Finance Summaries 100

7/26/2019 Finance Summaries 100

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Module 1: The Basic Ideas, Scope and Tools of Finance........................................... 5

Financial Markets and Participants ....................................................................................... 5

Market Interest Rates and Prices ........................................................................................ 6

A Simple Financial Market ....................................................................................................... 6

Shifting Resources in Time ................................................................................................... 6

Investing ........................................................................................................................................... 7

Net Present Value ....................................................................................................................... 7

Internal Rate of Return ............................................................................................................ 8

A Simple Corporate Example .............................................................................................. 8

More Realistic Financial Markets ......................................................................................... 9

Multiple-Period Finance ......................................................................................................... 9

Compound Interest ..................................................................................................................... 9

Multiple-Period Cash Flows ................................................................................................. 9

Multiple-Period Investment Decisions ..........................................................................10

Calculating Techniques and Short Cuts in Multiple-Period Analysis........10Interest Rates, Interest Rate Futures and Yields ..........................................................11

The Yield to Maturity ..............................................................................................................12

Forward Interest Rates ............................................................................................................13

Interest Rate Futures .................................................................................................................14

Interest Rate Risk and Duration.........................................................................................15

Module 2: Fundamentals of CompanyInvestment Decisions ..................................16

Investment Decisions and Shareholder Wealth ............................................................16

Corporate Equity ........................................................................................................................16

The Market Value of Common Shares ..........................................................................16

Investment and Shareholder Wealth ...............................................................................17

Investment Decisions in All-Equity Corporations ......................................................17

Investment Decisions in Borrowing Corporations .....................................................18

Share Values and Price/Earnings Ratios ..........................................................................18

Module 3: Earnings, Profit and Cash Flow.........................................................................20

Corporate Cash Flows .................................................................................................................20

Cash Flows and Profits ...............................................................................................................21

Module 4: Company Investment Decisions Using the Weighted Average

Cost of Capital .....................................................................................................................................22

Free Cash Flow and Profits for Borrowing Corporations ......................................22Investment Value for Borrowing Corporations ............................................................22

Overall Corporate Cash Flows and Investment Value .........................................22

Investment NPV and the Weighted Average Cost of Capital ..............................23

The Adjusted Present Value Technique............................................................................25

The Choice of NPV Techniques ............................................................................................25

Module 5: Estimating Cash Flows forInvestment Projects .......................................28


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Module 6: Applications of Company Investment Analysis ......................................30

The Payback Period ..................................................................................................................30

The Average (Accounting) Return on Investment .................................................31

Internal Rate of Return vs. Net Present Value ..........................................................31

The CostBenefit Ratio and the Profitability Index ..............................................33

Capital Rationing............................................................................................................................34

Investment Interrelatedness ......................................................................................................35

Renewable Investments ..............................................................................................................35

Inflation and Company Investment Decisions ..............................................................36

Leasing .................................................................................................................................................37

The Economics of Leasing ...................................................................................................37

Evaluating Leases ......................................................................................................................38

Managing the Investment Process ........................................................................................38

Using Economic Income in Performance Measurement (EVA, EP, etc.)38

Module 7: Risk and Company Investment Decisions ..................................................39Risk and Individuals .....................................................................................................................39

Risk, Return and Diversification .......................................................................................41

The Market Model and Individual Asset Risk..............................................................44

The Market Model or Security Market Line ..............................................................47

Using the Capital Asset Pricing Model in Evaluating Company Investment

Decisions .............................................................................................................................................48

Estimating Systematic Risk of Company Investments ........................................50

Estimating the WACC of an Investment ......................................................................51

Other Considerations in Risk and Company Investments ......................................51

Certainty Equivalents ...............................................................................................................51

Risk Resolution across Time ...............................................................................................52

Conclusion..........................................................................................................................................52

Module 8: Company Dividend Policy ...................................................................................53

Dividend Irrelevancy ...................................................................................................................53

Dividends and Market Frictions ............................................................................................54

Taxation of Dividends .............................................................................................................54

Transaction Costs of Dividend Payments ....................................................................56

Flotation Costs .............................................................................................................................57

Combined Frictions ...................................................................................................................57Dividend Clienteles: Irrelevancy II .....................................................................................57

Other Considerations in Dividend Policy ........................................................................57

Dividends and Signalling ......................................................................................................57

Dividends and Share Repurchase .....................................................................................58

Conclusion..........................................................................................................................................58

Module 9: Company Capital Structure ..................................................................................60


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Capital Structure, Risk and Capital Costs .......................................................................60

Capital Structure Irrelevance I: M&M ..............................................................................62

Arbitrage and Prices a Digression ................................................................................62

Summation of Capital Structure Irrelevancy I: Connections with Capital

Costs and Values ........................................................................................................................62

Capital Structure Decisions and Taxes ..............................................................................64

Capital Structure Relevance with Taxes .......................................................................64

Summation of Capital Structure Relevance with Taxes:

Connections with Capital Costs and Values .................................................64Capital Structure Irrelevancy II: Taxes .........................................................................67

Summary of Company Borrowing under Taxation ................................................68

Capital Structure and Agency Problems ...........................................................................69

Default and Agency Costs ....................................................................................................69

Conclusion to Agency Considerations in Borrowing ...........................................70

Making the Company Borrowing Decision ....................................................................71

Book Values and Borrowing ...............................................................................................71

Techniques of Deciding upon Company Capital Structure ...............................71

Suggestions for Deciding about Capital Structure .................................................72

Module 10: Working Capital Management ........................................................................73

Risk, Return and Term ................................................................................................................73

Risk and Rates of Return on Assets by Term ............................................................73

Risk and Rates of Return on Financings by Term ..................................................73

Combining Risk and Rates of Return on Assets and Financings...................74

Management of Short-Term Assets and Financings .................................................74Optimisation and Short-Term Investment ...................................................................75

Management of Cash Balances ..........................................................................................76

Management of Receivables ................................................................................................79

Management of Short-Term Financings .......................................................................80

Cash Budgeting and Short-Term Financial Management ......................................81

Conclusion..........................................................................................................................................81

Appendix Financial and Ratio Analysis .......................................................................81

Liquidity Ratios ...............................................................................................................................81

Profitability Ratios ........................................................................................................................82

Capital Structure Ratios .............................................................................................................82

Efficiency Ratios ............................................................................................................................82

Financial Analysis and Internal Accounting: an Integrated Approach...........83

The Foreign Exchange Markets .............................................................................................84

Exchange Rates and the Law of One Price .................................................................84

Spot and Forward Exchange Rates ..................................................................................84


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Exchange Rates and Interest Rates ..................................................................................84

Forward Exchange, Interest Rates and Inflation Expectations........................85

International Financial Management ..................................................................................86

Hedging International Cash Flows ..................................................................................86

Investing in Foreign Real Assets ......................................................................................87

Financial Sources for Foreign Investment ...................................................................87

Financial Solutions to Other International Investment Risks..........................88

Conclusion..........................................................................................................................................88

Module 12: Options, Agency, Derivatives and Financial Engineering ..............90

Options .................................................................................................................................................90

Option Characteristics .............................................................................................................90

An Introduction to Options Valuation ...........................................................................91

Calculating the Value of a Simple Option ...................................................................92

Valuing More Realistic Options ........................................................................................94

Relationships Among Options ............................................................................................95Applications of Option Valuation ....................................................................................96

Real Options and `Strategic Finance ............................................................................96

An Example of a Real Option Decision........................................................................97

Other Real Options ....................................................................................................................97

Agency ..................................................................................................................................................97

Derivatives .........................................................................................................................................98

Participation in Derivative Markets ................................................................................98

The Types of Derivatives ......................................................................................................98

Swaps ................................................................................................................................................99

Exotics ..............................................................................................................................................99

Financial Engineering ..................................................................................................................99

The Elements of Financial Engineering......................................................................100


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Module 1: The Basic Ideas, Scope and Tools of Finance

Finance is the economics of allocating resources across time.

Ways in which resources are reallocated in time:

- borrowing and lending of money by individuals, but bygovernments, corporations and other institutions.- issuing equity capital by companies, that is, it is accepting money

now and giving in exchange a promise to return money in the future

(in the form of corporate dividends).

Financial Markets and Participants

Participants in financial markets:- Individualsborrow from and lend to financial institutions such as

banks.- Corporations similarly transact with banks, but they also usefinancial markets through other intermediaries such as investment

bankers (companies that help raise money directly from other

companies and individuals), and insurance companies (which lend

your insurance premiums to other companies).

- Governments also borrow and lend to individuals, companies andfinancial institutions.

Financial markets:

- Participation in financial markets is driven in part by the desire to shift

future resources to the present so as to increase personal consumption,and thus satisfaction.- Or one may shift resources to the future by lending them, buying

common stock, etc. In exchange, they get an expectation of increased

future resources, in the form of interest, dividends, and/or capitalgains.

- Where financial investments serve the purpose of reallocating thesame resources over time, real asset investment (such as building anew factory or buying a piece of equipment to be used in production)

can actually create new future resources.

- The provision of funds for real asset investment is important, as is theallocative information that financial markets provide to those

interested in making real asset investment.

- Financial markets can help tell the investor whether a proposedinvestment is worthwhile by comparing the returns from theinvestment with those available on competing uses.

- Financial markets allow participants to shape the riskiness of theirposition by combining borrowings, lendings, the buying and selling ofshares, and other transactions (risk adjustment). Notice that financial


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market participants are risk-adverse, i.e. they would choose the less

risky of two otherwise identical investments.

Market Interest Rates and Prices

- The market interest rate is the rate of exchange between present andfuture resources. It tells participants how many pounds are expected to

be provided in the future for each pound of resources provided now.- It is determined by the supply and demand of resources to be borrowed

and lent.

- At any given time there are numerous market interest rates coveringdifferent lengths of time in the future, and different riskinesses of

transactions.

A Simple Financial Market

Shifting Resources in Time

- A financial exchange line is comprised of any transaction that aparticipant with an initial amount of money may take by borrowing orlending at the market rate of interest.

- The line appears on a graph CF1, the cash flow expected `later (t1) onthe vertical axis and CF0, the `now (t0) cash flow on the horizontal.


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- If a participant had 1000 at t0and will get 1540 at t1, but he wantedto consume more than 1000 now

- He can promise to give the lender 1540 at t1, but how much wouldthe lender give him at t0? Assume a 10% interest rate.

Thus in our example:

The participant could borrow 1400 with a promise to repay 1540 at

t1. The maximum amount the participant could consume at t0 is thus2400 (present wealth). 1400 is the present value of 1540.

- Present value is defined as the amount of money you must invest orlend at the present time so as to end up with a particular amount of

money in the future.- Finding the present value of a future cash flow is often called

discountingthe cash flow.

- Present value is also an accurate representation of what the financialmarket does when it sets a price on a financial asset. It is the market

value of a security when market interest rates or opportunity rates of

return (`costs of doing this instead of something else) are used asdiscount rates.

Investing

- Investing in real assets allows for an increase in wealth because it doesnot require finding someone to decrease their own.

- It creates new future cash flows that did not previously exist.- Real-asset investments are wealth-increasing only if the present value

of the amounts we give up is lower than the present value of what we

gain from the investment

Net Present Value

- It is the present value of all of its present and future cash flows (i.e. thepresent value of the difference between an investment's cash inflows

and outflows) discounted at the opportunity cost of those cash flows.These opportunity costs reflect the returns available on investing in an

alternative of equal timing and equal risk.

- It is equal to the change in the wealth of the participant accepting theinvestment and measures the change in market value of the investor'swealth.

- It is the discounted value of the amounts by which an investment'scash flows exceed those of its opportunity cost. When NPV is positive,


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the investment is expected to produce (in present value total) more

cash across the future than the same amount of money invested in thecomparable alternative.

01 CF)i1(

CFPVoutflowlowinfPVNPV

++++========

For example; an outlay of 550 at t0 returns 770 at t1, withinterest = 10%

NPV = 770/((1+0.1) 550= 700-550 = 150

Note: if the investor put 550 into the financial markets @10% they would have made 605 (1.1 * 550).

Internal Rate of Return

- It tells us how good or bad an investment is by calculating is theaverage per-period rate of return on the money invested in an

opportunity.

- It is best calculated by finding the discount rate that equates thepresent values of an investment's cash inflows and outflows, i.e. the

discount ratethat would cause the NPV of the investment to be zero.

- To use IRR, we compare it with the return available on an equal-riskinvestment of comparable cash-flow timing. When IRR exceeds theopportunity cost (as a rate) of an investment, the investment will have

a positive present value, and therefore be acceptable. When the IRR is

lower than its opportunity cost NPV is negative and therefore weshould reject the investment.

- IRR and NPV usually give us the same answer as to whether aninvestment is acceptable, but offer different answers as to which oftwo investments is better. NPV describes an investment by the amount

of the wealth increase that would be experienced by the participant

who accepts it, whereas IRR tells us how the average earning rate on

the investment compares with the opportunity rate.

0

1

01

CF

CF)IRR1(

CF)IRR1(

CF0NPV

====++++

++++

========

A Simple Corporate Example

- The sole task of a company is to maximise the present wealth of itsshareholders.


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- A company would accept investments up to the point where the nextinvestment would have a negative NPV or an IRR less than itsopportunity cost.

More Realistic Financial Markets

Multiple-Period Finance

- Multiple period exchange rates (interest) are written as (1 + In)n, where

n is the number of periods.

Compound Interest

- Compounding of interest (earning interest on interest) means that theexchange rate between two time points is such that you earn interestnot only on your original investment but also (in subsequent periods)

on interest you earned previously. The amount of money you end upwith by investing CF0at compound interest is:

where i is the interest rate, m is the number of times per period

that compounding takes place, and t is the number of periods the

investment covers.- The most frequent type of compounding is called `continuous.

Continuous compounding means that interest is calculated and added

to begin earning interest on itself without any passage of time between

compoundings. In the general compounding formula above, that means

m is infinitely large and, without belabouring the algebra, the formula

reduces to:

where e= 2.718 , the base of the natural logarithm system.

Multiple-Period Cash Flows

- The general method for finding the present value of a cash flowoccurring at any future time point is:

where tcan be any time.

- The present value of a set (we call this a `stream) of cash flows is thesum of the present values of each of the future cash flows associatedwith the asset.

3

3

3

2

2

2

1

1

111 )i(

CF

)i(

CF

)i(

CFPV

++

++

+=


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Multiple-Period Investment Decisions

- Calculating NPV when the investment decision will affect severalfuture cash flows must include all present and future cash flows

associated with the investment.

3

3

32

2

2

1

1

111 )i(CF

)i(CF

)i(CFPV

++

++

+=

- Finding the IRR of a set of cash flows that extends across severalfuture periods involves finding the discount rate that causes the present

value of all cash flows (NPV) to equal zero.

3

3

2

210

1110

)IRR(

CF

)IRR(

CF

)IRR(

CFCF

++

++

++=

- The only way to solve for the IRR of a multiple-period cash flowstream is with a technique called `trial and error . This means we

choose some arbitrary discount rate for IRR in the above equation, and

calculate NPV. We then examine the result to decide whether the ratewe used was too high or too low, choose another rate that appears to

be better than the one we just used, and again calculate NPV. We

continue this process until we find the IRR (or as close anapproximation to it as seems necessary) that creates an NPV equal to

zero.

Calculating Techniques and Short Cuts in Multiple-Period Analysis

- The present value of any future cash flow can be found by:

- The instruction to calculate a present-value that has different cashflows across the future and different discount rates for these cash flows

is:

- When discount rates are consistent across the future we use thesame per-period discount rate for all cash flows. Equation 1.2

becomes

- Another commonly used technique of finding present values relieson present value tables. Present value tables give the present

values per pound of future cash flow, either for a single cash flow(1.1) or a stream of constant cash flows discounted at constant


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discount rates (1.3). They are useful in calculating the present

value:1. of a single cash flow located far into the future when your

calculator cannot perform exponentiation (i.e. raising

numbers to powers).

2. of annuities. A constantannuity is a set of cash flows that arethe same amounts across future time points.- Aperpetuityis a cash flow stream that is assumed to continue for

ever. To find the present value of a perpetuity one merely dividesthe (constant) per-period cash flow by the (constant) per-period

discount rate. The formula for the present value of a perpetuity is:

- A slight modification of Equation 1.4 allows for the assumptionthat the cash flows will continue for ever, but will grow or declineat a constant percentage rate during each period. The perpetuity

formula becomes

where gis the constant per-period growth rate of the cash flow.- This equation does not work when the discount rate i is less than

or equal to the growth rate g.Perpetuities can often be used as reasonable approximations for

cash-flow streams from very long-lived assets

Interest Rates, Interest Rate Futures and Yields

- Interest rates: ratios or rates of exchange used when shifting

resources across time.- A Coupon is the amount a bondholder will receive in interest

payments. Its expressed as a % of the principal ie. the amount of

money you will get back once bond matures

- Spot interest rates: interest rates that begin at the present and run tosome future time point.

- The set of spot rates in a financial market is called the term structureof interest rates.

- A coupon bondhas aface value(usually called the principal) that isused, along with its coupon rate (usually called the interest), to

figure a pattern of cash flows promised by the bond.

- These cash flows comprise interest payments each period whichcontinue until the maturity period, when the face value itself, as aprincipal paymentplus the final interest payment, is promised.

- Spot rate is the interest rate now for a certain period vs. forward rate isthe interest at time x in the future for a period of y


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The Yield to Maturity

- Theyield to maturityof the bonds (YTM) is the IRR that discounts abond's promised cash flows to equal its market price and is the

`average per-period earning rate on the money invested in the bond

- Another way of putting this is that YTM is the discount (interest) ratethat represents a bonds future cash flow to its current price (value)- Bonds can have the same spot rates, cash-flow risk, and number of

interest payments, yet have different YTMs. This is caused by adifference in the cash-flowpatternsof each bond.

- This is dubbed the coupon effect on the YTM. Named as such becausethe size of the coupon of a bond determines the pattern of its cashflows, and thus how its YTM will reflect the set of spot rates that exist

in the market.

- It is unwise to make comparisons among securities on the basis of theirYTMs unless their patterns of cash flows (or coupons, for bonds) are

identical.- YTMs express both earning rates and the amounts invested acrosstime.

Example:

Say the face Value of three bonds are all 1000.

a) 4% coupon rate, maturing at t2 and its current value (t0) is 919.97b) 10% coupon rate, maturing at t2, YTM is 8.5595%c) 8% coupon rate, maturing at t3 with current value (t0) of 1014.59

Current one period spot rate is 10%.

Lets lay this bad boy out:

T0 T1 T2 T3 YTM

A 919.97 40 (4% of

1000)

1040

(maturingwith 1000 +

40)

?

B ? 100 1100 8.5595%

C 1014.59 80 80 1080 ?

1) Whats the current price of bond B?

We use the YTM, knowing that if we use YTM as discount rate, it will tell us thecurrent value (price) of bond:PV (B) = 100/1.085595 + 1100/(1.085595)2= 92.11 + 933 = 1025

2) Whats the current two period spot rate of interest?We know the PV of A and that can be used to get the two period spot rate (wealready know the one period spot rate is 10%):


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919.97 = 40/1.1 + 1040/(1+x)2

= 36.36 + 1040/(1+x)2

(1+ x)2= 1040/883.6 = 1.177

1+x= square root of 1.177

x2+ 2x = 0.177

x = roughly 8.5%

Forward Interest Rates

- Interest rates that begin at some time point other than the present (t o).- The amount invested in an asset across time can be found by accruing

past invested amounts outward at the same rates that were used to

discount cash flows back in time.

- This amount allows for a calculation of a forward interest rate.- (1+1f2) = CF1/Present Value (CF1)

- Forward interest rates are usually indicated as with a left subscriptindicating the rates start time point and a right one indicating theending time point. Suppose 1009 invested in bond B at t1produces a

payment of 1080 at t2. The implied earning or interest rate for bond B

between t1and t2(noted as 1f2) must therefore be:

- This formula calculates the impliedforward ratefor a bond.- The relationship between the rates is:

where: i2 = spot rate of second period

- If forward rates are known, the spot rate of interest can be found bymultiplying together 1 plus each of the intervening forward rates,

taking the nth root of that product (where n = number of periodscovered), and subtracting 1.

- If the spot rates are known, the forward rates can be found by aprocess of solving first for the forward rate nearest the present, andsuccessively working to rates further in the future.

Question:

Using example above:

1) What is the one period forward rate of interest for the second period (1f2)Taking bond C:

T0 T1 T2 T3 YTM

A 919.97 40 (4% of

1000)

1040

(maturing

with 1000 +40)

?

B ? 100 1100 8.5595%


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C 1014.59 80 80 1080 ?

The relationship between spot rates and forward interest rates is:

We know the one period spot rate for the second period is 8.5% (from answer above) ,and the one period spot rate = 1f2 = 10% then(1+0.085)2= (1 + 0.10)(1+1f2)

1.177/1.1 = 1 1f2

1f2 = 7%

2) What is the one period forward rate interest for the third period?This can be found if we know the three period spot rate going from t0 to t3. Ifthere were no interest payments in t1 and t2 then the answer would be:

(1+ i3)3= 1080/1014.59

But this ignores the fact that we have other cash flows at t1 and t2 which artificially

inflate the current value. So we need to take the Present Value of these cashflows at t1and t2 away from the current value of the bond.

1014.59 = 80/1.1 + 80/(1+0.085)2+ 1080/(1+i3)

3

i3 = 7.3% = third period spot rate

Now we have enough info to get 2f3:(1+0.073)3 = (1+0.1)(1+0.085)(1+2f3)

2f3 = 5%

3) After interest is paid at t1, what is the current expectation for the price of bond Bat t1 (its forward price at t1)?

We know the forward interest rate 1f2 = 7% so:

1+ 0.07 = 1100/PV(CF2)

PV(CF2) = 1028

4)

Interest Rate Futures

- The futures market in interest rates allow you to avoid (or hedge) therisk that interest rates might change unexpectedly (therefore,

potentially, reducing an NPV to a point where an investment is no

longer worthwhile).- Expectations around future interest rates and future values are almost

never completely accurate because, between the time the expectation is

formed (t0) and the realisation occurs (t1), additional information will


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have appeared that causes the market to revise its cash flow

expectations, its opportunity costs, or both.- Financial futuresmarkets allow participants to guard against this kind

of risk by buying and selling commitments to transact in financial

securities at future time points at prices fixed as the present.

- This allows to guarantee set of discount rates for an assets NPV byagreeing to sell securities at set prices across the life of the real asset.- Hedging works in both directions to remove the effects of interest rate

changes and therefore takes away both good and bad surprises.

Interest Rate Risk and Duration

- As interest rates move up and down with time while other factorsremain the same, values will move down and up.

- The variability of values due to changes in interest rates is the effect ofinterest rate risk.

- Interest rates change across time because of changes in a number ofinfluences on the opportunity costs of investing (such as the effect ofinflation on the purchasing power of eventual cash payments of

interest and principal, or changes in the creditworthiness of bond

issuers, or changes in the rates of return available on real asset

investments).- Such changes in interest rates imply changes in value and therefore in

wealth.

- Duration is a kind of index that tells us how much a particular bondvalue will go up and down as interest rates change. It measures the

`exposure of the value of a bond to changes in interest rates.

- It is the number of periods into the future where a bonds average valueis generated. The greater the duration of a bond, the farther into the

future its average value is generated, and the more its value will react

to changes in interest rates.- Duration can be calculated by weighting the time points from which

cash flows are generated:

Duration = (1) [CF/(1+i1)/Bond value] + (2)[CF/(1+i2)

2/Bond value] + (3) [..]

- Duration is the starting point for an important aspect of professionalbond investing called immunisation, which allows certain portfolios of

coupon bonds or other types of investments to be shielded againstunexpected changes in interest rates


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Module 2: Fundamentals of Company Investment Decisions-

Investment Decisions and Shareholder Wealth

- A corporate investment NPV translates directly into a wealth increase

of that amount for the shareholders of the company

Corporate Equity

- When a company issues shares to raise money from the capital marketit creates a security known as one of the following: ordinary shares,

common stock, equity, etc.

Important things to remember about this type of capital claims are;

1. It is a residual claim- Equity has no specific contract with the company that requires

any particular amounts of money to be paid to shareholders atany particular time.

- Shareholders have only the entitlement to vote for the directorsof the company and to expect that the directors andmanagement make decisions in the best interests of them

- Directors and management are agentsof the shareholders.2. Equity has limited liability

- The possible losses that a shareholder can incur are limited tothe value of the shares that the shareholder owns.

3. Shareholders have the right to claim ownership of the resources of thecompany only after all other claims have been satisfied (residual

claim). Once met however, they have an ownership claim on allof theremaining corporate resources.

- Corporations in making financial decisions attempt to maximise thewealth of their existing shareholders.

- Shareholder wealth consists essentially of the market value of thecommon shares or equity of the company.

- So the company, in maximising the wealth of its shareholders, mustattempt to maximise the market value of its common shares, i.e. bychoosing corporate investments with the highest NPVs.

The Market Value of Common Shares

- The market value of the common shares of a company is the presentvalue of the future dividends expected to be paid to the currently

existing shares of the company.- Dividends are the amounts of money that the company pays to its

shareholders


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- The return that shareholders expect to earn on their shares oftencomprises both dividends and price increases (or capital gains). Yetthe basis for the future value of a companys common shares in the

financial market are dividends alone.

Or,

Et = equity value at time t

Divt= expected dividendsre = equity discount rate

The value of your shares at t0is really:

- The market price depends upon all of the future dividends that thoseshares are expected to receive

Investment and Shareholder Wealth

- The use of a properly calculated NPV does result in an increase in the

present value of shareholders, and is consistent with the desire tomaximise shareholder wealth.

Investment Decisions in All-Equity Corporations

Suppose a company undertakes an investment that costs 100 000 now

and returns 50.000 net per year in perpetuity. The discount rate is 10per cent. So the investment has a corporate net present value of:

Changes in shareholder wealth due to investmentCash Value Net

If dividend is not paid:

Old shareholders -100 000 +500 000 +400 000

New shareholders 0 0 0

If dividend is paid:

Old shareholders 0 +400 000 +400 000New shareholders -100 000 +100 000 0


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- The total value of a company increases by the NPV of the investmentplus what it cost to undertake it. In the example above, the market

value of the company increases 500.000 (NPV 400.000 +

investment costs 100.000).- The shareholders experience a wealth increase equal to the

investments NPV (400.000).- Existing shareholders of the company get a wealth increase equal toNPV (400.000) regardless of who contributes the money necessary toundertake the investment (i.e. forgone dividend, new equity holders, or

even the original holders).

Investment Decisions in Borrowing Corporations

- Corporate NPV is equal to the change in wealth of existingshareholders even if some of the money for an investment comes fromcreditors instead of equity holders.

Share Values and Price/Earnings Ratios

- The multiplier or price/earnings (P/E) ratioof a company's shares isthe ratio of its market value to its earnings, usually on a per-sharebasis.

- P/E ratios are offered as signals that the market is providing as to thecompanys future earnings prospects, growth rate, riskiness, etc.

- A high P/E ratio is often taken as a signal of the market's high opinionof a company's shares, and also as a sign that the company's share

prices may be too high.

- The P/E ratio is nothing more or less than the ratio between the presentvalue of all the company s future dividends (its market price) and itsexpected earnings during the first period.

- It is influenced by a number of factors, i.e. dividends paid, its payoutratio, discount rate and expected earnings.

- For certain companys with very simple cash-flow patterns (i.e.constant, or constant growth perpetuities) we can derive a specificrelationship between P/E ratios and equity discount rates;

For companies who are paying out all earnings as dividends:

If dividends = earnings:


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re= equity discount rate

For companies who are not paying out all earnings as dividends:

g= dividends growth rate

Relationship between the price/earning ratio and the discount rate:

wherepayout ratiois the percentage of earnings paid as dividend.

- The basic difficulty with the P/E ratio is that the market price of acompany's shares is the net result of a great number of factors, only

one of which is the initial period's earnings that appear in thenumerator of the ratio.

- Thus, unless we can feel comfortable that all but one of the factorsinfluencing market price are reasonably similar among companiesbeing compared, the P/E ratio can give little conclusive or useful

information about the market's relative opinions about the prospects

for such companies.


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Module 3: Earnings, Profit and Cash Flow

Total Corporate Value Change:

The increase or decrease in the market value of all of a corporations capital claims thatwould take place if the investment were accepted.

Corporate Cash Flows

Cash flows between a corporation and others:

- Financial cash flowsare the cash amounts that are excepted to occur atthe times for which the expectations are recorded.

Typical Cash Flows (Company with zero debt, 100% equity financed) (000s)

Now Yr 1 Yr 2 Yr 3

Customers 0 +17 500 +23 500 +4 000

Operations 0 -7 000 -3 830 -5 200

Assets -10 000 -4 000 -2 000 0Government 0 -4 000 -8 085 +5 600

Capital (Free cash flow) -10 000 +2 500 +9 585 +4 400


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1. Customers The amounts of cash expected to take in from salesand/or selling used assets.

2. Operations Cash flows that are paid in cash that year, be deductiblefor taxes that year, and not be a payment to a capital supplier.

3. Assets While the cash flow is made at time listed, it is not deductibleat that point and must therefore be capitalisedand depreciated acrosstime.

4. Government Taxes paid due to the investment.5. Capital The amounts of cash that could be taken out by capital

suppliers from the company as a result of the investment while leaving

all of the plans of the company unchanged (AKA Free Cash Flow). Ifcompany is financed only by equity, Capital cash flows in future years

can be regarded as the increases in dividends that we expect the

investment to allow.

Cash Flows and Profits- Cash flows are not the same as the numbers that appear in financial

statements of corporations.

- One of the biggest differentiation is that accounting figures oftenreport cash flows for time periods other that that which the flowoccurs.


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Module 4: Company Investment Decisions Using the Weighted AverageCost of Capital

The weighed average cost of capital(WACC) is a discount rate that combines the capitalcosts of all the various types of capital claims that a company issues, i.e. the costs of

equity capital, debt capital, and any other capital claims outstanding.

Free Cash Flow and Profits for Borrowing Corporations

- The cash flows of a company must service all of its outstanding capitalclaims including the claims of those from whom the company hasborrowed.

- When a company borrows money the creditors or debt capitalsuppliers of corporations have a contract with the company thatrequires the company to pay them particular amounts of money at

particular times.

- Financial markets place values on corporate debt claims bydiscounting with risk-adjusted rates the amounts of cash that thecompany is expected to pay to those claims.

- Debt has a higher priority claim to cash than does equity.- Tax laws that allow corporations to reduce their taxes by deducting

interest expense. This is called a corporation interest tax shield.

- Dividends, on the contrary, are not a deductible expense.- As a consequence a partially debt financed investment, ceteris paribus,

will have higher free cash flows than one which is 100% equity

financed.

- Income tax shields can be calculated by taking the expected interest

payment in each period and multiplying it by the corporate income taxrate.

Investment Value for Borrowing Corporations

- Debt suppliers wealth should be unaffected by the investment. Figuredby taking the interest principal for each period and dividing by thedebt interest rate.

- Equity wealth change is figured out by comparing the investment-induced change in equity value to any foregone dividend. Value

changeis calculated by subtracting principal and interest from the FCF

for each period and dividing that by an appropriate discount rate.

Overall Corporate Cash Flows and Investment Value

- The most commonly used techniques for finding the NPVs and IRRsof investment projects use the corporate cash flows as a whole, ratherthan separating those for debt and equity.


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- To figure out NPV as a whole, the FCFs must be discounted with arate that is commensurate with their risk.

- To find this discount rate the debt and equity rates must be combinedin proportion to their claims on the corporate cash flow. So the overall

project rate is a market-value weighted average of the rates required

by the various capital claims upon the investment or;

raterequiredEquityxuemarket valTotal

uemarket valEquity

raterequiredDebtxuemarket valTotal

uemarket valDebtrateOverall +=

Note: Total Market Value = total market value of capital invested inbusiness (total value of equity + t.v. of debt +.)

Equity Market value: price per share x numbr of outstanding shares

Debt market value: typically you look at the book value of debt

- Valuing the security is now easy:

= +

=n

0ttrate)requiredOverall(1

FCFprojecttheofValue

- Notice that the value of the project must equal the sum of itsconstituent capital claims values, i.e. the projects equity and debt

values.

- Of course the NPV of the investment is simply the difference betweenthe market value created by undertaking it and what it cost.

- This technique gives us the correct investment NPV by discounting a

project's free cash flow with the market-value weighted average of thediscount rates of the capital claims that will be generated by theproject.

Investment NPV and the Weighted Average Cost of Capital

- The above technique is the overallNPV method.- Common practice in financial analysis of corporate investment is that

when estimating the cash flows of a project, its interest tax shields are

not included in the cash flows.

- In order to calculate an accurate NPV using cash flows that exclude

interest tax shields, the effect must be included in the discount rate.- The WACC is the discount rate that;

a. accounts for the basic operating risks of the projects;b. is consistent with the projects proportional claims of debt and

equity;

c. includes the effect of interest deductibility for the debt-financed portion of the project, since the cash flows whichoperates do not.


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- In order to reflect interest deductibility in the discount rate (WACC),the weighted average must use the companys after-tax cost of debtrather than the debt suppliers required rate.

- Cost of debt in a company with deductible interest is simply debtsrequired return multiplied by the complement of the corporate income

tax rate; rate)taxincomeCorporate(1return xrequiredDebtcostDebt =

- WACC, defined as the market-value weighted average of the project'sequity required rate and debt cost, is therefore calculated as follows:

raterequiredEquityxuemarket valTotal

uemarket valEquity

ratecostDebtxuemarket valTotal

uemarket valDebtW +=ACC

- The WACC-NPV analysis of an investment project is performed bydiscounting the projects FCF, not including the interest tax shields

that the projects financing will generate (these FCFs are the same aswould be expected if the investment were financed totally by equity).

- This method adjusts for the deductibility of corporate interest in thediscount rate as opposed to the cash flows of the project.

- The WACC-NPV yields NPV answers identical to those of both theoverall techniqueand the separated debt and equity value process.

- The overall techniqueand the separated debt and equity value processboth require that we know exactly how much debt financing will beissued by the company for the project.

- The WACC-NPV, on the other hand, does not require that the exactamount of debt to be used in the project be known in order to calculatethe project's NPV. The cash flows used in the WACC-NPV are those

that would be expected if the investment were all-equity financed.

(The interest tax shields are not included in the free cash flows of theproject.) So in terms of the data necessary to estimate free cash flow,

the WACC-NPV technique is less demanding.

- Companies using the WACC-NPV are those willing to specify theexpected proportions of debt and equity in terms of their market

values, but they do not know exactly what the claims will be worth

until after the analysis is complete.

- The reason that companies prefer this WACC-NPV method over theothers is that it does not require that the amounts of debt to be issued

are known, nor does it require that the market values of any of the

resulting claims be estimated beforehand. The only informationnecessary comprises estimates of the required rate for equity, debt's

after-tax cost rate, the all-equity free cash flows, and the proportions

intended for debt and equity financing.


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The Adjusted Present Value Technique

- WACC-NPV requires that the proportions of debt and equity marketvalues be known, but knowledge of the cash amounts of such

financing is not necessary for the final result.

- The APV, on the other hand, does not require that the proportions ofdebt and equity be known, but does require that the interest tax shieldsof the project's debt be estimated.

- The APV technique is therefore preferred for corporations comfortablein estimating the amounts of debt their projects will use, but not the

value proportions that will be generated, while the WACC-NPV

method is best for companies that are willing to estimate market valueproportions of financing for investments, but not the actual amounts

that will be generated.

- If performed correctly both APV and WACC-NPV will give the sameanswers.

- APV finds the NPV by first finding the value of an investment as if itwere financed only by equity, and then adds the PV of the projectsinterest tax shields.

- All-equity value is calculated by adding all the CFs discounted by the(an) all equity discount rate.

- Interest tax shields value is calculated by discounting the shield CFsby the risk-adjusted rate for debt cash flows.

costPresentvalue)shieldtax(Interestue)equity val(AllAPV +=

The Choice of NPV Techniques

Separated debt andequity value process

Overall technique WACC-NPVanalysis

APV technique

Requires that actualamounts of debt to be

issued be known


issued be known

Does not require thatactual amounts of

debt to be issued be

known


issued be known

Requires that theproportions of debt

and equity market

values be known


and equity market

values be known


and equity market

values be known

Does not require thatthe proportions of

debt and equity be

known

The interest tax

shields are includedin the free cash flows

of the project

The interest tax

shields are includedin the free cash flows

of the project

It adjusts for the

deductibility ofcorporate interest in

the discount rate as

opposed to the cash

flows of the project.

Requires that the

interest tax shields ofthe project's debt be

estimated.

Finds the presentvalue by discounting

the claims cash

flows separately

(including interest


the combined claims

cash flows (including

interest tax shields)


the combined claims

cash flows (not

including interest tax

Finds present valuesby splitting up the

cash flows into the

all-equity cash flows)

and the interest tax


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tax shields) shields) shield cash flows.

These are each then

discounted separately

at rates appropriate to

their individual risks.

- When complexities such as tax credits, cash costs, in addition to

interest and its deductions (i.e. cost of bankruptcy proceedings), etc.appear relevant to a companys financial decisions, the APV approach

may be easier to use.- The reason for this is that APV treats these cash-flow effects

separately, by first estimating the cash flows, then discounting each

one at a rate appropriate to their unique risk.- On the negative side, APV does not have the automatic characteristic

of being consistent with maintaining an intended ratio between the

various kinds of financing a company uses.

Notations

Cash flowsFCFt = Free cash flow: the amount of cash that the corporation can distribute to its capital

suppliers at time tdue to an investment, consistent with the company's contractual

and operating expectations. This can be a negative amount if the investment is

expected to raise more cash than it pays to capital suppliers at a given time. FCFis the net amountof the cashamounts to be transacted with customers (as cash

receipts), government (as taxes and subsidies), and suppliers of labour and assets

(as their cash costs).

It = Interest cash flow at time t.

Tc = Corporate income tax rate.ITSt = Interest tax shield cash flow: the reduction in corporate income taxes at time t

caused by interest deductibility of the debt issued for the investment; equal to I tTc.

FCF*t = Unleveraged (ungeared) free cash flow: the amount of free cash flow that the

company is expected to generate at time tdue to a project, not including interest

tax shields; equal to FCFt- ITSt.

Market valuesEt = Market value of the equity of the investment at time t.

Dt = Market value of the debt of the investment at time t.

Vt = Market value of the investment at time t; equal to Et+ Dt.

Discount ratesre = Required return on the equity of the investment; required returns are not usually

time-subscripted, but can be.

rd = Required return on the debt of the investment.rd* = Cost of debt as a rate to the investment; equal to rd (1 - Tc).

rv = Overall weighted average return on the capital claims of the investment; equal to

rv* = The weighted average cost of capital (WACC) of the investment; equal to:


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ru = All-equity or unleveraged (ungeared) required return on the investment; the rate that

would be required on the investment were it to be financed purely with equity.

Investment evaluation techniques

WACC-NPV:

APV:


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Module 5: Estimating Cash Flows for Investment Projects

- Estimating investment cash flows means that financial managers mustkeep the following in mind:

1. Inclusion of all corporate cash flows affected by the investmentsometimes means that financial analysts must invoke the ideaof economic opportunity costs, such as the amount for whicha plant could be sold, or the amounts of cash that the plant

would generate if it were used in the best alternative to the

project in question and management's time.

2. Inclusion of all relevant cash flows means that analysts mustinclude cash flows from interactions of the investment with

other activities of the corporation, such as the reduction in the

cash flows from a company's product induced in the company's

cash flows if a new product is introduced.

3. Inclusion of all relevant cash flows also means that analystsmust know what things should be omitted from the investmentscash flows. For example sunk costs are to be ignored. An

investment should be discontinued if its future cash flows

present value is less than the company would obtain by selling

or abandoning the project, now or later.4. Inclusion of all relevant cash flowsmeans that analysts must be

very careful that the accounting numbers provided for a project

are interpreted correctly. For example overhead costs aretypically not indicative of the incremental cash flows that a

project will require. Accounting numbers can include non-cash

expenses (depreciation), and arbitrary activity measures such asfloor-space devoted to the manufacture of a product. It is

however correct to include as cash outflows the increments to

overall corporate expenses caused by the acceptance of theproject.

- There are many corporate cash flows that should not be includedbecause they are not incremental (i.e. managers salaries); they would

not be affected by the acceptance or rejection of a project.

#1- Calculate Depreciation Expenses for Tax PurposesStraight-line depreciation involves equal amounts for each year.Salvage value is registered in year asset is liquidated.

#2- Calculate Change in Taxes Should Company Accept the Project withP&L

Sales RevenueOther Revenue

Subtotal


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Direct ExpenseLaborOtherManagementMarketing

SubtotalDepreciationSubtotal

Total ExpenseProfit Before TaxLess TaxesTotal Net Income

#3-Calculate Working CapitalAccounts ReceivableAccounts Payable

Cash and Inventories

#4-Project Cash FlowsSales RevenueTotal Direct ExpenseChange in Net Working CapitalAssetsTaxesFCF-Free Cash Flow

Summary

- All changes that would be caused in the cash flowsof a corporationby its accepting a project must be included in the analysis of theproject.

- Only cash flowsare to be included.


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Module 6: Applications of Company Investment Analysis

Other techniques used by companies in their investment decisions are:

1. Payback period2. Average (accounting) return on investment (AROI)

3. Internal rate of return (IRR)4. CostBenefit Ratio (CBR) and Profitability index (PI)

The Payback Period

- The payback period is the number of periods until a projects cashflows accumulate positively to equal its initial outlay. It is a measure

of the length of time expected before the investment outlay is

recouped.- Companies use this methods by picking a maximum period of time

beyond which an investments payback will be unacceptable, and

rejecting all investment proposals that do not promise to recoup theirinitial outlays in that time or less.

- Payback periods and NPV can yield different answers.- Problems with the payback period include;

a. It ignores all cash flows beyond the maximum acceptablepayback period.

b. It does not discount the cash flows within the maximumacceptable period, thereby giving equal weight to all of them.This is inconsistent with shareholder opportunity costs.

- Some companies have altered their payback period techniques to bediscounted payback periods. This procedure calculates the present

values of cash flows, and dictates a minimum acceptable period untilthe discounted cash flows accumulate to equal the initial outlay.

Concern a above is still valid.

- If a company feels it must use the payback period, a rudimentaryestimate of the maximum allowable period should be set:

wherenis the number of periods in the projects total lifetime.

rv* = WACC

- This payback is generally only accurate for projects with fairlyconsistent cash flows each period.

- If these restrictions are met, the above will show the number of periodsacross which, if the original outlay is not returned (in FCF*), the

investment will have a negative NPV.


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The Average (Accounting) Return on Investment

- The average (accounting) return on investment (AROI) calculates arate of return on the investment in each period by dividing expected

accounting profits by the net book value of the investments assets.- These numbers are then added and the sum is divided by the number

of periods for which rates of return have been calculated. The result isthen compared to a minimal acceptable return (often an industry or

company average).

- The AROI does not discount cash flows and the numbers used are thewrong ones.

- The AROI does have some value as an evaluation of control device tocheck the progress of an ongoing project on a period-by-period basis.

Internal Rate of Return vs. Net Present Value

- Most of the time, when the decision to be made is simply whether ornot a particular project should be accepted (so that the choice does not

involve finding the best among a set of competing projects), IRR gives

the correct answers. There is, however, one exception to this rule.- When there is an outlay, an inflow, and another outlay (in the form of

an opportunity cost), multiple IRRs can exist Sign changes across

time can yield multiple IRRs.

- A pattern of sign changes can also product a project that has a totallyupward sloping relationship between NPV and IRR. To correctly

accept a project in this case the IRR would have to be less than the


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hurdle rate. The hurdle rate is the minimum rate of return that must be

met for a company to undertake a particular project.- There are various means that can be used to make the IRR come up

with a correct answer in a particular situation. The difficulty being that

you must know beforehand that you are going to have a problem with

the IRR, and what the solution is.- Another situation in which the IRR can cause problems is in multiple-period cash flow investments which require a different discount ratefor each cash flow. The cash flows IRR can still be found, but at which

hurdle rate is it compared? The YTM of a security with the same risk

and cash flow patterns as the investment would have to be found. The

likelihood of regularly finding such securities when necessary is low.

IRR vs. NPV in Mutually Exclusive Investment Decisions

- In situations where multiple investment options must be compared and

subsequently ranked NPV technique is best.- When IRR must be used the incremental cash flow analysistechniqueshould be used. The steps are;

1. Take any two projects out of the group.2. Find the one that has the highest net positive cash flow total

(sum of all FCF*s). The investment with the highest net cashflow is the defender, the other the challenger.

3. At each time point, subtract the cash flows of the challengerfrom those of the defender, the resulting stream are theincremental cash flows.

4. Find the IRR of the incremental cash flows.5. If the IRR is greater than the appropriate hurdle rate, keep the

defender and throw out the challenger and visa versa.

6. Pick the next project out of the group and repeat the processusing the winner of step 5 until only one investment remains.

7. Calculate the IRR of the winner. If it is greater than the hurdlerate, accept it, if not then reject all the projects.

- This algorithm works because it looks at the IRR of choosing oneproject over another, instead of comparing investments IRRs.

- There are also situations in which the incremental cash flow method ofchoosing among investments should never be used;

1. When the incremental cash flows have more than one changeof sign across time.

2. When the projects differ in risk or financing, so that theyrequire different hurdle rates.

Summary of IRR vs. NPV

1. Both techniques are `discounted cash flow methods, with the IRRcomparing the average per-period earnings rate of an investment


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to the minimum rate necessary to maintain shareholder wealth,

and the NPV using the latter rate as the discount rate in a present-value investment cash-flow calculation, which results in the

change in shareholder wealth caused by the investment.

2. The IRR and NPV will usually give the same indication ofinvestment desirability if the question is simply whether or not toaccept a particular project. The IRR, however, will not generally

give correct rankings of several alternative (mutually exclusive)

projects. When such decisions must be analysed with IRR, theincremental rate algorithm should be used.

3. The IRR has significant problems in application when the cashflows from which it is to be calculated have more than one changeof sign across time. When that occurs, the IRR should not be used.

4. The IRR is unlikely to be useful if each cash flow must be

considered as having a unique discount rate.

The CostBenefit Ratio and the Profitability Index

The CostBenefit Ratio

- The costbenefit ratio (CBR) is defined as the ratio between thepresent value of the cash inflows and the cash outflows of aninvestment:

where:n= number of time periods applicable for the investment

Inflowst+ Outflowst= FCF*t.- An investment is accepted if CBR is >1, and rejected is CBR is 1 would have a positive NPV, and a CBR


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- A PI >1 signals an acceptable investment.- The PI is only used when the present cash flow (FCF*0) is a net outlay.

- The PI is the ratio of the accumulated present values of future cash

flows to the present cash flow of an investment.- The PI is a ratio measure and therefore suffers from the same problems

of CBR.- PI is unsuitable for ranking investments because it displays another

relative measure, the wealth increase per pound of initial outlay

instead of the wealth increase itself.

Capital Rationing

- There are instances when there is not enough money available for allprofitable investments a corporation wishes to undertake, such as:

1. The headquarters of the company that set the periods capitalbudget for divisional investment or managerial talent that dictate

limits upon divisional investment and its attendant growth indemand for overall corporate attention.

2. The external capital markets that disagree with the corporation as tothe desirability of the investment. In this situation the company

may find itself unable to raise the amounts of cash at the rates ofreturn or interest that its analyses of projects indicate should beavailable from the market.

- The set of methods used to choose a group of projects that will

maximise shareholder wealth while having limited funds available iscalled capital rationing techniques.

- When having to choose between a few projects, one simply looks at allthe possible combinations of investments that lie within the budget and

choose the package with the greatest NPV. This is called exhaustive

enumeration.

- When confronted with many projects to choose from, one commonmethod is to calculate the profitability indices for the investments, andto list them in declining order of PI. Investments are then accepted in

order of PI, until the budget has been exhausted.

- A project may be skipped because its outlay is too large, and the next

one having a small enough outlay taken as you work down the list.- The PI technique must be used with some caution in ranking

investments when the highest PI projects do not use up the entirebudget.

- Being under capital rationing is an undesirable situation. It can meanthat you have not been able to solve internal

organisation/communication problems, or that the capital market isunconvinced of your prospects. This implies that you will be forced to


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forego investments that would have increased the wealth of

shareholders.- The existence of high market required rates should not be interpreted

as a capital-rationing situation. This is simply a signal that your capital

costs are also high.

- The capital rationing situation implies that financing beyond thebudget constraint carries not a high but an infinitecost.

Investment Interrelatedness

- This is when the acceptance or rejection of one investment affects theexpected cash flows on another.

- Mutual exclusivity and capital rationing situation are a form ofeconomic inter-relatedness.

Economic relatedness of investment cash flows

- Pure contingency: the cash flows of a particular project cannot existunless those associated with another investment are accepted

- Mutual exclusivity: the acceptance of a particular alternative impliesthe rejection of the cash flows of all that are mutually exclusive of it

- Economic independenceimplies that the acceptance or rejection of oneproject has no effect upon the cash flows of the projects with which it

is economically independent.- If investments are economically independent, they may be considered

individually and judged on the basis of their cash flows alone.

- But if a group of projects exhibits any shading of interrelatedness ofthe types described above, the financial manager must first specify all

possible combinations of interrelated investments, along with their

unique cash flows and NPVs. Next, the combination with the highestNPV is chosen.

Renewable Investments

- When a company faces a decision between renewable assets that are ofdifferent lifetimes, the equivalent annual costtechnique is used.

- The technique is as follows;1. The NPV of a single lifetime or cycle for each asset is found.2. Divide each NPV by the annuity present value factor for the

number of years in each assets replacement cycle at theappropriate discount rate.


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3. The result is the constant annuity outlay per period that has thesame NPV as the asset.

4. Compare the per-period equivalent annuity outlay for eachasset and choose that which the lower cost per period.

Inflation and Company Investment Decisions

- Inflation is an increase in price unaccompanied by any other changes(such as quantity, quality, and so forth). With inflation, we must pay

more money across time to acquire the same goods and services.

- A `Nominal price is the actual number of s (or whatever currency)that would change hands at the time the purchase is made.

- A `Real price is the number of s (or whatever currency) that wouldhave been exchanged to purchase something before the inflation took

place.- We call the `inflation-free return the real rate, and the return that

compensates for both that and inflation, the nominal rate. The nominalreturn is thus given by:

Inflation)return)(1Real(1return)Nominal(1 ++=+

- The nominal cash flows are the real cash flows for each time pointmultiplied by (1 + inflation rate)t, where tis the time point at which the

cash flow is expected. The result is the actual (nominal) amount ofcash that is expected to be available at that time.

- The real cash flow, which is the t0 purchasing power that theinvestment is expected to provide at that time point.

- The real rate of return is the difference between the nominal rate andthe expected influence of inflation on required rates for some time in

the future. Because there is no way to measure such expectations

effects, the real rate is not measurable.- For this reason almost no companies attempt to estimate and use real

rates and cash flows in their decisions.

- Nominal cash flows and nominal discount rates should be used whendealing with inflation on corporate investment decisions. If the

analysis is performed carefully, the impact of inflation on the

investment, and on shareholder wealth, will appear in the NPV.

- The most common error that investment analysts make in dealing withinflation is using nominal discount rates (the `observable ones, which

include inflation's influence and are therefore higher than the

associated real rates) with real cash flows.- Investment analysts should always be explicit in requesting inflated

future cash flow estimates.

- Another trait is because in most countries government allowscorporations to reduce taxable income by the amounts spent for

productive assets only according to a defined schedule across time

(called depreciation). When inflation occurs, the costs of productive

assets will increase across time more or less with other cash flows, but


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depreciation expenses for assets bought in the past will not. The net

effect can be to make taxes increase across time faster than theinflation rate, and thereby to make corporate free cash flow (FCF*)

increase at less than the inflation rate.

- Accelerating depreciation schemes have been put in place to help

offset this effect. For example double-declining balance, or sum-of-the-years digits methods.

- The double-declining balance method allows a deduction equal totwice what the straight-line amount would be if calculated on the

depreciable amount and time remaining in each period.

- The sum-of-the-years'-digits method allows a deduction equal to theproportion found by dividing the remaining depreciable life of theasset by the sum of the years of the asset's total life.

- Debt suppliers can be particularly concerned about inflation andrequired rates. The reason for this is that debt contracts promisespecific amounts of nominal cash at particular times in the future. If

the nominal interest rate that suppliers get at the inception of theirinvestment turns out to be a poor estimate of actual inflation, debtsuppliers will achieve a real return different from their initial

expectations.

Leasing

- `Leasing is a contractual arrangement between an asset owner (thelessor) and a company that will actually operate the asset withoutowning it (the lessee).

- In essential economic terms the lessee rents the asset from the lessor.In exchange for allowing the lessee to operate the asset, the lesseemust pay the lessor lease payments during the period that the lessee

has the use of the asset.

- The most common type of lease is a financialor capitallease wherethe lessor is usually in the business of leasing assets.

The Economics of Leasing

Advantages

- Leasing allows for higher tax benefits that the alternative of borrowingand purchasing an asset.

- Information asymmetries exist on certain types of assets, and leasingcan serve to lower the costs of such information problems.- There are economies of scale in the management of specialised asset

leasing.

Misconceptions- Leasing saves money because the lessee does not have to make a large

capital outlay to purchase an asset.


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- Lessee debt capacity is higher since they do not need to borrow moneyto buy the asset.

Evaluating Leases

- Cash flows used would include; cost of purchasing, lost depreciationtax shields, lease payments, and lease payment tax shields.- The correct discount rate for performing an NPV is the after tax

interest rate (rd*).

- It is important to know what lease rate would allow for a positive NPVwhen negotiating lease agreements with a lessor.

Managing the Investment Process

Using Economic Income in Performance Measurement (EVA, EP,etc.)

- The application of `economic income concepts has become anincreasingly popular approach to measuring the economic performance

of management.

- These methods have the attribute of charging a capital cost against thenet cash flows of a company division in a given period, and seeing if

there is anything left over.

- This cost is typically calculated by multiplying a WACC by aninvested amount to produce a -stated capital cost.

- If there is a positive residual amount left over, the division's revenueshave covered not only the costs that are typical of those on its

accounting income statement, but also the opportunity costs of itscapital suppliers, leaving a `economic profit for its shareholders.

- If there is a negative residual, the division has not done as well asshareholders could have done in a comparable-risk investmentelsewhere.

- The strength of economic profit measures is that they explicitlyrecognise that all capital suppliers, not just creditors, require adequatereturns: the total of invested capital must be compensated for its

opportunity costs. And the WACC is the best measure of the rate of

such necessary compensation.- Economic profit measures have the strength of uncovering company

operations that are profitable in an accounting sense, but not in aneconomic sense. The company's activities that produce positive

economic profit have positive effects on share value, the activities thatdo not generate positive economic profit cause share value to decline.


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Module 7: Risk and Company Investment Decisions

Relationship between risk and return the security market line

- The security market line or SML describes the relationship betweenrisk and return as being positive; the higher the risk, the higher the

required return.

Risk and Individuals

- To an individual capital supplier, risk is best measured by the standarddeviation of rates on return on the entire portfolio of assets

- This is a measure of the extent to which the portfolios possibleoutcomes are likely to be different from its mean or expected average

outcome.- In order to figure out the riskiness of a set of securities one must quote

the probabilities of various rates of return or the probability

distributions of returns, for example:

Portfolio probability distribution

Rate of return Probability

8.5% 35%11.0% 10%

13.5% 30%

16.0% 25%

- The next step is to calculate the mean of these probabilities, or;


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- The standard deviation is calculated:

The square root of 0.00090469 = 0.03008 or 3.008 per cent, and

this is by definition the standard deviation of the portfolio of yourholdings.

- The result is a reflection of the risk inherent in a portfolio.- Unfortunately, studies to date show that the empirical relationship

between risk (measured as standard deviation of return) and the actuallevel of return earned is not good.

Empirical relationship: standard deviation of return and rate ofreturn


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- In the 1950s Harry Morowitz was the first to show that companysecurity holders are indeed risk-averse, and require higher returnswhen the risk (measured as standard deviation of return) is higher.

- He also showed that the resulting positive relationship between returnand standard deviation of return would only be true for the entire

portfolio and not for the individual assets within.- This is because part of the standard deviation of return for individualassets is diversified away when included in a portfolio with otherassets.

Risk, Return and Diversification

- Continuing with the above example:Table 7.2 Individual security (assets A and B) probabilitydistributions

Return outcome Probability

Asset A: 10% 45%

20% 55%

Asset B: 7% 65%

12% 35%

- Expected returns per asset are:

- Standard deviations are:-

the square root of which is 0.0497 or 4.97%, and:

the square root of which is 0.0239 or 2.39%.

- The logical way to find the risks and returns of the portfolio formedtherefore seems to be to take the average of the returns and standard

deviations for the two individual assets;


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(same as the portfolios expected rate of return above!).

(differs from the std deviation for the portfolio of 3.008%).

- Obviously the weighted average standard deviation of return ofindividual assets in the portfolio is not a correct way to calculate thestd deviation of return of the portfolio because it ignores the

interactions of returns represented by the joint probability distribution..

- In order to derive the portfolios return probability distribution, wemust know how individual asset returns interact. This informationcomes in the form of ajoint probability distribution;

Joint probability distribution of assets A and B

- Each cell inside a box describes the probability of a particular set ofreturns being simultaneously earned by both assets A and B. This is

called a joint probability.- The joint (interior) probabilities must sum in rows and columns toequal the original probabilities of the individual security returns while

the sum of all cells must equal 100% (1.0) probability.

Portfolio events and probabilities

Returns

Asset A Asset B Portfolio Probability

Event 1: 10% 7% 8.5% .35

Event 2: 10% 12% 11.0% .10

Event 3: 20% 7% 13.5% .30Event 4: 20% 12% 16.0% .25

- `Portfolio is simply the equally weighted average of the returnsindicated for the assets in the respective events.


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- The portfolio return probability distribution is the specification of thelikelihoods for joint events from the joint probability distribution ofthe assets in the portfolio

- The whole portfolio has less risk than the average risk of the securitiesin it because of diversification.

- The more positively related are securities' returns within a portfolio,the less there will be to gain from diversification.- The less positively

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