BF Practise

RMIT International University- BAFI 3184

Exercise booklet 1

Exercise booklet


Exercise booklet 2

Course guideCourse guideCourse guideCourse guide

Introduction

The theory of finance stems from the broad area of applied economics. Over the past thirty or so years extensive research and theoretical developments have resulted in the emergence of this discipline as a science in its own right. Today, the theory of finance is a field that equips the individual with techniques and skills that ensure the objective analysis and evaluation of alternatives, resulting in effective financial decision-making. These techniques and skills are applicable in a number of sectors of our economy, namely financial markets (including financial products such as derivative instruments), financial institutions and the financial management of companies.

The theory of finance plays a significant role in the area of business, or corporate, finance. The effective financial management of firms, large or small, private or publicly listed, is paramount for the wellbeing of any economy. However, not only does its importance lie in its benefit to the economy as a whole, but it is vital that financial managers are capable of developing sound financial policies for the benefit of the firm itself and its owners, the shareholders. Financial managers must have a sound framework that will provide the analytical tools to competently evaluate alternatives and make objective decisions both in the short term and in the long term. Investment options and financing choices must be analysed and assessed using techniques that have a solid theoretical base.

Business Finance provides an introduction to some of the key skills required for good financial management. It introduces financial concepts and issues that will provide the necessary guidelines to solve many corporate finance problems. It also introduces some of the more important theories in modern finance to provide a substantial grounding in the discipline.

Business Finance is a second year course and consequently is taught on the assumption that students

have an understanding of the basic concepts, principles and analytic techniques found in the

introductory courses in the fields of statistics and microeconomics.

You are requested to ensure that you are correctly enrolled in this course by checking that it appears on

your enrolment confirmation. If the course code does not appear, you will not have a result recorded for

this course. Please see the School’s student administration officer at once if you are not correctly

enrolled in this course.


Exercise booklet 3

A. Course Identification

Course code: BAFI-3184

Course name: Business Finance

Duration: one semester

Credit points: 12 credit points

Contact hours: class contact - 3 hours per week comprising lectures and tutorials.

B. Course Outline

Topic 1: Introduction - Overview of Business/Corporate Finance

Topic 2: First Principles of Valuation: Financial Mathematics/Time Value of Money

Topic 3: Valuation of Bonds and Shares

Topic 4: Capital Budgeting/Project Evaluation

Topic 5: Risk and Return

Topic 6: Weighted Average Cost of Capital (WACC)

Topic 7: Capital Structure

C. Objectives/Learning Outcomes

At the conclusion of this course you should be able to:

a. demonstrate an understanding of fundamental concepts in finance b. apply the ideas of time value of money for decision making c. understand why wealth maximisation is an appropriate corporate goal d. assess the impact of interest rates on business decisions e. demonstrate an understanding of the concepts of portfolio theory and competence in calculating

portfolio returns and risk f. understand the applicability of the Capital Asset Pricing Model to share valuation g. determine whether shares are under/overvalued h. understand and use valuation models for equity, debt instruments and the firm as a whole


Exercise booklet 4

i. understand the advantages and disadvantages of the most commonly used methods of investment evaluation

j. differentiate between the various costs of capital and calculate these costs k. evaluate the profitability of potential investments, using the net present value method l. understand the importance of capital structure in decision making

D. Prescribed Text

Frino, A., Hill, A., and Chen, Z., , Introduction To Corporate Finance, 4th Ed., Pearson Education Australia, Sydney, 2009.

myfinancelab e-workbook available at www.pearsoned.com.au/myfinancelab

E. Reference Texts

Bishop, S., Faff, R., Oliver, B., and Twite, G., Corporate Finance, 5th Ed., Pearson Education Australia, Sydney, 2004.

Correia, C., Mayall, P., O’Grady, B., and Pang, J., Corporate Financial Management, 2nd Ed., Skystone Investments Pty Ltd, Perth, 2005.

Peirson, G., Brown, R., Easton, S., and Howard, P., Business Finance, 8th Ed., McGraw-Hill, Sydney, 2002.

Petty, J., Keown, A., Scott Jr., D, Martin, J., Martin, P., Burrow, M., and Nguyen, H., Financial

Management, 4th Ed., Pearson Education Australia, Sydney, 2006.

Ross, S., Thompson, S., Christensen, M., Westerfield, R., and Jordan, B., Fundamentals of Corporate

Finance, 3rd Ed., McGraw-Hill/Irwin, Sydney, 2004.

E. Assessment schedule

Assessment Weight Release date Due date Topics covered

In-Class quiz 1 5% (TBA) TBA

In-Class quiz 2 5% (TBA) TBA

Midterm 20% Week 7/8 (TBA) 1-4

Homework assignment 1 5% TBA TBA

Homework assignment 2 5% TBA TBA

Final exam 60% Week 13/14 1-7


Exercise booklet 5

TOPIC 2: Time value of moneyTOPIC 2: Time value of moneyTOPIC 2: Time value of moneyTOPIC 2: Time value of money

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Question 1

If you placed $1000 in a bank for one year, how much would you have accumulated in one year if the

rate of return was 6.75%?

Question 2

What is the rate of return on an asset priced at $4695 today that will pay $5000 in one year?

Question 3

Would you pay $98,000 today for an asset that will pay $105,000 in one year if the rate of return is

currently 6% p.a. Explain.

Question 4

You bought a share at $10 which promised a dividend of $1.5 at the end of year 1. It is also expected

that you can sell the share at $16 at the end of year 1. What is the rate of return on this investment?

Question 5

$100 to be received at the end of 3 years is worth how much today, assuming a discount rate of

(i) 10 per cent

(ii) 100 per cent

(iii) 0 per cent?

Question 6

Would you rather receive $1,000 today or $2,000 in 10 years? Assume a discount rate of 8 percent?

Question 7

You have $30,000 today. You want to deposit in a bank at a simple interest rate of 10% for 4 years.

How much of interest will you receive at the end of year 4?

Question 8

You wish to place $1000 in a bank account for five years, at an interest rate of 7% p.a. How much

would you accumulate after five years assuming (a) simple interest and (b) compound interest? Explain

the difference between (a) and (b)


Exercise booklet 6

Question 9

An investment repays $40,000 in five years and a further $60,000 in ten years. If the interest rate over

the period of investment is 12% p.a, compounded monthly, what is the investment’s present value?

Question 10

You are the lucky winner of yours state’s lottery of $5 million after taxes. You invest your winning in a

five year certificate of deposit (CD) at a local financial institution. The CD promises to pay 7 percent

per year compounded annually. This institution also let you reinvest the interest at that rate for the

duration of the CD. How much will you have at the end of five years?

Question 11

An institution offers you the following terms for a contract. For an investment of ¥2,500,000, the

institution promises to pay you a lump sum six years from now at an 8 percent annual interest rate.

What future amount can you expect?

Question 12

An Australian bank offers to pay you 6 percent compounded monthly. You decide to invest A$1

million for one year. What is the future value of your investment if interest payments are reinvested at

6 percent?

Question 13

Your grandmother has a debt that she may repay by paying $5,000 now or $10,000 in four years’ time.

If the interest rate is 14% compounded monthly, would you advise her to repay the debt now or in four

years.

Question 14

What is the amount of money a person must be given now to make them indifferent to receiving a

stream of 10 annual payments of $70 each, where the first payment is received immediately. Assume

the interest rate is 12%.

Question 15

How much would you pay for an investment which will help you earn an annual cash flow of $100 for

10 years given the interest rate of 15%?

Question 16

If Miss Smith is offered the choice of:

(iv) (a) $628.06 now; or


Exercise booklet 7

(v) (b) $50 per quarter for four years at 12% per annum compounded

quarterly; or

(vi) (c) $1007.85 at the end of four years;

Assume that three investments are compounded quarterly, which alternative should you recommend

that she accept?

Question 17

A four year security is selling today for $25,000. The applicable interest rate is 8% and the security

offers an equal annual cash flow at the end of each year. What cash flow would the purchaser of this

security receive each year?

Question 18

Ms. Lan Huong wants to invest in raw land. She expects to own the property for 10 years and to sell it

at the end of the 10th year for $5 million. There are no other cash flows. What is the most she would be

willing to pay for the property if the appropriate discount rate is 12 percent?

Question 19

Suppose you deposit $1,000 in an account at the end of each of the next four years. If the account earns

12 percent annually, how much will be in the account at the end of seven years?

Question 20

After 3 years, how much will a $20,000 investment earning 11%, compounded quarterly accumulate

to? What is the effective interest rate?

Question 21

Your friend is celebrating his 35th birthday today and wants to start saving for his anticipated

retirement at age 65.

He wants to be able to withdraw $10,000 from his savings account on each birthday for 10 years

following his retirement; the first withdrawal will be on his 66th birthday.

Your friend intends to invest his money in the local savings bank, which offers 8 per cent interest per

year.

He wants to make equal, annual payments on each birthday in a new savings account he will establish

for his retirement fund. What are annual payments he needs to make from 36th birthday till 65th birthday

to meet his retirement spending?


Exercise booklet 8

Question 22

A well-known insurance company offers a policy known as the ‘estate creator six pay’.

Typically, the policy is bought by a parent or grandparent for a child at the child’s birth. The details of

the policy are as follows:

The purchaser (say, the parent) makes the following six payments to the insurance company:

1st birthday $730 4th birthday $855

2nd birthday $730 5th birthday $855

3rd birthday $730 6th birthday $855

After the child’s 6th birthday, no more payments are made.

When the child reaches age 65, he or she receives $143,723.

If the relevant interest rate is 6 percent for the first 6 years and 7 per cent for all subsequent years, is the

policy worth buying?

Question 23

John H. Faustus, a naive business student, is considering an offer from Mephistopheles calling for 20

payments of $10,000.

The first payment will be 15 years from today.

Owing to an unexpected strike at the Hades Mint, the payment 17 years from today will be skipped;

however, $20,000 will be paid 18 years from today to make up for the skipped year.

No other gap in yearly payments will be allowed.

Discounting at 10%, Faustus wants to know the present value of the series of payments.

Question 24

Calculate an equivalent annual income for 20 years on the following income stream received over 30

years if the interest rate is 10% per annum compounded annually.

Year Income stream p.a

1 to 15 $15,000

16 to 20 $20,000


Exercise booklet 9

21 to 30 $25,000

Question 25

Warren Reed just turned 40. He has decided that he would like to retire when he is 65.

He thinks that he will need $1,500,000 in his special retirement account at age 65 to maintain his

current lifestyle.

For the next 15 years he can afford to put $12,000 per year into the account.

At age 55 he will need to withdraw $40,000 to purchase membership in the local country club.

The retirement account earns 11% compounded annually.

Required:

How much will Warren’s account will be worth at age 55?

What will be the value of the account when Warren is age 65?

How much will Warren need to deposit into the retirement account each year for the last ten years of

his work career to attain the $1,500,000 goal?

Question 26

Assume you have won first prize in a national lottery and, as a consequence, you will receive an

annuity of $5,000 every six months for 10 years.

You will receive the first payment three years from today.

Required:

a) Determine the present value of this annuity if the required rate of return is 10 percent per annum?

b) If the organisers of the lottery offer you a lump sum of $50,000 today instead of the annuity, would

you accept the offer? Why or why not? Explain your answer.

Question 27

X originally borrowed $25,000 from the bank to be repaid over 15 years, at a nominal annual rate of

interest of 10%, compounded quarterly.

The bank now advises that the interest rate has increased to 12% per annum, compounded quarterly.

There is still 10 years to go before the loan is fully repaid.

(a) What are the present quarterly payments?


Exercise booklet 10

(b) How much will the quarterly payments be after the interest rate rise?

Question 28

X borrows $20,000 to buy a house.

The loan involves equal annual repayments over 20 years and r = 10 %

(a) How much are the annual repayments?

(b) What is the value of the interest element of the 14th repayment?

(c) How much is needed to pay off the loan at the time of the 16th repayment assuming the 16th

repayment has not been made?

Question 29

You are considering the purchase of a new car at a total on-the-road cost of $12,500.

After saving diligently you have accumulated a deposit of $6,500.

Two alternatives are available to you to raise the remaining $6,000 required.

Alternative 1:

A personal loan of $6,000 from the ZNA Bank at the "low cost of 10% pa". Upon further enquiry, you

establish that interest is compounded quarterly.

Alternative 2:

The car dealer can arrange a hire - purchase agreement for the remaining $6,000. Repayments would

be $232.49 per month for two and a half years.

Required:

Which alternative provides the cheapest means of financing?

Question 30

Suppose your company’s defined contribution retirement plan allows you to invest up to €20,000 per

year. You plan to invest €20,000 per year in a stock index fund for the next 30 years. Historically, this

fund has earned 9 percent per year on average. Assuming that you actually earn 9 percent a year, how

much money will you have available for retirement after making the last payment?

Question 31

An insurance company has issued a Guaranteed Investment Contract (GIC) that promises to pay

$100,000 in six years with an 8 percent return rate. What amount of money must the insurer invest

today at 8 percent for six years to make the promised payment?


Exercise booklet 11

Question 32

Suppose you own a liquid financial asset that will pay you $100,000 in 10 years from today. Your

daughter plans to attend college four years from today, and you want to know what the asset’s present

value will be at that time. Given an 8 percent discount rate, what will the asset be worth four years from

today?

Question 33

The manager of a Canadian pension fund knows that the fund must make a lump sum payment of C$5

million 10 years from now. She wants to invest an amount today in a GIC so that it will grow to the

required amount. The current interest rate of GICs is 6 percent a year, compounded monthly. How

much should she invest today in the GIC?

Question 34

Suppose you are considering purchasing a financial asset that promises to pay €1,000 per year for five

years, with the first payment one year from now. The required rate of return is 12 percent per year.

How much should you pay for this asset?

Question 35

You are retiring today and must choose to take your retirement benefits either as a lump sum or as an

annuity. Your company’s benefits officer presents you with two alternatives: an immediate lump sum

of $2 million or an annuity with 20 payments of $200,000 a year with the first payment starting today.

The interest rate at your bank is 7 percent per year compounded annually. Which option has the greater

present value?

Question 36

At retirement, a client has two payment options: a 20-year annuity at €40,000 per year starting after one

year or a lump sum of €500,000 today. If the client’s required rate of return on retirement fund

investment is 6 percent per year, which plan has higher present value and by how much?

Question 37

A German pension fund manager anticipates that benefits of €1 million per year must be paid to

retirees. Retirements will not occur until 10 years from now at time t=10. Once benefits begin to be

paid, they will extend until t=39 for a total of 30 payments. What is the present value of the pension

liability if the appropriate annual discount rate for plan liabilities is 5 percent compounded annually?

Question 38


Exercise booklet 12

The British government once issued a type of security called a consol bond, which promises to pay a

level of cash flow indefinitely. If a consol bond paid £100 per year, what would it be worth today if the

required rate of return were 5 percent?

Question 39

Consider a level perpetuity of £100 per year with its first payment beginning at t=5. What is its present

value today (at t=0), given a 5 percent discount rate?

Question 40

You are planning to purchase a $120,000 house by making a down payment of $20,000 and borrowing

the remainder with a 30-year fixed rate mortgage with monthly payments. The first payment is due at

t=1. Current mortgage interest rates are quoted at 8 percent with monthly compounding. What will your

monthly mortgage payments be?

Question 41

Jill Grant is 22 years old (at t=0) and is planning for her retirement at age 63 (at t=41). She plans to

save $2,000 per year for the next 15 years (t=1 to t=15). She wants to have retirement income of

$100,000 per year for 20 years, with the first retirement payment starting at t=41. How much must

Grant save each year from t=16 to t=40 in order to achieve her retirement goal? Assume she plans to

invest in a diversified stock-and-bond mutual fund that will earn 8 percent per year on average?

Question 42

Suppose you plan to send your daughter to college in three years. You expect her to earn two thirds of

her tuition payment in scholarship money, so you estimate that your payments will be $10,000 a year

for 4 years. Assume that you can earn 8 percent annually on your investment. How much should you

set aside now to cover these payment?


Exercise booklet 13

TOPIC 3: VALUATION OF BONDS AND STOPIC 3: VALUATION OF BONDS AND STOPIC 3: VALUATION OF BONDS AND STOPIC 3: VALUATION OF BONDS AND SHARESHARESHARESHARES

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Question 43

Lisholm Ltd has issued bonds earning a 7 percent coupon rate. The interest is paid semi-annually and

the bonds mature in eight years. The bond face value is $1,000.

If your required rate of return is 8 per cent, what is the current price of the bond?

Question 44

You have some money to invest and you are considering purchasing unsecured notes (a bond-type

instrument) that have been issued by St Marks Ltd. The notes mature in five year time and have a

coupon rate of 10.75%, with coupons paid annually. What price (value) would you be prepared to pay

for the notes if your required rate of return is 10% per annum?

Question 45

You have some money to invest and you are considering purchasing unsecured notes (a bond-type

instrument) that have been issued by St Marks Ltd. The notes mature in five year time and have a

coupon rate of 10.75%, with coupons paid semi-annually. What price (value) would you be prepared to

pay for the notes if your required rate of return is 10% per annum?

Question 46

Abner Corporation’s bonds matures in 15 years and pay 9% annual coupons. If you purchased the

bonds for $1,250, what is your expected rate of return?

Question 47

An issue of Australian treasury bonds with par of $1,000 matures in 15 years and pays 8% interest

annually. The market price of the bonds is $1,085 and your required rate of return is 10%?

(a) Compute the bond’s expected rate of return

(b) Determine the value of the bond to you, given your required rate of return

(c) Should you purchase the bond?

Question 48

You have just purchased 10 newly issued $100 five year ABC Company Ltd. debentures at par.

These debentures pay $6 (per debenture) in interest semi-annually.


Exercise booklet 14

You are also negotiating the purchase of 10 $100 debentures issued by the DEF Company Ltd. 4 years

ago, that return $3 per debenture in semi-annual interest payments and have six years remaining to

maturity.

What is the maximum price you should offer for the DEF Company Ltd. Debentures, assuming the

DEF company is in the same risk class as the ABC company?

Question 49

A debt security has a face value of $20,000 that will pay $1,500 interest annually for five years. The

required rates of return are 4% for the first year, 6% for the second year, 3% for the third year and 5%

for the fourth year and 4.5% for fifth year. What is the debt security’s price?

Question 50

Consider the following four bonds:

Bond Years to Maturity Coupon rate (% p.a.)

A 2 10

B 3 12

C 3 10

D 3 8

Each bond has a face value of $100 pays interest twice a year and the current market interest rate is 9

per cent per annum.

• Calculate the current price of each bond

• Calculate what the price of each bond would be if the market interest rate increased to 11 per

cent per annum.

• What would be the percentage capital loss on each bond?

• Keeping the Coupon rate constant what is the relationship between the change in price and the

time to maturity?

• Keeping the time to maturity constant what is the relationship between the change in price and

the coupon rate?

Question 51

The current interest rates on government bonds are as follows;


Exercise booklet 15

Years to maturity Interest rate (% p.a.)

1 6.00

2 6.50

3 6.90

4 7.20

5 7.40

Assume that the term structure of interest rates can be explained by the expectations theory, of future

interest rates. Calculate the expected 1-year interest rates for the next 4 years.

Explain why it is not possible in this market for the interest rate on government bonds with 6 years to

maturity to be 6 per cent per annum.

Question 52

If at t=0 the one period rate of interest is 6% , the two year is 8% per annum and the three year rate is

10% per annum what is the expected two period interest rate expected to prevail at t=1?

Question 53

You buy a two year bond with an interest rate of 7%. In year 5, you plan to purchase another two year

bond with an interest rate of 9%. What is the interest rate of three year bond sold in year 2 according to

expectation theory given the 7 year-bond rate of 8.5%.

Question 54

Gromixs Ltd is experiencing a period of rapid growth. Earnings and dividends are expected to grow at

a rate of 18 per cent during the next two years, 15 per cent in the third year, and then at a constant rate

of 6 per cent thereafter. Gromix’s last dividend, which has just been paid, was $0.115. If the required

return on the shares is 12 per cent, what is the price of a share today?

Question 55

Newsite Ltd is expanding rapidly. Its dividend growth rate for the coming year is projected at 25 per

cent. This rate will decline by 5 percentage points per year until it reaches the industry average of 5 per

cent. Once it reaches 5 per cent, it will stay there indefinitely. The most recent dividend was $0.85 per

share, and the market requires a return of 16 per cent on investments such as this one. What is the price

per share for Newsite?


Exercise booklet 16

Question 56

You have predicted the following dividends for the next three years on Noitall’s Production’s

shares:

Year Projected dividend

1 $0.50

2 0.60

3 0.70

Beginning in the fourth year, you project that the dividend will grow at an 8 per cent rate

indefinitely. The required return is 15 per cent.

Calculate the price today P0

Calculate the prices P1 P2 P3

Calculate the dividend yield and capital gains yield in each of the first four years. What do you

observe?

Question 57

Atorus Pty Ltd last paid a dividend of $0.30 per share.

This dividend is expected to grow at 12% per annum for three years, then at 10% per annum for the

next three years, after which it is expected to grow at a 4% rate forever.

Required:

What is the price you would pay for the share if your required rate of return is 8%?

Would the price change if you expected to hold the share for only three years? Explain.

Question 58

In the year ended December 2007, National Australia Bank (NAB) generated EPS of 269 cents, paid a

dividend of 182 cents per share and its return on (book) equity was estimated at 17%. Assuming that

ROE and the payout ratio of NAB are stable, what is its expected future earnings and dividend growth

rate?

Question 59

BBB Ltd is a shoe manufacturing business. Its finance manager expects earnings of $0.75 per share at

the end of this year and has forecast that these earnings will growth at a rate of 4% p.a in perpetuity.

The company’s historical dividend payout ratio has been constant at 60% of EPS and is expected to


Exercise booklet 17

remain at that level. At what price should BBB Ltd shares be trading if the required return on equity is

12% p.a?

Question 60

Suppose that an investor is contemplating at the beginning of the year the purchase of RMI Ltd.

ordinary shares and has gathered the following data. At the end of the year RMI is expected to pay an

ordinary share dividend of $1.64 and the market price for each share is projected to be $22. The rate of

return required by the company’s ordinary shareholders is 18%. Determine the intrinsic value of RMI

ordinary shares?

Question 61

An ordinary share has just paid a $2 dividend to shareholders and is expected to continue paying

dividends every year from now to infinity, with the dividend amount expected to grow at a rate of 10%

per annum. Based on an assessment of the riskiness of the shares, the rate of return required by

investors is 15%. What should the price of share be?

Question 62

You intend to purchase Marigo Ltd’s ordinary shares at $50 per share, hold them for one year, and sell

after a dividend of $6 is paid. How much will the share price have to appreciate if your required rate of

return is 15%?

Question 63

Wayne Co.’s outstanding ordinary shares are currently selling in the market for $33. Dividends of

$2.30 per share were paid last year, and the company expects annual earnings and dividend growth to

be 5% per annum.

(a) Given that you require a 15% rate of return, what is the value of a share to you?

(b) Determine the return that can be expected from a Wayne Co. share

(c) Should you purchase Wayne Co. shares


Exercise booklet 18

TOPIC 4: CAPITAL BUDGETING/PROJECT VALUATIONTOPIC 4: CAPITAL BUDGETING/PROJECT VALUATIONTOPIC 4: CAPITAL BUDGETING/PROJECT VALUATIONTOPIC 4: CAPITAL BUDGETING/PROJECT VALUATION

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Question 64

What is the payback if the initial investment is $60,000 and the cash flows are:

Year 1 $20,000

Year 2 $25,000

Year 3 $30,000

Year 4 $10,000

Year 5 $ 5,000

Question 65

Year 0 1 2 3 4

Net cash flows ?? 1500 2500 3000 1500

The payback period is 2.5 years and the cost of capital is 11%. What is the NPV of this project?

Question 66

A firm with a cost of capital of 15% is evaluating three projects. The rates of return for each project are

as follows:

Project 1 IRR = 14%

Project 2 IRR = 17%

Project 3 IRR = 16%

Question 67

An investment of $100,000 is expected to generate an after-tax cash flow of $40 in year 1, $80 in year

2, and $120 in year 3. The required rate of return is 20 percent. What is the net present value?

Question 68

Kim Corporation is considering an investment of 750 million won with expected after-tax cash inflows

of 175 million won per year for seven years. What is the project’s payback period?


Exercise booklet 19

Question 69

Shirley Shea has evaluated an investment proposal and found that its pay-back period is one year, it has

a negative NPV and it has a positive IRR. Is this combination of results possible?

Question 70

Project 1 and 2 have similar outlays, although the patterns of future cashflows are different. The cash

flows as well as the NPV and IRR for the two projects are shown below. For both projects, the required

rate of return is 10 percent.

Cash flow

Year 0 1 2 3 4 NPV IRR

Project 1 -50 20 20 20 20 13.4 21.86%

Project 2 -50 0 0 0 100 18.3 18.92%

If the two projects are mutually exclusive, what is the appropriate investment decision?

If the two projects are independent, what is the appropriate investment decision?

Question 71

You are evaluating a project that requires an initial investment of $350,000, and which will provide a

net cash flow of $30,000 during the first year. The net cashflow is projected to grow at 8% p.a

constantly forever. Assuming the cost of capital is 15%:

(a) Is this project acceptable?

(b) If you are uncertain about the projected 8% growth rate, at what constant growth rate will the

company just break even?

Question 72

The Salte Corporation is an Australian-based company with a large proportion of foreign shareholders.

Its core business is the production of machinery used in the heavy-industry sector. It has recently

completed a $400,000 two year marketing study on whether to introduce a new machine to the market.

Based on the results of the study, Salte has estimated that 10,000 of its new machines can be sold

annually over the next six years at a price of $9,615 each. Variable costs per machine are $7,400 and

fixed costs total $12 million a year. Working capital specifically for this project is estimated to be $2

million and will be returned at the end of the project’s life.

The cost of the machine includes $40 million to build production facilities and $2.4 million in land.

The $40 million investment will be depreciated to zero over the life of the project. At the end of the


Exercise booklet 20

project the facilities, including the land, will be sold for an estimated $8.4 million. The market value of

the land, which is not tax-deductible, is not expected to change.

Finally, start-up costs also entail fully tax-deductable expenses of $1.4 million, which are deductable at

the end of the first year of production. The tax rate applicable to Salte is 30%. The after-tax discount

rate is 10%.

Calculate the NPV of the project and advise Salte whether it should proceed with the project.

Question 73

A company has the opportunity of buying a new high-tech metal cutter that will save the company

$14,000 each year in labour costs. This metal cutter will cost $70,000 and will have a useful life of 7

years. It is expected to have a salvage value of $16,000 and will be depreciated using a straight-line

method of depreciation.

If the company purchases the metal cutter it can sell its old cutter for $5,000, even though it has a book

value for tax purposes of $8,000.

The new machine will require a working capital injection of $4,500 for the acquisition of additional

scrap metal. The working capital will be recovered at the end of the 7 year period. The company’s

required rate of return is 10% and the tax rate is 30%.

Should the company acquire the new metal cutter?

Question 74

You have been observing the surge in health awareness in Australia for some time and realise the time

is right to start and run an aerobic fitness centre. Your family owns a wharehouse which will meet your

needs, and is currently being rented out at $48,000 p.a.You estimate you will need to spend $100,000 in

total, made up of an initial cost of $50,000 to renovate the premises, $45,000 for new equipment, and

$5,000 to install the equipment. You have done a market survey, at a cost of $3,000, which leads you to

believe that you will get 500 memebers each paying $1,000 p.a.

You have also found five instructors you can hire at $30,000 each p.a. For tax reasons you will expense

the renovation costs immediately and depreciate the equipment 9including the installation cost) over

ten years using the straight-line method. Howver, you will expect the equipment to be fully functional

for 15 years, which is the life of the operation. Due to the nature of fitness equipment it will be unlikely

to have a salvage value at the end of ten years. Assume the initial investment is made today and all

cash-flows are received or paid at the end of each year. Your discount rate is 15% and your tax rate is

40%.

Should you invest in the project?


Exercise booklet 21

Question 75

What is the present value at a 15 percent discount rate of depreciation tax shield which occurs in the

third year for a firm in the 40 percent tax bracket that purchases a $50,000 asset being depreciated

straight line over ten years to zero salvage value?

Question 76

Firm X borrows $40,000 which will be repaid in terms of annual payment for next 5 years. At an

discount rate of 10%, what is the interest tax shield’s present value?


Exercise booklet 22

TOPIC 5: RISK AND RETURNTOPIC 5: RISK AND RETURNTOPIC 5: RISK AND RETURNTOPIC 5: RISK AND RETURN

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

Question 77

You are given the following information about the possible returns from an investment.

Return Probabilities

12% .15

9% .60

6% .25

Required:

(a) Calculate the expected return

(b) Calculate the variance of the return

(c) Calculate the standard deviation of the return.

Question 78

An investor invests 40 per cent of her funds in Company A's shares and the remainder in Company B's

shares. The standard deviation of the returns on A is 20 per cent and on B is 10 per cent. Calculate the

variance of return on the portfolio assuming the correlation between the returns on the two securities is:

A) +1.0

B) +0.5

C) 0

D) -0.5


Exercise booklet 23

Question 79

Consider the following information:

Economy Probability Share A

Returns

Share B

Returns

Share C

Returns

Boom .40 10% 15% 20%

Bust .60 8% 4% 0%

a) What are the expected returns on the three shares? What are the standard deviations of the three

shares?

b) What is the expected return on an equally weighted portfolio of the three shares?

Question 80

Assume you have obtained forecasts of the following data on three securities, (as well as the market

portfolio and the risk less asset) in a large and well-traded securities market. Calculate the expected

return and standard deviation of return on the following portfolios? Which portfolio is preferable?

Portfolio X 40% A 0% B 60% C

Portfolio Y 20% A 30% B 50% C

Return SD A B C M

Correlation Matrix

Security A 0.09 0.24 1.0 0.4 0.5 0.6 0.0

Security B 0.10 0.18 0.4 1.0 0.8 0.7 0.0

Security C 0.06 0.15 0.5 0.8 1.0 0.8 0.0

Market

Portfolio(M)

0.15

0.12

0.6

0.7

0.8

1.0

0.0

RisklessAsset (F) 0.10 0.00 0.0 0.0 0.0 0.0 1.0


Exercise booklet 24

Question 81 a) If the expected return on the market is 12% while the risk-free rate is 5%, does the following

description of securities constitute an equilibrium situation?

Security Actual

Return

ββββ i

1 15.5% 1.5

2 6.4% 0.2

3 1.5% -0.5

4 9.5% 0.8

5 14.8% 1.2

b) For those securities that are not in equilibrium, are the securities expected to rise in price or fall in price?

Question 82

Asset A has an expect return of 10% and a beta of 1.2.

Asset B has an expected return of 14% and a beta of 1.4

a) If the risk free rate is 6% what is the reward to risk ratio for Asset A? b) If the risk free rate is 6% what is the reward to risk ratio for Asset B? c) Expalin why Asset B is undervalued or overvalued compared to Asset A.

Question 83

Consider two investors, Henry and John, each of whom have $100,000 to invest. Both investors wish to

hold a well-diversified portfolio which comprises some cash and fixed interest and some growth assets.

They have both selected a growth fund which has an annual expected return of 16% and a standard

deviation of 12%. The return on 90-day treasury bonds is a proxy for the risk free rate of interest and is

currently 6%. Their concern is in determining the proportion of their investment that they will place in

the growth fund and the proportion they will place in cash and fixed interest (“risk-free” assets).


Exercise booklet 25

Henry is relatively risk tolerant and you have been able to determine that he would be comfortable with

his total portfolio having a standard deviation of 10%. John is relatively risk averse. He is only

comfortable with a standard deviation in his portfolio of 7%.

Question 84 You have obtained forecasts of the following data on three securities, the market portfolio and the risk-

free asset in a large and well-traded securities market.

Correlation Matrix

E(Ri) σ(Ri) A B C M F

Security A 0.08 0.14 1.0 0.3 0.7 0.5 0

Security B 0.1 0.16 0.3 1.0 0.4 0.6 0

Security C 0.13 0.2 0.7 0.4 1.0 0.8 0

Market Portfolio M 0.1 0.1 0.5 0.6 0.8 1.0 0

Risk-free Asset F 0.05 0 0 0 0 0 1.0

You are contemplating investing in a portfolio with the following asset weights:

Weight

Security A 40%

Security B 25%

Security C 35%

Required:

(a) Calculate the standard deviation of the portfolio. (b) Calculate the beta coefficient of Securities A, B and C. (c) Calculate the equilibrium returns for Securities A, B and C based on the Capital Asset Pricing

Model. (d) State whether Securities A, B and C are correctly priced, underpriced or overpriced based on the

CAPM.


Exercise booklet 26

EFFICIENT MARKET HYPOTHESIS

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

Question 85

Assume that the Australian stock market is weak-form efficient only. Which of the following

situations should not provide an opportunity to earn excess (abnormal) returns? Explain

your answers.

(a) Your investment adviser calls to tell you that his company’s technical analyst has been tracking

the performance of Patrick Corporation Ltd stock for the past 12 months and is certain that its

price is about to increase by 40-60% in the next two weeks. You should buy some quickly.

(b) BHP announces an earnings-per-share figure that is 20% higher than the majority consensus of

market analysts.

(c) A friend who works at a solicitor’s office has advised you to buy shares in a company that is in

confidential negotiations to be taken over.

(d) You have discovered that each time the price of gold-mining stock drops by 25% in any four-

week period it falls by another 20% before the price increases again.

(e) CBA pays a dividend that is 25% higher than the prior dividend.

Question 86

Assume that the Australian stock market is semi-strong form efficient. Which of the

following situations could be expected to provide an opportunity to earn excess (abnormal)

returns? Explain your answers.

(a) BHP announces an earnings-per-share figure that is 20% higher than the average consensus of

market analysts.

(b) Your friend who works at BHP tells you that tomorrow the company will announce an earnings-

per-share figure that is 20% higher than the average consensus of market analysts.

(c) A listed Australian company, Large Ltd, announces a takeover bid for a company that you are

thinking of investing in, Small Ltd.


Exercise booklet 27

(d) An analyst tells you that company ABC will announce an earnings-per-share figure that is

double previous levels. However, the higher EPS will arise as a result of a change in the

company’s accounting practices.

(e) You have discovered that each time the price of a gold-mining stock drops by 20% in any four-

week period it falls by another 20% before the price increases again.

(f) CBA pays a dividend that is 25% higher than the prior dividend.


Exercise booklet 28

TOPIC 6: WEIGHTED AVERAGE COST OF CAPITALTOPIC 6: WEIGHTED AVERAGE COST OF CAPITALTOPIC 6: WEIGHTED AVERAGE COST OF CAPITALTOPIC 6: WEIGHTED AVERAGE COST OF CAPITAL

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

Question 87

Calculate the weighted average cost of capital for the Peach Computer Company. The book value of

Peach’s outstanding debt is $10 million. Currently, the debt is trading at 90 percent of book value and

is priced to yield 12 percent. The 1 million outstanding shares of Peach stock are selling for $20 per

share. The required return on Peach stock is 20 percent. The tax rate is 30 percent.

Question 88

Assume that ABC Corporation has the following capital structure: 30 percent debt, 10 percent preferred

stock, and 60 percent equity. ABC Corporation wishes to maintain these proportions as it raise new

funds. Its before-cost of debt is 8 percent, its cost of preferred stock is 10 percent, and its cost of equity

is 15 percent. If the company’s marginal tax rate is 40 percent, what is ABC’s weighted average cost of

capital?

Question 89

Jorge Ricard, a financial analyst, is estimating the costs of capital for the Zeale Corporation. In the

process of this estimation, Ricard has estimated the before-tax costs of capital for Zeal’s debt and

equity as 4 percent and 6 percent, respectively. What are the after-tax costs of debt and equity if Zeal’s

marginal tax rate is 30 percent?

Question 90

Alcoa has one class of preferred stock outstanding, a $3.75 cumulative preferred stock, for which there

are 546,024 shares outstanding. If the price of this stock is $72, what is the estimate of Alcoa’s cost of

preferred equity?

Question 91

Valence Industries wants to know its cost of equity. Its CFO believes the risk-free rate is 5 percent,

equity risk premium is 7 percent, and Valence’s equity beta is 1.5. What is Valence’s cost of equity

using the CAPM Approach?

Question 92

John Smith Ltd. recently asked a team of management consultants to determine an appropriate cut-off for

investment projects with the same risk as the firm. Unfortunately, part of the report was lost and, as the

investment manager of Smith, you have been asked to calculate the missing figures. Fortunately, the

following facts were available from the report.


Exercise booklet 29

• The consultants estimated that the required rate of return was 13.635%

• Shares were selling for $1.20.

• The Beta of Smith's equity was estimated at 0.7, rm at 20% and rf at 12%.

• The interest rate on debentures was 13% per annum.

• A balance sheet extract showed:

Liabilities $ (000)

Mortgage loan 1,500

Debentures 2,500

Shareholders funds

Paid-up capital ($1 par) 5,000

Reserves 3,500

Total 12,500

• Debt items were recorded as market values.

• The consultants believed the market value capital structure was optimal.

• The corporate tax rate as 40%.

Compute the before-tax rate of interest on mortgage loans to arrive at the consultants' estimate of the

cut-off rate.

Question 93

Pluto Ltd. commenced operations many years ago. Relevant details relating to the company include

the following:

Extract from Balance Sheet

Liabilities

Debentures ($100 par, 8% coupon rate) $4,000,000

Bank Overdraft $500,000

Owners Equity

Ordinary Shares $5,500,000

Retained Earnings $2,500,000

Preference Shares (7% cumulative) $1,500,000


Exercise booklet 30

Additional Information

i. An interest payment in relation to the debentures has just been made. Interest is paid annually and they will mature three years from today.

ii. If the company were to issue debentures today it would have to offer a coupon rate of 10 percent.

iii. The preference shares are trading on the market at $3.00 and a dividend of 21 cents per share has just been paid.

iv. Forecasts in relation to market returns are: expected risk-free rate of return is 6.5 percent; expected return on the market portfolio is 12 percent. Pluto’s beta co-efficient is 0.9.

v. Pluto has 500,000 issued preference shares. vi. Pluto’s ordinary shares, which were issued at 50 cents each, are trading on the market at 63

cents each. vii. The company’s after-tax weighted average cost of capital is 9.25%. Assuming a corporate tax rate of 30 percent, calculate the before-tax cost of the bank overdraft.

CAPITAL

BASE

MARKET

VALUE

WEIGHT

COST

BEFORE

TAX

COST

AFTER

TAX

AFTER TAX

WEIGHTED

COST OF

CAPITAL

????

0.13635


Exercise booklet 31

TOPIC 7: CAPITAL STRUCTURETOPIC 7: CAPITAL STRUCTURETOPIC 7: CAPITAL STRUCTURETOPIC 7: CAPITAL STRUCTURE

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

Question 94

It has been suggested that if the equity and long-term capital of a company is valued at market price,

and if the rate of return on that capital is calculated from earnings before loan interest, and taxation is

ignored, then that rate of return will be identical for all companies having the same total risk. The

relevant data for two such companies are given below:

Company A

(levered)

Company B

(un-levered)

Current value of capital:

Number of ordinary shares 90,000 150,000

Market price per share $1.20 $1.00

Market value of equity $108,000 $150,000

6% secured non-redeemable debt

at par $60,000

Earnings before interest (NOI) $18,000 $18,000

NI

$14,400

i.e. $18,000 less $3,600 (i.e.

NOI less interest) $18,000

Return on equity (re)

13.33%

i.e. $14,400/$108,000

12%

i.e. $18,000/$150,000

Value of Company

$168,000

i.e. $108,000 (equity) plus

$60,000 (debt) $150,000

All income after loan interest is distributed as dividend (i.e. NOI less interest = NI)


Exercise booklet 32

Required:

a) Explain and illustrate the process by which, through investors’ actions, the market values of the two companies might be brought into equilibrium. Suppose the individual has 900 shares in A.

b) List the further assumptions implicit in your calculations. c) Comment on the likely effect of taxation on the market values of the two companies. No

calculations are required.

Question 95

Company A and Company B are in the same risk class, and are identical in every respect except that

Company A is levered while Company B is not. Company A has $3m in 5% debentures. Both firms

earn 10% before interest and taxes on their $5m of total assets. Assume a company tax rate of 60%, and

a capitalization rate of 10% for equity be it in the levered or un-levered company.

Required:

(a) Compute the value of each firm using net income.

(b) The values for firms A and B computed in part (a) above are not in equilibrium. If a situation like

this exists, an investor in the overvalued firm can, through the arbitrage process, secure the same

income at lower cost. Assuming you own 1% of A’s shares, show the process which will give you the

same amount of income but at less cost.

BF Practise

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