New WACC

WACC = rD(1-TC)(D/V)+rE(E/V)

Capital Structure

Valuations

Adjusted Present Value (APV) =

Base Case NPV + PV Impact

Base Case = All equity finance firm NPV

PV Impact = all costs/benefits directly resulting from project

Capital Structure

Valuations

Example:

Project A has a NPV of $150,000. In order to finance the project we must issue stock, with a brokerage cost of $200,000.

Project NPV = 150,000

Stock issue cost = -200,000

Adjusted NPV - 50,000

don’t do the project

Capital Structure

Valuations

Example:

Project B has a NPV of -$20,000. We can issue debt at 8% to finance the project. The new debt has a PV Tax Shield of $60,000. Assume that Project B is your only option.

Project NPV = - 20,000

Stock issue cost = 60,000

Adjusted NPV 40,000

do the project

Capital Structure

Valuations

debt)for avail CF(loan Equivalent PV

Disocunting the safe, nominal cash flow at an after-tax borrowing rate

Capital Structure

Valuations

Capital Structure

WACC


Theories of capital structure:

Traditional approach

MM

Conflicts of interest


Valuations/ WACC cont.

Dividend Policy

Capital Structure

How Dividends Are Paid

How Do Companies Decide on Dividend Payments?

Information in Dividends and Stock Repurchases

Dividend irrelevance: MM

Dividend relevance

Dividend Policy

Cash Div Regular Cash Div

Special Cash Div (one –off special div)

Stock Div

Stock Repurchase (3 methods)

1. Buy shares on the market

2. Tender Offer to Shareholders

3. Private Negotiation (Green Mail)

Dividend Policy

How dividends are paid

Cash Dividend - Payment of cash by the firm to its shareholders.

Ex-Dividend Date - Date that determines whether a stockholder is entitled to a dividend payment; anyone holding stock before this date is entitled to a dividend.

Record Date - Person who owns stock on this date received the dividend.

Dividend Policy

How dividends are paid

Dividend Policy

How dividends are paidWhen

dividend is announced share is said to be cum dividend

When dividend

entitlement recedes the

share goes ex dividend

Note: the stylised share price (the green line) implies the market reacted positively to the

dividend announcement, since initially the share price increases. (It could have fallen initially if

the market reacted negatively to the dividend announcement).

When the share goes ex dividend its price will always drop.

1. Firms have longer term target dividend payout ratios.

2. Managers focus more on dividend changes than on absolute levels.

3. Dividends changes follow shifts in long-run, sustainable levels of earnings rather than short-run changes in earnings.

4. Managers are reluctant to make dividend changes that might have to be reversed.

Lintner’s “Stylized Facts”

(How Dividends are Determined)

Dividend Policy

Dividend decision

Attitudes concerning dividend targets vary

Dividend Change

Dividend changes confirm the following

1

1

EPS ratiotarget

dividendtarget DIV

01

01

DIV-EPS ratiotarget

changetarget DIV-DIV

01

01

DIV-EPS ratiotarget rate adjustment

changetarget rate adjustmentDIV-DIV

Dividend Policy

Dividend decision

Investors do not worry about the level of company’s dividend, but

about change in that level.

Dividend cuts are usually taken by investors as bad news (stock price fall)

Dividend increases are good news

Share repurchase, one off happening, done when:

Company accumulated more cash then they can invest profitably, or

When company wishes to increase its debt level

Dividend Policy

Information content

Assumptions:

No transaction costs for investors

No transaction costs for companies (issuing new shares)

No taxation

Perfect capital markets

Dividend Policy

Dividend irrelevance

Under these assumptions Miller & Modigliani (M&M) suggest that investors don’t

mind whether returns to equity come from capital gains or dividend payments…

…what matters is simply the overall return on equity

Since investors do not need dividends to convert shares to cash they will not pay higher prices for firms with higher dividend payouts.

In other words, dividend policy will have no impact on the value of the firm.

Dividend Policy


𝑃0 = 𝑑1 + 𝑃1P0 – the market price before dividend is announced

P1 – expected ex-dividend share price

d1- cash value of the dividend paid to shareholders

Example - Assume Company X has no extra cash, but declares a $1,000 dividend. They also require $1,000 for current investment needs. Using M&M Theory, and given the following balance sheet information, show how the value of the firm is not altered when new shares are issued to pay for the dividend.

Record Date Pmt Date Post Pmt

Cash 1,000 0 1,000 (91 sh @ $11)

Asset Value 9,000 9,000 9,000

Total Value 10,000 + 9,000 10,000

New Proj NPV 2,000 2,000 2,000

# of Shares 1,000 1,000 1,091

price/share $12 $11 $11

NEW SHARES ARE ISSUED

Dividend Policy


Example - continued - Shareholder Value

Record Pmt Post

Stock 12,000 11,000 12,000

Cash 0 1,000 0

Total Value 12,000 12,000 12,000

Dividend Policy


Stock = 1,000 sh @ $12 = 12,000Stock = 1,000sh @ $11 = 11,000Stock = 1,091sh @ $11 = 12,000

Assume stockholders purchase the new issue with the cash dividend

proceeds.

MM assumptions don’t hold in real world

Investors cant replicate what the company does

‘Bird in the hand argument’ (Linter, 1956 and Gordon 1959)

Dividends are ‘certain’ (thus valuable) vs. uncertain capital gains

Dividends as signals to investors

The clientele effect

Investors might prefer dividends over capital gains

Taxation issues

Dividend Policy

Dividend relevance

Dividends as Signals

Dividend increases send good news about cash flows and earnings. Dividend cuts send bad news.

Because a high dividend payout policy will be costly to firms that do not have the cash flow to support it, dividend increases signal a company’s good fortune and its manager’s confidence in future cash flows.

Dividend Policy

Dividend relevance

Clientele Effect

There are natural clients for high-payout stocks,

but it does not follow that any particular firm can benefit by increasing its dividends. The high dividend clientele already have plenty of high dividend stock to choose from.

These clients increase the price of the stock through

their demand for a dividend paying stock.

Dividend Policy

Dividend relevance

Tax Consequences

Companies can convert dividends into capital gains by shifting their dividend policies.

If dividends are taxed more heavily than capital gains, taxpaying investors should welcome such a move and value the firm more favorably.

In such a tax environment, the total cash flow retained by the firm and/or held by shareholders will be higher than if dividends are paid.

Dividend Policy

Dividend relevance

0.101000.10100(%)return of rateAfter tax

78.9)94.04()72.410(1050.2)50.120(taxes)-gain cap(div

incomeTax After Total

94.072.4.202.5012.50.2020% @Gain Capon Tax

4.0010.40050% @ divon Tax

05.151005.12100(%)return of ratePretax

4.7212.50gain Capital

97.78100pricestock sToday'

112.50112.50payoffpretax Total

100Dividend

102.50112.50price syear'Next

dividend)(high

B Firm

dividend) (no

A Firm

97.789.78

10010

97.7814.72

10012.5

Dividend Policy

Dividend relevance

2000 Marginal Income Tax Brackets

Income Baracket

Marginal Tax Rate Single Married (joint return)

15% $0 - $26,250 $0 - $43,850

28 26,251 - 63,550 43,851 - 105,950

31 63,551 - 132,600 105,951 - 161,450

36 132,601 -288,350 161,451 - 288,350

39.6 over 288,350 over 288,350

Dividend Policy

Dividend relevance

Cash Flow

Operating Income 100

Corporate tax at 35% 35

After Tax income (paid as div) 65

Income tax paid by investors at 39.6% 25.7

Cash to Shareholder 39.3

In U.S., shareholders are taxed twice (figures in dollars)

Different investors might have different tax advantages

Dividend Policy

Dividend relevance

Rate of Income tax

15% 30% 47%

Operating Income 100 100 100

Corporate tax (Tc=.30) 30 30 30

After Tax income 70 70 70

Grossed up Dividend 100 100 100

Income tax 15 30 47

Tax credit for Corp Pmt -30 -30 -30

Tax due from shareholder -15 0 17

Cash to Shareholder 85 70 53

Under imputed tax systems, such as that in Australia, Shareholders receive a tax credit for the corporate tax the firm pays (figures in Australian dollars)

Dividend Policy

Dividend relevance

Example - Sangria Corporation - continued

ED r

V

Er

V

DTcWACC )1(

%84.10

1084.

146.125

7508.

125

50)35.1(

WACC

Valuations

After Tax WACC

How Dividends Are Paid

How Do Companies Decide on Dividend Payments?

Information in Dividends and Stock Repurchases

Dividend irrelevance: MM

Dividend relevance

Dividend Policy

Options

A derivative is a financial instrument whose value derives from the value of something else, generally

called the underlying(s).

Underlying:

a barrel of oil,

a financial asset,

an interest rate,

the temperature at a specified location

...

Derivatives:

Options

Futures/Forwards

Swaps

Options

Options

Calls and Puts

Pay-off diagrams

How to price an option: Binomial model

No-Arbitrage Argument Valuation

Risk Neutral Valuation

Put-Call Parity

Options

Call Option

Right to buy an asset at a specified exercise (strike) price on or before the exercise date.

Calls and Puts

Options

Put Option

Right to sell an asset at a specified exercise (strike) price on or before the exercise date.

Option ObligationsBuyer Seller

Call option Right to buy asset Obligation to sell asset

Put option Right to sell asset Obligation to buy asset

Calls and Puts

Options

The value of an option at expiration is a function of the stock price and the exercise price.

Example - Option values given a exercise price of $55

00051525ValuePut

25155000Value Call

8070605040$30PriceStock

Pay-off diagrams

Options

Call option value (graphic) given a $55 exercise price (strike price).

Share Price

Cal

l op

tio

n p

ay-o

ff (

valu

e)

55

$20

Options

Pay-off diagrams

75

Put option value (graphic) given a $55 exercise price.

Share Price

Pu

t o

pti

on

pay

off

( v

alu

e)

55

$5

Options

Pay-off diagrams

50

Call option payoff (to seller) given a $55 exercise price.

Share Price

Cal

l op

tio

n $

pay

off

55

Options

Pay-off diagrams

Put option payoff (to seller) given a $55 exercise price.

Share Price

Pu

t o

pti

on

$ p

ayo

ff

55

Options

Pay-off diagrams

If you are the holder of a call option, you want the stock price at expiry to exceed the strike price.

K

STK

Payoff

Then, you exercise the option to buy at the strike price, and immediately sell at a profit ST - K.

If the stock price at expiry is less than the strike price, you let the option die.

Payoff diagram for a Call Option

A call option for which the

current stock price St is

above the strike price K is

said to be in the money.



below the strike price K is

said to be out of the money.



equals the strike price K is

said to be at the money.

out of the money

at the money

Long position in a Call Option

𝑚𝑎𝑥 0, 𝑆𝑇 − 𝐾

Options

Pay-off diagrams

K

STK

Payoff

Payoff diagram for a Put Option

Long position in a Put Option

out of the money

at the money

𝑚𝑎𝑥 0, 𝐾 − 𝑆𝑇

Options

Pay-off diagrams

100

110

90

100

120

80

t=0 t=0.5 t=1

0*0.5+10*0.5=54.878

19.512

11.897

10*0.5+30*0.5=20

4.878*0.5+19.512*0.5=12.195

Consider an European put option with time to expiry of 1 year, and a strike price of 110.

The current price of the underlying is 100. Divide the time to expiry into two 6-month intervals.

Suppose that in each interval, the price can either rise by 10 or fall by 10, with equal probabilities.

The risk-free rate is 5% per annum, simply compounded.

The price movements can

be represented by a diagram

called a binomial tree.

An underlying assumption

is that the underlying price

follows a binomial process .

The value calculation proceeds backwards from T to t. Each step involves:

finding the terminal value of the option;

calculating its expected value of the option; and finally

discounting it by the risk-free rate (make sure that you use the right rate).

Risk-neutral valuation on

objective probabilities.

0

10

30

What is the value of the option?

Binomial modelOptions

11.897

4.878*0.5+19.512*0.5=12.195

0*0.5+10*0.5=5

10*0.5+30*0.5=20

19.512

4.878

100

110

90

100

10

120

0

80

30

t=0 t=0.5 t=1

0*0.5+10*0.5=5>4.878

>19.51

>11.897

10*0.5+30*0.5=20

4.878*0.5+19.512*0.5=12.195

0.4

0.6

0.4

0.6

0.4

0.6

Suppose that the probabilities of rise& fall were 40/60 instead of 50/50.

Without doing any further calculation, can you determine how the option price would change?


5exp(-0.05*0.5)=4.878

100

110

90

100

120

80

t=0 t=0.5 t=1

10*0.5+0*0.5=54.878

0

2.3795

0*0.5+0*0.5=0

4.878*0.5+0*0.5=2.439

Now, let’s redo the question above, but assuming an European call option instead.

Suppose that the probabilities of rise & fall were 60/40 instead of 50/50.

Without doing any further calculation, can you determine how the option price would change?

0

0

10

What if we don’t know the probabilities? 1. No-Arbitrage Argument Valuation

2. Risk Neutral Valuation with Risk Neutral Probabilities


S0

f

S0U

fU

S0D

fD

No arbitrage argument

Consider a stock whose price is S0 and option on the stock whose current price is f.

Option lasts for time T, and in that time the stock price moves to either S0U (where U > 1) or to S0D (where D < 1).

fU is option payoff if stock moved to S0U and fD option payoff is stock moved to S0D.

Consider a portfolio consisting of a long position in Δ shares and a short position in one option.

Calculate Δ that makes the portfolio riskless (i.e. portfolio has the same payoff regardless if the stock price increased or

decreased):

𝑆0𝑈∆ − 𝑓𝑈 = 𝑆0𝐷∆ − 𝑓𝐷 ∆ =𝑓𝑈 − 𝑓𝐷

𝑆0𝑈 − 𝑆0𝐷

S0UΔ -

fU

S0DΔ -

fD

S0Δ - f



For arbitrage opportunities not to exist the riskless portfolio must earn risk-free interest rate.

If r is the risk-free interest rate, then the present value of the portfolio is:

(𝑆0𝑈∆ − 𝑓𝑈)exp(−𝑟𝑇) = (𝑆0𝐷∆ − 𝑓𝐷)exp(−𝑟𝑇)

whereas the cost of creating this portfolio today is:

𝑆0∆ − 𝑓

Therefore:

𝑆0∆ − 𝑓 = (𝑆0𝑈∆ − 𝑓𝑈)exp(−𝑟𝑇)

𝑓 = 𝑆0∆(1 − 𝑈𝑒𝑥𝑝 −𝑟𝑇 ) + 𝑓𝑈exp(−𝑟𝑇)

Let’s substitute 𝑓𝑈−𝑓𝐷

𝑆0𝑈−𝑆0𝐷for Δ:

𝑓 = 𝑆0

𝑓𝑈 − 𝑓𝐷

𝑆0𝑈 − 𝑆0𝐷(1 − 𝑈𝑒𝑥𝑝 −𝑟𝑇 ) + 𝑓𝑈exp(−𝑟𝑇)

Options

Binomial model


=𝑓𝑈 1 − 𝐷𝑒𝑥𝑝(−𝑟𝑇) + 𝑓𝐷 𝑈𝑒𝑥𝑝(−𝑟𝑇) − 1

𝑈 − 𝐷

𝑓 = 𝑆0

𝑓𝑈 − 𝑓𝐷

𝑆0𝑈 − 𝑆0𝐷(1 − 𝑈𝑒𝑥𝑝 −𝑟𝑇 ) + 𝑓𝑈exp(−𝑟𝑇)

= exp(−𝑟𝑇) 𝑝𝑓𝑈 + (1 − 𝑝)𝑓𝐷

where: 𝑝 =exp(𝑟𝑇) − 𝐷

𝑈 − 𝐷

The model allows to price an option when stock price movements are given by a one-step binominal tree, under the

assumption there are no arbitrage opportunities in the market.

=𝑓𝑈 − 𝑓𝐷 − 𝑈𝑒𝑥𝑝 −𝑟𝑇 𝑓𝑈 + 𝑈𝑒𝑥𝑝 −𝑟𝑇 𝑓𝐷 + 𝑓𝑈 exp −𝑟𝑇 𝑈 − 𝑓𝑈 exp −𝑟𝑇 𝐷

𝑈 − 𝐷

= exp(−𝑟𝑇)𝑓𝑈 exp(𝑟𝑇) − 𝐷 + 𝑓𝐷 𝑈 − exp(𝑟𝑇)

𝑈 − 𝐷


20

f

22

fU =1

18

fD = 0


Example: Stock price today is equal to 20, and in 3 months it will be either 22 or 18.

What is a value of 3 month European call option with a strike price of 21.

The risk free rate is 12% (continuous compounding).

22∆ − 1 = 18∆ − 0

4∆ = 1

∆ = 0.25

18∆ − 0 = 18 × 0.25 = 4.54.5 exp −rT = 20∆ − 𝑓 4.5 exp −0.12 ×

3

12= 5 − 𝑓

4.367005 = 5 − 𝑓 𝑓 = 0.632995

Step 1: Calculate Δ

Step 2: Calculate portfolio

value at horizonStep 3: Calculate portfolio value today, and thus calculate f

Options

Binomial model


Utility:

The usual assumptions are that u’(.) > 0 and u”(.) < 0 .

Utility Function

In risk-neutral world, risk-neutral investors do not increase the expected return they require from an investment to

compensate for increased risk.

in economics it is the fundamental measure of value.

Utility function u(x): tells us the unit of “satisfaction” that x gives us.

in finance, x usually represents the amount of money or profit.

two assumptions are normally required regarding the function u(.) :

1) slope of the function;

2) curvature, i.e. how the function “bends”.

This implies positive but decreasing marginal utility.

When x is random, then u(x) becomes a random variable.

The assumption about the curvature becomes critical as it implies the view towards risks.

In this aspect, we may classify utility functions according to their risk preferences.


E(W)=C

E

X

U(X)


Risk Preferences

Risk neutral Individuals who are indifferent between the lottery and the sure sum of $50

𝑢 50 = 0.5 × 𝑢 0 + 0.5 × 𝑢(100)

A general condition for risk

neutrality is that u”(.) = 0 (linear).

Real-life examples of risk preferences:

Risk-averse: Individual investors, pension

funds;

Risk-loving: Hedge funds;

Risk-neutral: Institutional investors, large

companies – Management being risk-

loving while owners being risk-averse.

Binomial model

Risk-averse individuals prefer receiving the sure sum of $50 to being given a lottery whose expected return is $50.

Suppose that an individual holds a lottery that yields $0 or $100 with equal probabilities.

This lottery gives the expected return of $50 = 0.5*$0 + 0.5*$100

𝑢 50 > 0.5 × 𝑢 0 + 0.5 × 𝑢(100)

Risk-loving individuals prefer the lottery to the sure sum of $50.

𝑢 50 < 0.5 × 𝑢 0 + 0.5 × 𝑢(100)

Options


Risk neutrality proves very interesting since it implies that investors only care about expected returns, and not risks

associated with the investment.

Suppose there are only two assets in the economy: one risky (‘stock’) and the other riskless (‘bond’).

Risk-neutral investors will hold the stock alone – no matter how risky it is – provided that such a stock gives a higher

expected return than the bond.

If we’re willing to assume that everybody in the world is risk-neutral, then it must be the case that the returns on both

assets must be equal.

A risk-neutral world has two features that facilitate pricing derivatives:

(1) Expected return on stock (or any other instrument) is risk-free

(2) The discount rate used for the expected payoff on an option (or any other instrument) is risk-free rate.

Let 𝑝 =𝑒𝑟𝜏−𝐷

𝑈−𝐷be interpreted as the probability of an up movement in a risk-neutral world..

Thus the expected future payoff from an option in risk neutral world is:

𝑝𝑓𝑈 + (1 − 𝑝)𝑓𝐷



Stock price today is equal to 20, and in 3 months it will be either 22 or 18.

What is a value of 3 month European call option with a strike price of 21.

Example

The risk free rate is 12% (continuous compounding).

p could be calculated as:

Thus non-arbitrage arguments and

risk-neutral valuation give the

same results.

22𝑝 + 18 1 − 𝑝 = 20𝑒0.12×312

4𝑝 = 20𝑒0.12×312 − 18 𝑝 = 0.6523

or as:

𝑝 =𝑒𝑟𝜏 − 𝐷

𝑈 − 𝐷=

𝑒0.12×312 − 0.9

1.1 − 0.9= 0.6523

thus:𝑓 = 0.6523 × 1 + (1 − 0.6523) × 0 𝑒−0.12×

312

= 0.6523𝑒−0.12×312

= 0.633

20

f

22

fU

18

fD = 0

= 1


50

C

60

A

40

B

48

4

72

0

32

20

t=0 t=1 t=2𝑝 =

𝑒0.05∗1 − 0.8

1.2 − 0.8= 0.6282

A:

0.6282*0+0.3718*4=1.4872

1.4872*exp(-0.05)=1.41668

B:

0.6282*4+0.3718*20=9.9488

9.9488*exp(-0.05)=9.463591

C: 0.6282*1.41668+0.3718*9.463591 = 4.40725

4.40725*exp(-0.05) = 4.192306

Two-Step Binominal Trees

In order to calculate the option price at the initial node of the tree, one needs to start

with calculating option price at the final nodes and then working out option price at

the earlier nodes.

Example:Consider 2-year European put option with a strike price of 52, whose stock is currently trading at 50.

There are two 1-year steps. In each step stock price can increase by 20% or decrease by 20%. The risk-free interest rate is 5%.

C

A

B

0

4

20

Is p constant in the whole tree?


Binomial Model → Black-Scholes Formula

n → ∞

n steps


put

stock

call

bond

STK

STK

0

ST

K-ST

ST

ST-K

K0

K

= =

Put-Call Parity

The put-call parity defines a relationship between the price of a call and a put – both with identical K and t.

It allows us to calculate c from p, and vice versa. The underlying assumption is that there is no arbitrage opportunities.

The parity is given by: 𝑝𝑡 + 𝑆𝑡 = 𝑐𝑡 + 𝐾𝑒−𝑟𝜏

We can prove this by considering two portfolios which always give the same payoffs at maturity:

(1) A put & a stock

(2) A call & a zero-coupon bond (or cash)

It can be shown that both portfolios give the same payoffs regardless of the terminal stock price.

ST > K ST < K

Therefore, their current values must be identical.


Calls and Puts

Pay-off diagrams

How to price an option: Binomial model

No-Arbitrage Argument


Put-Call Parity

Options

EXERCISES

Question 1

The ordinary shares of NTC currently trade at 80p. The dividend per share

is 15p and has been constant at this level for 10 years.

NTC plans to finance a new investment opportunity out of retained

earnings. This will mean that for the next two years the dividend per share

will fall to 10p.

The benefits of the investment will mean that from year 3 onwards

dividend per share will increase to 18p per share for year 3 and

subsequent years.

Assuming all this information is known to shareholders; use the dividend

growth model to calculate a fair share price.

Question 2

It is 31 January 2009 and the managers of Watsons are considering a

change in the company’s dividend policy. Earnings per share for 2008 for

the company were 22.8 pence, and the finance director has said that he

expects this to increase to 25.0 pence per share in 2009. The increase in

earnings per share is in line with market expectations of the company’s

performance. The pattern of recent dividends, which are paid each year on

31 December, is as follows:

The Managing Director has proposed that 70% of earnings in 2009 and

subsequent years should be retained for investment in new product

development. It is expected that, if this proposal is accepted, the dividend

growth rate will be 8.75%. Watson’s cost of equity capital is estimated to

be 12%.

Calculate the share price of Watson’s in the following circumstances.

(a) The company decides not to change its current dividend policy.

(b) The company decides to change its dividend policy as proposed by the

Managing Director and announces the change to the market.

Question 3 & 4

3

4

Question 5 & 6

5

6

7

8

Question 7 & 8

Pfizer, one of the largest pharmaceutical companies in the United States, is considering what its debt capacity is. In March 1995, Pfizer had an outstanding market value of equity of $ 24.27 billion, debt of $ 2.8 billion and a AAA rating. Its beta was 1.47, and it faced a marginal corporate tax rate of 40%. The treasury bond rate at the time of the analysis was 6.50%, and AAA bonds trade at a spread of 0.30% over the treasury rate.

a. Estimate the current cost of capital for Pfizer.

b. It is estimated that Pfizer will have a BBB rating if it moves to a 30% debt ratio, and that BBB bonds have a spread of 2% over the treasury rate. Estimate the cost of capital if Pfizer moves to its optimal.

c. Assuming a constant growth rate of 6% in the firm value, how much will firm value change if Pfizer moves its optimal? What will the effect be on the stock price?

d. Pfizer has considerable research and development expenses. Will this fact affect whether Pfizer takes on the additional debt?

Question 9

GenCorp, an automorive parts manufacturer, currently has $25 million in outstanding debt and has 10 million shares outstanding. The book value per share is $10, while the market value is $ 25. The company is currently rated A, its bonds have a yield to maturity of 10%, and the current beta of the stock is 1.06. The six-month T.Bill rate is 8% now, and the company's tax is 40%.

a. What is the company's current weighted average cost of capital?

b. The company is considering a repurchase of 4 million shares at $25 per share with new debt. It is estimated that this will push the company's rating down to a B (with a yield to maturity of 13%). What will the company's weighted average cost of capital be after the stock repurchase?

Question 10

Current price of the stock is 100. The stock price can either go up by 10 or down by 10 each month. What is the value of European call option with a strike price 95 and 2 month to expiry? Assume the continuous compounding risk free rate is 5%

Question 11

(1) Leasing

(2) Mergers

(3) Corporate control and

corporate governance

Lecture 4:

Leasing

What is a Lease?

Why Lease?

Equivalent annual cost

Leasing

Operating leases

Short-term or cancellable during the contract period (by the lessee), usually full-service lease

Common examples are cars and photocopiers

Usually full-service lease where lessor is responsible for maintenance and servicing

Finance leases

Extend over most of the estimated economic life of the asset, cant be cancelled or if can lessor is reimbursed for any losses. The lessee ‘owns’ the item in all but name.

Usually net lease where lessee is responsible for maintenance and servicing

Leasing

Lease terms

Sensible Reasons for Leasing

Short-term leases are convenient

Cancellation options are valuable

Maintenance is provided

Standardization leads to low costs

Leasing

Why lease?

Dubious Reasons for Leasing

Leasing avoids capital expenditure controls

Leasing preserves capital

Leases may be off balance sheet financing

Leasing effects book income

Leasing

Why lease?

The annual rental payment sufficient to coverthe present value of all the costs of owningand operating it.

Leasing


Example: Operating Lease

Acme Limo has a client who will sign a lease for 7 years, with lease payments due at the start of each year. The following table shows the NPV of the limo if Acme purchases the new limo for $75,000 and leases it our for 7 years.

Year

0 1 2 3 4 5 6

Initial cost -75

Maintenance, insurance, selling, -12 -12 -12 -12 -12 -12 -12

and administrative costs

Tax shield on costs 4.2 4.2 4.2 4.2 4.2 4.2 4.2

Depreciation tax shield 0 5.25 8.4 5.04 3.02 3.02 1.51

Total -82.8 -2.55 0.6 -2.76 -4.78 -4.78 -6.29

NPV @ 7% = - $98.15

Break even rent(level) 26.18 26.18 26.18 26.18 26.18 26.18 26.18

Tax -9.16 -9.16 -9.16 -9.16 -9.16 -9.16 -9.16

Break even rent after-tax 17.02 17.02 17.02 17.02 17.02 17.02 17.02

NPV @ 7% = - $98.15

Leasing


Example: Financial Lease

Greymare Bus Lines is considering a lease. Your operating manager wants to buy a new bus for $100,000. The bus has an 8 year life. The Bus Saleswoman says she will lease Greymare the bus for 8 years at $16,900 per year, but Greymare assumes all operating and maintenance costs.

Should Greymare Buy or Lease the bus?

Year

0 1 2 3 4 5 6 7

Cost of new bus 100.00

Lost Depr tax shield (7.00) (11.20) (6.72) (4.03) (4.03) (2.02) -

Lease payment (16.90) (16.90) (16.90) (16.90) (16.90) (16.90) (16.90) (16.90)

Tax shield of lease 5.92 5.92 5.92 5.92 5.92 5.92 5.92 5.92

Cash flow of lease 89.02 (17.98) (22.18) (17.70) (15.01) (15.01) (13.00) (10.98)

Cash flow consequences of the lease contract to Greymare

Leasing


Cash flow consequences of the lease contract to Greymare :

Greymare saves the $100,000 cost of the bus

Loss of depreciation benefit of owning the bus

$16,900 lease payment is due at the start of each year

Lease payments are tax deductible

Leasing

Example: Financial Lease

Greymare Bus Lines is considering a lease. Your operating manager wants to buy a new bus for $100,000. The bus has an 8 year life. The Bus Saleswoman says she will lease Greymare the bus for 8 years at $16,900 per year, but Greymare assumes all operating and maintenance costs.

Should Greymare Buy or Lease the bus?


Example - cont

Greymare Bus Lines Balance Sheet with out lease

Equivalent lease balance sheet

Greymare Bus Lines (figures in $1,000s)

Bus 100 100 Loan secured by bus

All other assets 1000 450 Other loans

550 Equity

Toital Assets 1100 1100 Total liabilities

Greymare Bus Lines (figures in $1,000s)

Bus 100 100 Financial lease

All other assets 1000 450 Other loans

550 Equity

Toital Assets 1100 1100 Total liabilities

Leasing


Example - cont

Greymare Bus Lines can borrow at 10%, thus the value of the lease should be discounted at 6.5% or .10 x (1-.35). The result will tell us if Greymare should lease or buy the bus.

$700-or 70.

1.065

10.98-

1.065

13.00-

1.065

15.02-

1.065

15.02-

1.065

17.71-

1.065

22.19-

1.065

17.99-89.02lease NPV

765

432

Leasing


Example - cont

Greymare Bus Lines lease cash flows can also be thought of as loan equivalent cash flows.

Year

0 1 2 3 4 5 6 7

Amount borrowed

at year end 89.72 77.56 60.42 46.64 34.66 21.89 10.31 0.00

Interest paid @ 10% -8.97 -7.76 -6.04 -4.66 -3.47 -2.19 -1.03

Tax shield @ 35% 3.14 2.71 2.11 1.63 1.21 0.77 0.36

Interest paid after tax -5.83 -5.04 -3.93 -3.03 -2.25 -1.42 -0.67

Principal repaid -12.15 -17.14 -13.78 -11.99 -12.76 -11.58 -10.31

Net cash flow of

equivalent loan 89.72 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98

Leasing


Example - cont

The Greymare Bus Lines lease cash flows can also be treated as a favorable financing alternative and valued using APV.

$3,0008,000-5,000APV

lease of NPV project of NPVAPV

Leasing


What is a Lease?

Why Lease?


Leasing

Mergers

Sensible Motives for Mergers

Some Dubious Reasons for Mergers

Estimating Merger Gains and Costs

The Mechanics of a Merger

Takeover Battles and Tactics

Mergers

Mergers

Mergers: type

HORIZONTAL

VERTICAL

CONGLOMERATE

Economies of Scale

A larger firm may be able to reduce its per unit cost by using excess capacity or spreading fixed costs across more units.

$ $$Reduces costs

Mergers

Sensible Reasons for Mergers

Economies of Vertical Integration

Control over suppliers “may” reduce costs.

Over integration can cause the opposite effect. Pre-integration (less

efficient)

Company

S

S

S

S

S

S

S

Post-integration (more efficient)

Company

S

Mergers


Combining Complementary Resources

Merging may results in each firm filling in the “missing pieces” of their firm with pieces from the other firm.

Firm A

Firm B

Mergers


Mergers as a Use for Surplus Funds

If your firm is in a mature industry with few, if any, positive NPV projects available, acquisition may be the best use of your funds.

Mergers


Diversification

Investors should not pay a premium for diversification since they can do it themselves.

Mergers

Dubious Reasons for Mergers

The Bootstrap Game

Acquiring Firm has high P/E ratio

Selling firm has low P/E ratio

After merger, acquiring firm has short term EPS rise

Long term, acquirer will have slower than normal EPS growth due to share dilution.

Mergers


The Bootstrap Game

World Enterprises

(before merger) Muck and Slurry

World Enterprises

(after buying Muck

and Slurry)

EPS 2.00$ 2.00$ 2.67$

Price per share 40.00$ 20.00$ 40.00$

P/E Ratio 20 10 15

Number of shares 100,000 100,000 150,000

Total earnings 200,000$ 200,000$ 400,000$

Total market value 4,000,000$ 2,000,000$ 6,000,000$

Current earnings

per dollar invested

in stock 0.05$ 0.10$ 0.067$

Mergers


Earnings per dollar invested

(log scale)

NowTime

.10

.067

.05

Muck & Slurry

World Enterprises (before merger)

World Enterprises (after merger)

Mergers


Questions

Is there an overall economic gain to the merger?

Do the terms of the merger make the company and its shareholders better off?

PV(AB) > PV(A) + PV(B)

Mergers

Estimating Merger Gain

Economic Gain

Economic Gain = PV(increased earnings)

= New cash flows from synergies

discount rate

Mergers

Estimating Merger Gain

Mergers

Accounting for Merger

Tools Used To Acquire Companies

Proxy Contest

Acquisition

Leveraged Buy-Out Management Buy-Out

Merger

Tender Offer

Mergers

Take-over Methods

White Knight

Friendly potential acquirer sought by a target company threatened by an unwelcome suitor.

Shark Repellent

Amendments to a company charter made to forestall takeover attempts.

Poison Pill

Measure taken by a target firm to avoid acquisition; for example, the right for existing shareholders to buy additional shares at an attractive price if a bidder acquires a large holding.

Mergers

Take-over Defence

Goal of the firm

When managers do not fear stockholders, they will often put their interests over stockholder interests Greenmail: The (managers of ) target of a hostile takeover buy out the

potential acquirer's existing stake, at a price much greater than the price paid by the raider, in return for the signing of a 'standstill' agreement.

Golden Parachutes: Provisions in employment contracts, that allows for the payment of a lump-sum or cash flows over a period, if managers covered by these contracts lose their jobs in a takeover.

Poison Pills: A security, the rights or cashflows on which are triggered by an outside event, generally a hostile takeover, is called a poison pill.

Shark Repellents: Anti-takeover amendments are also aimed at dissuading hostile takeovers, but differ on one very important count. They require the assent of stockholders to be instituted.

Overpaying on takeovers: Acquisitions often are driven by management interests rather than stockholder interests.

Take-over Defence

Mergers

Take-over Defence

Sensible Motives for Mergers

Some Dubious Reasons for Mergers

Estimating Merger Gains and Costs

The Mechanics of a Merger

Takeover Battles and Tactics

Mergers

Control, Governance and Financial Architecture

Leveraged Buyouts, Spin-offs and Restructurings

Fusion and Fission in Corporate Finance

Conglomerates

Control and Governance


Corporate control

The power to make investment and financing decisions.

Corporate governance

Refers to the role of the board of directors, shareholder voting, proxy fights, etc. and to otheractions taken by shareholders to influence corporate decisions.


Definitions

The difference between leveraged buyouts and ordinary acquisitions:

A large fraction of the purchase price is debt financed.

The LBO goes private, and its share is no longer trade on the open market.


Leverage Buyouts

The three main characteristics of LBOs

High debt

Incentives

Private ownership


Leverage Buyouts

Acquirer Target Year Price ($mil)

KKR RJR Nabisco 1989 24,720$

KKR Beatrice 1986 6,250$

KKR Safeway 1986 4,240$

Thompson Co. Southland 1987 4,000$

AV Holdings Borg-Warner 1987 3,760$

Wing Holdings NWA, Inc. 1989 3,690$

KKR Owens-Illinois 1987 3,690$

TF Investments Hospital Corp of America 1989 3,690$

FH Acquisitions For Howard Corp. 1988 3,590$

Macy Acquisition Corp. RH Macy & Co 1986 3,500$

Bain Capital Sealy Corp. 1997 811$

Cyprus Group (w/mgmt) WESCO Distribution Inc. 1998 1,100$

Clayton, Dublier & Rice North Maerican Van Lines 1998 200$

Kohlberg & Co. (w.mgmt) Holley Performance Products 1998 100$

Doughty Hanson Trend Technologies 2000 318$

Berkshire Partners William Carter Co. 2001 450$

Heartland Industrial Partners Springs Industries 2001 846$

10 Largest LBOs in 1980s and 2000s examples


Leverage Buyouts

Spin offIndependent company created by detaching part of a parent company's assets and operations.

Carve-outsSimilar to spin offs, except that shares in the new company are not given to existing shareholders but sold in a public offering.

PrivatizationThe sale of a government-owned company to private investors.


Spin offs…

Motives for Privatization

Increased efficiency

Share ownership

Revenue for the government


Spin offs…

Amount Issued,

Country Company and Date $ millions

France St. Gobain (1986) 2,091.40$

France Paribas (1987) 2,742.00$

Germany Volkswagon (1961) 315.00$

Jamaica Caribbean Cement (1987) 45.60$

Jpan Japan Airlines (1987) 2,600.00$

Mexico Telefonos de Mexico (1990) 3,760.00$

New Zealand Air New Zealand (1989) 99.10$

Singapore Neptune Orient Lines (1981-1988) 308.50$

United Kingdom British Gas (1986) 8,012.00$

United Kingdom BAA (Airports)(1987) 2,028.00$

United Kingdom British Steel (1988) 4,524.00$

United States Conrail (1987) 1,650.00$

Examples of Privatization


Spin offs…

Sales Rank Company Numebr of Industries

8 ITT 38

15 Tenneco 28

42 Gulf & Western Industries 41

51 Litton Industries 19

66 LTV 18

73 Illinois Central Industries 26

103 Textron 16

104 Greyhound 19

128 Marin Marietta 14

131 Dart Industries 18

132 U.S. Industries 24

143 Northwest Industries 18

173 Walter Kidde 22

180 Ogden Industries 13

188 Colt Industries 9

The largest US conglomerates in 1979


Conglomerates

Financial architecture

US &UK:

capital market oriented financing

disperse ownership structure

Europe:

bank oriented financing

more concentrated ownership

Japan:

crossholdings: Keiretsu


Corporate Control and Governance

Ownership of Daimler Benz

Deutsch Bank

Kuwait Government

Mercedes Automobil Holding AG

Widely Held

Widely Held

Stern Auto Beteilig…

Stella Automobil Beteiligungsges

Widely Held

Bayerishe Landesbank

Robert Bosch Komet Automobil Beteiligungsges

Dresdner Bank

25% 25% 25% 25%

25% 25% 50%

28.3% 14% 25.23% 32.37%

Daimler Benz AG


Japanese Bank Ownership

Sumitomo Corporation

Sumitomo TrustSumitomo Bank

3.4%

5.9%

4.8%

1.8%

3.4%

2.4%

keiretsu


Leveraged Buyouts, Spin-offs and Restructurings

Fusion and Fission in Corporate Finance

Conglomerates

Control and Governance


Revision

7 Most Important Ideas in Finance

Net Present Value

Capital Asset Pricing Model (CAPM)

Efficient Capital Markets

Project Appraisal Techniques

Capital Structure Theory

Option Theory

Agency Theory

Revision

WACC & Debt Ratios

Example continued: Sangria and the Perpetual Crusher project at 20% D/V

Step 1 : unlevering the WACC: calculate r (opportunity cost of capital)at current debt of 40%

Step 2 – D/V changes to 20%

Step 3 – New WACC

12.)6(.146.)4(.08. r

13.)25)(.08.12(.12. Er

114.)8(.13.)2)(.35.1(08. WACC

Revision

8. GenCorp, an automorive parts manufacturer, currently has $25 million in outstanding debt and has 10 million shares

outstanding. The book value per share is $10, while the market value is $ 25. The company is currently rated A, its

bonds have a yield to maturity of 10%, and the current beta of the stock is 1.06. The six-month T.Bill rate is 8% now, and

the company's tax is 40%.

a. What is the company's current weighted average cost of capital?

b. The company is considering a repurchase of 4 million shares at $25 per share with new debt. It is estimated that this

will push the company's rating down to a B (with a yield to maturity of 13%). What will the company's weighted average

cost of capital be after the stock repurchase?

(a) Current Cost of Equity = 8% + 1.06 (5.5%) = 13.83%

Current Cost of Debt = 10% (1-0.4) = 6.00%

Current Cost of Capital = 13.83% (250/275) + 6.00% (25/275) = 13.12%

(b) If the firm borrows $ 100 million and buys back $ 100 million of stock

New Debt/Equity Ratio = 125/150 = 0.833333333

Unlevered Beta = 1.06/(1+0.6*.10) = 1.00

New Beta = 1 (1 + 0.6*0.8333) = 1.50

Cost of Equity = 8% + 1.50 (5.5%) = 16.25%

Cost of Capital = 16.25% (150/275) + 13% (1-.4) (125/275) = 12.41%

Revision

9. Pfizer, one of the largest pharmaceutical companies in the United States, is considering what its debt capacity is. In March

1995, Pfizer had an outstanding market value of equity of $ 24.27 billion, debt of $ 2.8 billion and a AAA rating. Its beta was

1.47, and it faced a marginal corporate tax rate of 40%. The treasury bond rate at the time of the analysis was 6.50%, and

AAA bonds trade at a spread of 0.30% over the treasury rate. Market premium equals 5.5%.

a. Estimate the current cost of capital for Pfizer.

b. It is estimated that Pfizer will have a BBB rating if it moves to a 30% debt ratio, and that BBB bonds have a spread of 2%

over the treasury rate. Estimate the cost of capital if Pfizer moves to its optimal.

c. Assuming a constant growth rate of 6% in the firm value, how much will firm value change if Pfizer moves its optimal?

What will the effect be on the stock price?

d. Pfizer has considerable research and development expenses. Will this fact affect whether Pfizer takes on the additional

debt?

a. Cost of Equity = 6.50% + 1.47 (5.5%) = 14.59%

Cost of Capital = 14.59% (24.27/(24.27+ 2.8)) + 6.8% (1-0.4) (2.8/(24.27+2.8)) =

13.50%

b. If Pfizer moves to a 30% debt ratio,

New debt/equity ratio = 30/70 = 42.86%

Unlevered Beta = 1.47/(1+0.6*(2.8/24.27)) = 1.37

Unlevered Beta= beta1/(1+(1-Tc)(D1/E1))

New Beta = 1.37 (1+0.6*0.4286) = 1.72

New Beta = unleveler beta * (1+ (1-Tc)(D2/E2)

New Cost of Equity = 6.5% + 1.72 (5.5%) = 15.96%

New Cost of Capital = 15.96% (0.7) + 8.5% (1-.4) (0.3) = 12.70%

c. If the savings grow at 6% a year in perpetuity, the change in firm value can be computed as follows –

Savings each year = (.1350-.1270) (24.27 + 2.8) = 0.21656 ! $ 216.56 million

PV of Savings with 6% growth = (216.56*1.06)/(.127-.06) = $3,426 ! $ 3.4 billion

Increase in Stock Price = 3426/24270 = 14.12% ! Stock Price will increas by 14.12%

d. The need for R& D increases the need for flexibility; therefore, Pfizer may not go to this higher optimal

debt ratio, the cost of capital notwithstanding.

Revision

EXERCISES

Question 1

1

Question 2

2

Question 3

3

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