FINM2401 Tutorial

Optional Maths Revision Tutorial Questions

1. Solve the following equation:

10 52 1

4x x+= +

for x.

2. Solve the following equation:

2 2 10y y y+ + = −

for y.

3.

1 2 3

1 2 3

If 2 3 4,

and 1 2 3.

x x xy y y

= =

= =

=

=

)

Then find:

( ) (3 2

1 1

.i i i ii i

x y x y= =

+ +∑ ∑

4. Using the same numbers as in question 3, find:

( )3

1

1 .i ii

x y=

−∑

5. Compute:

3 2 ,If 4.

a aa

−+=

6.

3 2Find ,

If 10.a aa

−×=

7.

( )If 100 20 1 0.10

Solve for .

n

n

= +

8. 1

2 5Solve for .

n

n=

9.

( ) 51 1.10

If 100,000 0.10

Find .

R

R

−⎡ ⎤−⎢ ⎥=⎢ ⎥⎣ ⎦

10. Compute the following sum:

( ) ( )2100 1.05 20 ,

If 10 316.227766

a

a

+ +

=

1

Maths Revision – Key Figure Answers:

Question Answer 1 x = 2 2 y = 2 3 23 4 17

5 161

64

6 10 7 n = 16.886 8 n = 0.4307 9 R = 26,379.75 10 1,889.953

2

3

Tutorial 1 – Questions

Unit 1: Firms and Financial Managers 1. Distinguish between investment, financing and income distribution decisions.

2. <deleted>

3. What is the financial manager’s overriding goal?

4. Match the following words and concepts with their definitions:

Word / Concept Definition a. Arbitrage 1. A tangible or intangible asset that directly

assists the company in generating its own cash flows. Examples include patents, factories, and office equipment.

b. Bank Bill 2. An excess profit earned without risk. c. Bill of Exchange 3. An accounting method for spreading the cost

of capital expenditures over their useful life. d. Bond / debenture 4. Another name for Net Assets, that is, Total

Assets less Total Liabilities. e. Cost of Capital 5. A distribution of income to shareholders. f. Depreciation 6. A claim against the future cash flows of a

company. g. Dividend 7. Income to debt holders. Computed as a

percentage of principal outstanding. h. Equity 8. The name given to transactions that represent

the direct offering of securities by a company. i. Financial asset 9. Transactions in company securities that have

previously been issued by the company. The company itself is generally not a party to these transactions.

j. Interest 10. A long-term corporate debt instrument. Payments to holders generally consist of regular interest payments (quarterly or semi-annually) followed by a re-payment of principal when the instrument matures.

k. Liability 11. An ownership interest in a company. Represents a residual claim on the assets and income of the firm.

l. Opportunity Cost 12. A claim on the cash flows generated by another entity.

m. Ordinary share 13. Income earned on the next-best use of the funds in question.

n. Primary Market 14. The average cost of acquiring funds for investment by the company.

o. Real Asset 15. A short-term debt instrument that requires payment of the face value on maturity.

p. Secondary Market 16. A bill of exchange that has been guaranteed by a bank.

4

Unit 2: The Time Value of Money Advice: In attempting these questions, particularly the more complex ones, draw a time-line to document the magnitude and timing of cash flows. Determine whether you are dealing with a single cash flow, or an annuity (or some combination thereof). Identify exactly what it is the question wants from you. Is it P (the present value), Fn (the future value after n periods), A (the annuity payment amount), etc.

1. How much will $500 grow to if invested for 10 years at an interest rate of 12% p.a. (compounded annually)?

2. What will the following investments accumulate to if interest is paid annually?

a. $1,000 invested at 10% p.a. for 6 years?

b. $125.47 invested at 12% p.a. for 8 years?

3. In 30 years time when I retire, I will have $4 million in my retirement fund. What is this worth in today's dollars? (i.e., what is the present value?) Assume an average annual interest rate of 10%.

4. You invest $100 for a period of 7 years, after which it has grown to $200. If interest was paid annually, what was the average rate of interest earned?

5. How long does it take $100 to grow to $150 if the interest rate is 10% p.a. (compounded annually)?

6. If the interest rate is 10% p.a. (compounded annually), what is the present value of the following cash flows:

a. $1,000 to be received in 3 year's time?

b. $1,500 to be received in 10 year's time?

7. You have just been signed to a major record label and have been promised $20,000 in one year’s time plus another $10,000 in two year’s time. What is the value of this consideration to you today assuming that you can invest your money at 5% p.a.?

5

Tutorial 1 – Key Figure Answers

Question Answer Unit 2

1 1,552.92 2a 2b

1,771.56 310.66

3 229,234.21 4 10.40895% p.a. 5 4.254 years 6a 6b

751.31 578.31

7 28,117.91

1


Unit 2: The Time Value of Money 1. At the end of each of the next 10 years, you will place $1,000 into an investment that

returns 12% p.a. How much will this investment have grown to by the end of year 10?

2. You wish to purchase a new car, valued at $55,000. The purchase will be financed as follows. An upfront payment of $10,000 is due immediately. The balance ($45,000) will be paid off over the next four years. Repayments are due at the end of each month. The finance company quotes an interest rate of 12% p.a. compounded monthly. Calculate the monthly repayment amount.

3. Reconsider the previous question. You will have trouble meeting the monthly repayments calculated in the previous question. If you can talk the finance company into allowing you to pay off the balance over five years (rather than four years), by how much does this reduce your monthly repayment?

4. Your child will commence university in 15 year's time. You wish to put away money regularly (one deposit at the end of each year) to provide for her education, which you estimate will cost $200,000. You anticipate that the average rate of return on an investment fund will be 8% p.a. How much will you have to put away at the end of each of the next 15 years so that you will have the $200,000 required?

5. Reconsider the previous question. As opposed to putting money away regularly to accumulate $200,000, you decide to make a once-off investment now. How much will you have to invest today to have the required $200,000 in 15 year’s time?

6. Your generous uncle decides to endow his alma mater with a scholarship of $5,000 per year in perpetuity. If the school can earn a return of 8% p.a. on the endowment, how much does he need to donate? The first payment will be made one year from now.

7. You have won a lottery and will receive $10,000 at the end of each year in perpetuity. If we assume an interest rate of 10% pa, what is the real value of your prize? That is, what is this infinite series of payments worth in today's dollars?

Aside: as an interesting exercise to prove the formula for the present value of a perpetuity, you might try preparing a spreadsheet. Listing the payments you will receive (maybe go out to 200 years), discount each $10,000 payment to present value using the interest rate and the relevant number of years, and add up the present values. You'll see that a payment made 200 years from now is effectively worthless in today's dollars.

8. What is the present value of $500 to be received in 5 year’s time if the interest rate is 8% p.a. compounded quarterly?

9. What will $550 amount to in four year's time at a nominal interest rate of 12% p.a.:

a. compounded annually?

2

b. compounded monthly?

c. if interest is paid on daily balances (assume that the bank ignores the extra day in leap years).

10. Different banks offer different interest rates. Which bank gives the greatest return?

• Commonstealth Compounded yearly at 15% p.a.

• Eastpac Compounded quarterly at 14.75% p.a.

• Metaway Compounded semi-monthly at 14.675% p.a.

• ANX Compounded monthly at 14.5% p.a.

11. You decide to start saving for a vacation to the Whitsunday Islands, leaving on New Year's day. You will invest $100 on the first day of each month (starting today 1st March), with the final investment on 1st December. Assuming you earn interest at a rate of 12% p.a. compounded monthly, how much will you have to spend?

12. It is the first day of January 2003. Starting from the first day of the year 2006 you will deposit $5,000 into a bank. You will continue to deposit this amount into the bank every New Year’s Day until the Year 2010. On New Year’s Day 2011, instead of depositing any money, you will instead withdraw all of your deposited funds and accumulated interest. Assuming an interest rate of 15% p.a., how much will you withdraw from your account?

13. You are considering the purchase of a home for $300,000. You have available a deposit of $50,000. The bank will lend you the balance ($250,000) at 6% p.a. over a period of 20 years. Interest is compounded monthly.

a. Calculate your regular monthly repayment.

b. Five years later, you have made 60 repayments. What is the payout figure on the loan? That is, how much do you still owe the bank?

c. Assume that, just after your 60th payment, the interest rate rises to 9% p.a. (still compounded monthly). Of course, this means your monthly payment must rise if you are to pay the loan off over 20 years in total (there are now 15 years to go). Calculate your revised monthly loan repayment.

Aside: a spreadsheet is ideal for checking and proving these calculations.

14. At the end of each of the next four years, you will receive a payment of $1,000. The interest rate is 10% p.a. compounded annually.

a. Schedule this series of payments on a time-line.

b. Equate this series of cash flows to a single cash flow received today. That is, calculate the present value of the 4-payment annuity.

c. Equate this series of cash flows to a single cash flow received at the end of year four. That is, calculate the future value of the annuity.

d. Take your answer to (b). Assume that you invest this amount for four years. How much will it grow to?

3

e. Take your answer to (c). If this was a once-off payment to be received at the end of four years, what is its present value.

f. Equate the original series of cash flows to a single cash flow received after two years.

g. Take your answer to (f) and discount it back to present value.

15. Consider the following series of cash flows. Today is time 0. You receive nothing for the first two years. At the end of years 3 and 4, you receive $2,000. At the end of years 5 and 6, you receive $5,000. The interest rate is 6% p.a. compounded annually. Calculate the present value of this series of payments (there are several different ways of approaching this question – all giving the correct answer).


Question Answer 8 17,548.74 9 1,185.02 10 Pmt reduced $184.02 11 7,365.91 12 63,048.34 13 62,500 14 100,000 15 336.49 16 FV4 = 865.44

FV48 = 886.72 FV1460 = 888.77

17 15.000% p.a. 15.586% p.a. 15.7547% p.a. 15.5035% p.a.

18 1,056.68 19 38,768.70 20a 20b 20c

1,791.08 212,249.28 2,152.77

21b 21c 21d 21e 21f 21g

3,169.87 4,641.00 4,641.00 3,169.87 3,835.54 3,169.87

22 10,524.52 (several ways of

doing this)

4


Unit 3: Valuation of Stocks and Bonds SHORT-TERM WORKING CAPITAL MANAGEMENT 1. Your accounting department has just completed a cash flow analysis and determined

that you will have a temporary cash deficit for the next six months. A large payable is due and there will be a cash shortage until a number of receivables fall due six months from now. Your job is to consider how this short-term cash deficit should be financed. Suppose that you have the following two options available:

• You can issue a 180-day bank-accepted bill. The current 180-day bank bill rate is 7.5% p.a.

• You can use the firm’s overdraft facility, on which interest is charged at the rate of 0.7% per month.

2. (question deleted)

3. Your primary supplier offers terms of 2/10 net 45. What is the cost of foregoing the discount to delay payment?

4. On 15 October 2002, BabyCo issues a 180-day bank bill with a face value of $400,000. The bill was accepted and discounted by BankFive on that date (be sure you can explain what this means). BankFive held the bill until 13 January 2003, when it sold the bill to ProfitBank. On 12 February 2003, ProfitBank sold the bill to YetAnotherBank. The quoted interest rates on bank bills on the dates in question were:

Date 60-day bills 90-day bills 180-day bills 15/10/02 4.57% 4.68% 4.90% 13/1/03 4.89% 4.96% 5.02% 12/2/03 4.48% 4.55% 4.82%

Compute the following amounts:

• How much did BabyCo receive when the bill was issued?

• What did BankFive sell the bill for on 13 January 2003?

• What did ProfitBank sell the bill for on 12 February 2003?

• What was ProfitBank’s effective annual yield for the period they held the bill?

Why isn’t ProfitBank’s effective yield the same as the bill’s quoted rate when purchased?

5. Your company is offered a 90-day bank bill with a face value of $100,000 at a current price of $98,750. What is the quoted rate on the bank bill? What is the effective annual interest rate on the bill?

6. You are analysing the accounts payable at your company and find that your major supplier offers terms of 1/10 net 45. You also know that the bank charges your company 11% p.a., compounded daily, on its overdraft account.

a. What are the effective annual rates on these two sources of finance?

b. You made a $250,000 purchase a few days ago. You’d like to get the discount by paying within 10 days, but your company is a little cash constrained at present. This cash flow problem will be resolved in one month when a large receivable will be paid. That is, you have no problem paying the full $250,000 within 45 days, but you don’t have enough cash to pay within 10 days to get the discount. You could, however, borrow the money using your bank overdraft facility to pay within 10 days. Does it make sense to do this? How much does it cost the company if you make the wrong decision?

BONDS 7. A 12% government bond with $100 face value pays interest twice yearly and

matures in 5 years. The current market yield on the bond is 10% p.a. compounded semi-annually. If a coupon payment has just been made, what is the current price of the bond?

8. A government bond with a face value of $100 and a coupon rate of 11% p.a. matures in 3 years. Coupon payments occur twice each year and a payment has just been made. If the current market yield on the bond is 13 % p.a., what is the current price of the bond?

9. A company intends to raise funds by selling bonds. The face value is $1,000, interest is paid semi-annually in arrears at the coupon rate of 10% p.a., and the maturity is two years.

a. Draw a time-line scheduling the cash flows to the buyer of the bond.

b. What price will the bond sell for?

c. I hope you didn’t get an answer for part (b)! Now suppose that, based on the company’s credit risk and the current term structure of interest rates, the appropriate yield for the two-year bond is 8% p.a. (with semi annual compounding). Now calculate the price of the bond. Before you do so, you should be able to predict whether the bond will sell at a discount or premium to the $1,000 face value.

2

d. Complete the following table:

Yield to Maturity

Value of Bond

8% p.a. $ 10% p.a. $ 12% p.a. $

If you were to plot the value of the bond against the yield, you’d see an inverse relationship – as the yield to maturity goes up, the value of the bond goes down.

10. A three-year bond with face value of $50,000 is selling for $47,291. Interest is paid semi-annually in arrears at a coupon rate of 4% p.a. (with semi annual compounding).

a. Without doing any calculations, is the yield on the bond greater than or less than the 4% coupon?

b. Derive the yield-to-maturity. (Hint: it’s a round number). Recall that the price of a bond is the present value of all cash flows from the bond, discounted at the yield to maturity. Note that this can only be done by trial and error. You might want to quickly setup a spreadsheet that enables you to try different yields. (Alternatively, Excel’s GOALSEEK or SOLVER could be used).

11. Consider two government bonds, both of which are considered to be risk-free. Both bonds have $1,000 face value and have a coupon rate of 8% p.a. with coupons paid semi-annually. Bond A has two-years to maturity, and Bond B has 10 years to maturity.

a. If the applicable yield-to-maturity for the bonds is 10% p.a., calculate the market price of each bond.

b. Now assume that the market yield-to-maturity for bonds of this risk increases to 12% p.a. Given the inverse relationship between yields and bond prices, the rise in yield will cause prices to decrease. Before doing any calculations, predict whether Bond A or Bond B will have the greater fall in value.

c. Now calculate the new market price of each bond and see whether your prediction in (b) was correct.

3

4



1 Bank Bill: 7.6426% Overdraft: 8.7310%

3 23.45% 4 6.04% 5 5.23% 6 $124.04 7 $107.72 8 $95.16 9c 9d

$1,036.30 $1,036.30 $1,000.00 $ 965.35

10b 6% p.a. (trial & error) 11a

11c

A: $964.54 B: $875.38 A: $930.70 B: 770.60


Unit 3: Valuation of Stocks and Bonds STOCKS 1. The required rate of return on the shares in the companies identified in (a) to (c)

below is 15% p.a. Calculate the current share price in each case. Assume that all companies pay one dividend per year.

a. The most-recent dividend (paid yesterday) of Lara Ltd. is $1.50. The company expects the dividend to remain constant for the foreseeable future.

b. Waugh Ltd.’s current dividend per share is 80 cents (paid yesterday). This dividend is expected to grow at a constant rate of 5% p.a. forever.

c. Akram Ltd.’s current dividend per share is 60 cents (paid yesterday). The dividend of the company has been growing at 12% p.a. in recent years, a rate expected to be maintained for a further 3 years. It is then envisaged that the growth rate will decline to 5% p.a. and remain at that level indefinitely.

2. Tendulkar and Co. pays annual dividends on its ordinary shares. The latest dividend of 75 cents per share was paid yesterday. The dividends are expected to grow at 8% p.a. for the next two years, after which a growth rate of 4% p.a. is expected to be maintained indefinitely. Estimate the value of one share if the required rate of return is 14% p.a.

3. If each of two stocks are currently paying an annual dividend of $1 per share (i.e., their last dividend was $1), but the dividends of Stock B are expected to grow at twice the 4% p.a. rate anticipated for Stock A, then Stock B would currently sell for twice the price of Stock A. True or false? Explain. Investors require a return of 10% p.a. on both A and B.

4. The common stock of Hussain Ltd. is selling on the market for $32.84. The company has just paid an annual dividend of $2.94 per share and dividends are projected to grow at 9.5% p.a. If you purchase the stock at the current market price, what is the expected rate of return?

5. The Cronje Corporation has just paid an annual dividend of $1.50 per share. At what price should Cronje shares sell:

a. if the dividends are expected to grow at a rate of 10% p.a. indefinitely.

b. if the dividends are expected to grow at a rate of 10% p.a. for only 5 years. After the year 5 dividend, no further growth in dividends is expected. That is, the dividend at year 5 will be paid in perpetuity from year 6 onwards.

The Cronje stockholders are known to demand a return of 20% p.a.

6. Trendy DotCom is a relatively-newly-listed tech stock. The company has announced that its forecasted annual dividend (to be paid in one year) is $1 per share. The current market price of Trendy DotCom is $6.67.

You are an analyst trying to get a feel for the “logic” of the market valuation of Trendy. You decide to use the constant growth in dividends model, and make the assumption that Trendy's dividends will grow at a rate of 10% p.a.

a. Given the current market valuation of Trendy DotCom at $6.67, what is the required return on equity (re) for this company?

b. Given your answer in (a), divide the return on equity into its ‘value’ and ‘growth’ components.

c. As an analyst specialising in tech stocks, you know that firms similar to Trendy DotCom usually trade at an earnings multiple of 5. Trendy's most recent earnings-per-share (EPS) figure is $2.00. Given the industry earnings multiple of 5, estimate the value of one Trendy DotCom share. Given the current market price of $6.67, is Trendy under- or over-valued according to your calculations?

2

3


Question Answer 12a 12b 12c

$10.00 $ 8.40 $ 7.527

13 $8.386 14 A: $17.33

B: $54.00 15 19.3% p.a. 16a 16b

$16.50 $10.676


Unit 4: Project Evaluation and Capital Budgeting 1. You have been considering going into business for some time and have been on the

look-out for opportunities. Partly from your astute business sense, and partly because your jeans have become surprisingly loose around the waist, you decide that West End is desperately in need of a gourmet pizza shop. You have made a series of enquiries, obtained relevant quotes, and compiled the following data:

• A shop can be leased for $800 per month payable in arrears. All fittings would have to be purchased. These include:

A wood-fired pizza oven at a cost of $5,000,

An industrial fridge/freezer at a cost of $7,000,

A smoke/burglar alarm at a cost of $2,000,

Miscellaneous cooking utensils at a cost of $10,000.

• All assets purchased will be depreciated (straight line) over a five-year useful life down to a salvage value of zero.

• The following data are relevant for estimating cash inflows and outflows. All figures are on a monthly basis:

sales: 700 pizzas at an average price of $12,

sales: you anticipate that every second pizza buyer will also order a one-litre softdrink. Your profit on softdrink is $1.50 per bottle.

costs: ingredients estimated at $3 per pizza,

advertising in letterboxes and newspapers, $500,

electricity and telephone, $800,

casual wages, 3,000.

Don't forget the lease cost!

• Other miscellaneous items are:

You will offer free delivery of pizzas to surrounding suburbs. This will be done in your own car, which was purchased (for private use) three years ago at a cost of $50,000. The car is currently valued at $30,000 and has an estimated remaining life of five years. You figure that business use of the car will amount to about 50% of the car’s total use, and that the business share of running expenses will amount to $3,000 per year (including additional petrol). For tax purposes, you will depreciate the car to a zero salvage value over its remaining life. If you decide not to start the pizza shop, you will just continue using the car for personal use.

The above-mentioned advertising will only be conducted in the first two years of the business. After that, you hope to have sufficient repeat business and word-of-mouth to maintain your sales at forecasted levels.

To establish the business, you will inject working capital of $20,000. This money will be recovered on closure of the business in five years.

You expect to pay tax at an average rate of 20%. Assume tax is paid at the end of each year.

Since the equipment has a five-year useful life, you are looking at this being a five-year project, after which you will move on to something else. Although many of the above estimates are on a monthly basis, you will ‘do the math’ by aggregating all figures to get yearly estimates.

REQUIRED:

a. Calculate the expected after-tax cash flows (on an annual basis) over the five-year life of the business.

b. You are unsure of what discount rate to apply to these cash flows. Your forecasts of sales and costs are pretty rough. Prepare an NPV profile to gauge the sensitivity of the NPV to the discount rate.

c. Finally, you conclude that a 25% p.a. discount rate is applicable for this line of business. Should you go ahead and establish the gourmet pizza shop?

2. The Outback Mining Company has constructed a town at Big Bore, near the site of a rich mineral discovery in a remote part of Australia. The town will be abandoned when mining operations cease after an estimated 10-year period. The following estimates of investment costs, sales and operating expenses relate to a project to supply Big Bore with meat and agricultural produce over the 10-year period by developing nearby land:

• Investment in land is $1 million, farm buildings $200,000, and farm equipment $400,000. The land is expected to have a realizable value of $1 million in 10 years’ time. The salvage value of the buildings after 10 years is expected to be $50,000. The farm equipment has an estimated life of 10 years and a zero salvage value.

• An investment of $250,000 in current assets is required at startup. This working capital will be recovered at the termination of the venture.

• Annual cash sales are estimated to be $2.48 million.

• Annual cash operating costs are estimated to be $2.2 million.

Is this project profitable, given that the required rate of return is 10% p.a.? The applicable tax rate is 30%.

Note that investments in land and working capital are not depreciable. Assume that buildings and equipment are depreciable straight line over their useful lives.

2

3. Pegasus Telecommunications Ltd (PTL) is considering rolling out a new cable Internet service. PTL is a taxable, publicly listed corporation operating in Australia. PTL’s management is in the process of analysing the project using the net present value method, and as a junior analyst you have been asked to gather the relevant information. For each of the following items explain briefly (no more than 1 sentence) why that item is or is not relevant to the NPV computation:

a. Last month the marketing department ran a focus group to determine consumer interest in the new service. An invoice for $2,500 has just arrived from the consultants involved in running the focus group.

b. PTL headquarters allocates central company costs to departments at a rate of $5,000 per employee per year.

c. PTL’s bank will charge an interest rate of 12% p.a. compounded monthly on the loan required to purchase the necessary hardware.

d. Equipment purchased will be depreciated straight line over 5 years.

e. The project will require the use of warehouse space already owned by PTL. The company estimates that the warehouse is worth $450,000.

3

4


Question Answer 1 +10,826 2 -43,073

1

FINM2401 Financial Management

Revision Questions for Mid-semester Exam (For tutorials in the week beginning 5 Sep 2011)

I. Role of the Firm

1. You’re looking at an investment opportunity in a small, un-listed (i.e. not on the ASX) company. The opportunity consists of purchasing ordinary shares of the company. It is anticipated that the shares will not be marketable for about 5 years, at which time additional shares will be floated on the ASX. Which of the following would be an appropriate opportunity cost to use in valuing the forecasted future cash flows from this investment? (explain your answers)

a. The current 90-day bank bill rate is 4.5%

b. The 10 year government bond rate is currently 6.2%

c. BHP Billiton bonds with 5 years to maturity trade at a yield of 7%.

d. The current rate on mortgages offered by the big four banks is around 6% p.a. compounded monthly.

e. You can take out a personal bank loan at 10.95% p.a. compounded monthly.

f. Talking to a venture capitalist friend, you find that unlisted companies in the same industry as your investment opportunity have a required return of 24% p.a.

2. Which of the following is an appropriate objective for financial managers (explain your answers)

a. Maximize market share

b. Maximize profit

c. Maximize share price

d. Maximize shareholder value

II. Time Value of Money

1. You have saved $60,000 and are in the market for your first home. After consulting with your local bank manager, you find that, based on the bank’s credit scoring model, you will be approved for a 25 year home loan as long as the monthly payments are no greater than $1,800. You will need to put aside $10,000 of your savings to cover closing costs and moving expenses.

a. If the bank’s current mortgage rate is 6% p.a. compounded monthly, what is the most expensive house you can afford to buy?

b. You find a house to your liking for $280,000, and end up borrowing $230,000. How much is your monthly payment? (The mortgage rate is still 6%)

c. What will the balance be on your loan after you’ve made 24 payments (2 years after purchase)? How much interest will you have paid over the first two years?

2

III. Bank Bills / Working Capital

1. A colleague has offered to lend you money at 6% p.a. compounding monthly so you can buy a $100 180-day Treasury bill that currently has a price of $97.81. Is this a good deal? What is the quoted rate on the Treasury bill? (NB: Treasury bills are priced with the same formula as bank bills)

2. Power Pack Ltd sells batteries and offers its customers the following terms: 2 per cent discount for payment within 7 days or full payment within 21 days. What effective annual interest rate is implicit in these terms?

3. To raise $97,000, a company draws up a bill of exchange with a face value of $100,000 payable in 180 days. What is the quoted rate (yield) on the bill? What is the implicit effective annual interest rate on the bill?

IV. Bonds

1. You have just bought a 10-year zero-coupon bond with a current yield of 8% and a face value of $10,000. If you sell the bond at the end of first year, what would your rate of return be? Assume that the current yield moves down to 7% at the time you sell.

2. You own some government bonds that have a face value of $2 million. The bonds have a coupon of 12% and mature a bit MORE than 6 years from today (91 days have passed since the last coupon payment). The current yield on these bonds is 9% p.a. How much would the bonds be worth if sold today? Draw a timeline!

3. You own 50 bonds issued by FlyByNite P/L. The bonds have a face value of $1000 each, a coupon rate of 10% p.a. with coupons paid annually, and mature 10 years from now. FlyByNite is currently in receivership the administrator has approached the debt holders with the following plan:

Debt holders will forgive the next two coupon payments – that is, there will be no coupon payments until 3 years from now.

FlyByNite will then pay all subsequent interest payments plus the face value as scheduled in the original bond instrument.

If debt holders do not approve the plan, FlyByNite will be liquidated and debt holders will receive 50 cents for each dollar of debt, payable immediately ($500 for each bond held). If the plan is approved, it is anticipated that FlyByNite will still be a fairly risky investment, and the appropriate opportunity cost for the bonds will be 30% p.a.

Should you vote to approve the plan? How much will the wrong decision cost you?

V. Shares

1. BAN is a company that pays just one dividend at the end of each year. The last dividend was $0.80 and was paid yesterday (thus, the next dividend is due in approximately one year). You task is to calculate the ‘theoretically correct’ share price for BAN. You are reasonably confident that a 12% per annum discount rate is

3

appropriate for companies with risk similar to BAN. Calculate BAN’s theoretical share price:

a. If you assume no growth in BAN’s dividend.

b. If you assume BAN’s dividend will grow at 1% per annum forever.

c. If you assume BAN’s dividend will grow at 1.5% per annum forever.

2. QuikGrow is forecasting dividends per share of 25 cents in 2004, 30 cents in 2005, 35 cents in 2006, 40 cents in 2007 and 45 cents in 2008. From 2009, dividends are expected to grow indefinitely at an annual rate of 2%. Assume that dividends are paid at the end of the year. If the required return on QuikGrow shares is 20% p.a., what are QuikGrow shares worth at the beginning of 2004? Draw a timeline.

3. You are a share analyst and have been asked to make a recommendation on QQQ Enterprises. After discussing the company’s prospects with management, and reading up on QQQ’s industry, you forecast next year’s dividend at 15 cents per share. Based on QQQ’s strategic plan, you believe that dividends will be constant for 8 years and will grow at a 3% rate after that. Based on the returns available on similar firms, you estimate the opportunity cost of equity for QQQ at 16% p.a. QQQ shares are currently selling at $0.80. What recommendation do you make and why?

VI. Net Present Value

1. (prior exam question1) Sculptorades Pty Ltd is in the business of making garden gnomes for sale to local landscape designers. As Chief Financial Officer of Sculptorades, you are investigating the purchase of a new gnome moulding machine. The machine costs $600,000. The machine will need to be replaced in two years, however, the machine manufacturer has agreed to repurchase the machine for $300,000 two years from now. For both book and tax purposes, the machine will be depreciated straight line to its salvage value of $300,000 over the two years. It is expected that the new machine will increase Sculptorades earnings by $300,000 per year in today’s dollars. Additionally, the increase in materials purchases will mean that Sculptorades will receive a discount of $10,000 per year in today’s dollars in each of the two years on materials used for their current line of garden gnomes. Sculptorades has already spent $25,000 investigating molding machines. You anticipate that inflation will be a constant 2% per year, and the relevant nominal opportunity cost is 15% p.a. For capital budgeting purposes, Sculptorades assumes all cash flows occur at the end of each year. Sculptorades faces a corporate tax rate of 30%.

a. Compute the annual net after-tax cash flows for the new gnome molding machine for years 0 through 2. (20 marks)

b. Compute the NPV of the gnome molding machine. (8 marks) c. Make a recommendation to management as to whether this machine should be

purchased. (2 marks)

1 This was a final exam question and was worth 30 points out of 100 on a two hour exam. It is much

more involved than any single question you might get on a 1 hour midsemester exam.

4

Selected Key Figure Answers

Question Final Answer

II. 1. c. Balance = $221,559.31 ($2)

Interest = $27,124.75 ($1)

III. 1. Quoted rate = 4.5403%

III. 2. EAR = 69.34%

III. 3. EAR = 6.3712%

IV. 1. One year return = 17.4314%

IV. 2. Price = $2,341,313.23

IV. 3. Wrong decision costs $12,720

V. 1. c. Price = $7.73

V. 2. Price = $2.02

V. 3. BUY

VI. 1. b. NPV = $63,181.70


Unit 4: Project Evaluation and Capital Budgeting 1. The Andy Aghastli Company (AAC) designs a range of eye-catching fluorescent tennis

clothing. The designers have always hand-drawn and painted their new fashion ranges. The owner, Mr Aghastli, is considering purchasing a new computer-aided design (CAD) package to allow his designers to create their designs on computers. The CAD project is expected to generate cost savings by improving productivity. Also, AAC can submit electronic templates of its latest designs to the manufacturers of its fashion ranges, which would also generate significant savings. The up-front hardware and software cost to AAC is estimated at $300,000. The computers and software have a 5-year useful life. After that, the technology will be obsolete and will have no salvage value. The CAD project is expected to save AAC approximately $88,000 (after tax) per annum.

REQUIRED:

Advise Mr Aghastli on the acceptability of the CAD proposal, applying the following capital budgeting methods:

a. Net Present Value,

b. Internal Rate of Return.

Assume that all cash flows occur at the end of each period, with the exception of the up-front outlay, which is paid at the commencement of the project. Assume that AAC’s required rate of return on this project is 10% p.a.

2. Kalorie Cola is considering buying a special-purpose bottling machine for $28,000. It is expected to have a useful life of 7 years with a zero disposal price. The plant manager estimates the following savings in cash-operating costs:

YEAR AMOUNT1 $10,0002 8,0003 6,0004 5,0005 4,0006 3,0007 3,000

Total $39,000

The Plant Manager argues that, since the total cash savings ($39,000) exceed the outlay ($28,000), Kalorie Cola should definitely purchase the machine.

REQUIRED:

a. Calculate whether the bottling machine should be purchased according to the following methods: (i) net present value, (ii) internal rate of return, and (iii) payback period. Kalorie Cola’s required rate of return is 16% p.a. and its policy is to reject projects that have a payback period in excess of 4 years.

b. Explain to the Plant Manager why his logic for purchasing the machine is flawed. Why can't we compare the total cash savings with the machine cost?

3. Toadstool Records intends to sign one of two bands to record a debut CD – Grim Reaper, a Melbourne grunge band, and Pretty Boys, a group of ex-hairdressers with a growing following in Sydney. For each band, the outlay costs (studio time, production, mastering, and video clip) differ. Grim Reaper’s CD would only cost $90,000 to produce because of the raw sound the band aims for. Pretty Boys’ CD would take considerably longer to record and the filming of the video clip would require extra expense for makeup and hairstyling – an expense not required for Grim Reaper.

The outlay costs to produce a CD are incurred up-front. Cash inflows from CD sales are expected over a two-year period; experience suggests that sales are minimal after that period. Toadstool Records management have forecast the following cash flows from signing each band:

YEAR GRIM REAPER

PRETTY BOYS

0 $(90,000) $(186,000) 1 60,000 120,000 2 60,000 120,000

Assume that all outlay costs are incurred up-front, while all cash inflows arise at the end of each year. Because of the risks involved in signing bands, Toadstool Records uses a 15% p.a. required rate of return.

REQUIRED:

a. Rank the projects in order of desirability according to net present value.

b. Rank the projects in order of desirability according to internal rate of return.

c. Why is there a difference in ranking between NPV and IRR?

d. When NPV and IRR give conflicting rankings, which method should be followed? Why?

4. Reconsider the cash flow data for Toadstool Records.

REQUIRED:

a. Complete the following schedule by calculating the net present value of signing each band, using a variety of required rates of return:

2

Net present value when required rate of return is: 0% 5% 10% 15% 20% 25% 30%

Grim Reaper Pretty Boys

b. Plot the data from the schedule in requirement (a) on a graph. Place the required rate of return on the horizontal axis and the NPV on the vertical axis. For each band, join the observations to form a line.

c. Calculate from the graph which band will be signed if Toadstool Records’ required rate of return is 15% p.a.

d. How can we interpret the point where each band’s line crosses the horizontal axis?

e. From the graph, explain why the NPV and IRR methods produce different ranking results. Which method is preferred.

5. A firm must choose a single project from two mutually exclusive alternatives: Projects X and Y. Each project requires a $10,000 initial outlay. The risk-adjusted discount rate on both projects is 10% p.a. Expected cash flows over each project’s useful life are:

Year X Y 0 $(10,000) $(10,000) 1 4,000 6,000 2 5,000 5,000 3 6,000 4,000

REQUIRED:

a. Before you do any calculations, just look at Projects X and Y. If you understand the concept of the time value of money, you should be able to immediately predict which project will have the higher NPV.

b. Calculate the net present value of each project. Was your prediction in (a) correct?

3

6. Consider the following after-tax cash flows for three mutually-exclusive projects:

Year A B C 0 -10,000 -8,000 -5,000 1 6,000 3,000 2,000 2 7,000 3,000 2,000 3 3,000 2,000 4 3,000 2,000 5 2,000

Clearly, the three projects have different scale (i.e., initial investment), as well as differing lives. Assume a 10% p.a. discount rate applies to all projects.

a. Assume that the projects will be repeated indefinitely. That is, Project A is repeated every two years, Project B is repeated every four years, and so on. Which project will you accept?

b. If the assumption that the projects can be repeated is invalid, which project will you accept.

c. Now just consider Projects A and B. Presumably in Part (a) you calculated annual equivalent annuities. We will get the same decision if we just assume Project A is repeated once at the end of its two-year life. Schedule the cash flows for Project A if it runs two cycles, calculate the NPV and compare it to Project B's NPV. Confirm that your ranking of projects in (a) is correct.

(If you are keen, you might do the same for A, B and C. That is, assume A is repeated 10 times, B is repeated 5 times, and C is repeated 4 times. Thus, you are equating projects over a 20-year horizon.)

7. Your office is about to purchase a new machine at a cost of $64,000. You have forecast the following data relating to salvage value and operating costs over the next five years:

YEAR

SALVAGE VALUE AT THE END OF THE YEAR ($)

ANNUAL CASH OPERATING EXPENSES ($)

1 50,000 11,000 2 40,000 13,000 3 30,000 18,000 4 23,000 24,000 5 3,500 28,000

If the machine is replaced every two years, $11,000 in expenses are incurred in year one and $13,000 in year two, and so on. The required rate of return is 15% p.a. The effects of company tax may be ignored (i.e., there is no need to calculate depreciation).

What is the optimum replacement policy for this machine? That is, should the office replace the machine every year, or every two years, or what?

4

5


Question Answer 4(a) +33,589 4(b) Between 14% and 15%

5 NPV = -2,631 IRR is close to 12%. Payback=3.8 years

6(a) NPVGR = 7,543 NPVPB = 9,085

6(b) IRRGR = 21.5% IRRPB = 18.8%

8 NPVX = 2,276 NPVY = 2,592

9(a) A is best 9(b) Depends 9(c) A is best 10 Replace every 2 years.

AE2 = -32,693


Note Q1 and Q2 deleted

3. Consider the following data for Assets 1 and 2:

Asset Expected Return

Standard Deviation

1 20% p.a. 40% p.a. 2 12% p.a. 20% p.a.

Your task is to construct a portfolio opportunity set. To do this we construct a graph with risk (the standard deviation of the portfolio) on the horizontal axis and the expected return of the portfolio on the vertical axis. The portfolio opportunity set is a line or curve that demonstrates the portfolio risk and return for different combinations of the two assets. For example, one possible portfolio involves 60% in Asset 1 and 40% in Asset 2, another involves 25% in Asset 1 and 75% in Asset 2, and so on. The portfolio opportunity set is a line or curve that shows the risk and return of every possible portfolio of the two assets. In this case, we want to construct a spreadsheet that takes the above data, plus the correlation between the returns of the two assets, as inputs. We want to be able to change any input and immediately see the effect on the portfolio opportunity set.

At the top of the spreadsheet, have an input area where you can enter the above information, as well as the correlation between the returns of the two assets (1,2) . All the formulae below should be cross-referenced to these input cells.

Create two columns of weights representing how much is invested in Asset 1 and how much is invested in Asset 2. Start with 100% in Asset 1 and 0% in Asset 2, the next row is 99% in Asset 1 and 1% in Asset 2, and so on right through to 0% in Asset 1 and 100% in Asset 2.

In the third column, write in the formula for the expected return of the portfolio.

In the fourth column, write in the formula for the standard deviation of the portfolio (don't forget to take the square root of variance).

Plot the fourth column on the horizontal axis and the third column on the vertical axis (use an “XY scatter plot” in Excel).

Start with correlation of -1.0. Your graph should look like two line segments. Now change the input cell for correlation to (say) +1.0. The portfolio opportunity set should now be a straight line. Now try correlation of 0.5. Try whatever values of correlation you like. Notice how the curve gets a bigger “loop” in it as the correlation gets smaller. This demonstrates that the lower the correlation between the assets, the greater the benefits from diversification.

2

4. You intend to make an investment in one stock and have the following stocks to choose from:

Stock

Expected Return

Standard Deviation

A 20% p.a. 10% p.a. B 30% p.a. 50% p.a. C 15% p.a. 12% p.a. D 20% p.a. 15% p.a. E 35% p.a. 40% p.a. F 25% p.a. 15% p.a.

Since every person's preferred investment will differ, depending on their level of risk aversion, we cannot say for certain which stock you will choose. The risk-return characteristics of some stocks, however, clearly dominate others.

a. Begin by plotting each stock on a graph with risk (standard deviation) on the horizontal axis and expected return on vertical axis. Just plot a single point for each stock.

b. If you had to choose just between stocks A and D, which dominates?

c. If you had to choose just between stocks D and E, which dominates?

d. If you had to choose just between stocks B and E, which dominates?

e. If you had to choose just between stocks A and C, which dominates?

f. If you had to choose just between stocks A and F, which dominates? How about E and F? How about C and D?

5. You plan to combine the following two stocks into a portfolio, with 25% in Stock 1 and 75% in Stock 2:

Stock

Expected Return

Variance 2

1 10% 0.0064 2 23% 0.0144

g. Assume the correlation between the two stocks is 0.12,1 . Calculate the

expected return and risk (ie. standard deviation) of the portfolio.

h. Now assume that the correlation between the stocks is more typical: 1,2 0.30 . Re-calculate the expected return and risk of the portfolio. Why is

the risk lower now than in (a)?

3

6. Use the same data table for Stocks 1 and 2 as Question 5, and assume the correlation between stocks is 0.30. You are less risk-averse than the average investor, and are aiming to construct a portfolio comprising Stocks 1 and 2 that has an expected return of 29.50%. You realize this portfolio will have a higher risk, but are happy to tolerate it.

i. What weighting in each stock will give a portfolio with the desired expected return? (Hint: you’ll need to short sell one of the two stocks.)

j. Calculate the risk (i.e., standard deviation) of this portfolio.

4


Question Answer 5(a) E(rp) = 19.75% p.a.

Std dev = 11% p.a. 5(b) E(rp) = 19.75% p.a.

Std dev = 9.788% p.a. 6(a) +150% in Stock 2 and -50% in Stock 1 6(b) 17.23% p.a.


Unit 5: Diversification and Portfolio Analysis 1. You construct a three-asset portfolio. Relevant information is as follows:

Asset Proportion Expected Return (%)

Standard Deviation (%)

1 0.3 10 12 2 0.3 12 30 3 0.4 14 20

Also suppose the correlation between the returns of the various assets is:

Correlation Matrix

1 2 3 1 1.0 0.3 0.4 2 0.3 1.0 0.2 3 0.4 0.2 1.0

What is the variance of this portfolio and what proportion of this variance is due to each of the three component assets?

Unit 6: The Capital Asset Pricing Model 1. Three stocks have the following risk-return characteristics:

Stock Expected Return

Standard Deviation

A 20% 38% B 12% 15% C 15% 28%

a. If there is no risk-free asset, does any of these three stocks clearly dominate

any other in terms of risk and return?

Now assume there is a risk-free asset with a guaranteed return of 5% p.a. You can now form a portfolio consisting of one risky asset plus the risk-free asset. You are willing to bear a standard deviation of 25% p.a. for your portfolio.

b. For a portfolio comprising Stock A and the risk-free asset, what weights will you assign to each in order to get the desired level of risk? What is the expected return on this portfolio? Repeat this for Stock B, then Stock C.

c. Which of the three assets is dominant? (There is a clear winner.)

Commentary:

• This question illustrates how the introduction of a risk-free asset enables us to clearly identify the dominant asset. We could not do this in (a) when there was no risk-free asset.

• The answers do not depend on my desired level of risk (standard deviation of 25% p.a. above). If you re-do the entire question with a desired level of risk of 10% p.a. standard deviation, you'll still get the same dominant asset.

• To see why one asset dominates, plot the risk-return characteristics of the three assets on the usual graph. Draw a line connecting each asset with the risk-free asset. The dominant asset is the one with the steepest slope.

2. Consider the following information for Stocks 1 and 2:

Stock

Expected Return

Standard Deviation

1 20% 40% 2 12% 20%

The correlation between the returns of these two stocks is 0.3.

a. How will you divide your money between Stocks 1 and 2 if your aim is to achieve a portfolio with an expected return of 18% p.a.? That is, what are the weights assigned to each stock? Also take note of the risk (i.e., standard deviation) of this portfolio.

Now assume that, in addition to the two risky stocks, there is a risk-free investment with a guaranteed return of 5% p.a. This gives you the opportunity to use the risk-free asset in your portfolio.

b. You create a portfolio with 79.65% of your funds invested in Stock 1 and 20.35% invested in the risk-free asset. Calculate the expected return and standard deviation of this portfolio.

c. How does the portfolio in (b) compare to the portfolio in (a)? Which portfolio do you prefer? Why?

d. Calculate the weights in the risk-free asset and Stock 2 that are required to achieve a portfolio with the same risk as in (a) and (b). How does its expected return compare? (Hint: you will have to borrow at the risk-free rate and invest the proceeds in Asset 2 to get the desired risk for this portfolio.)

e. Finally, consider a third risky asset: Stock 3. Stock 3 has an expected return of 15% p.a. and standard deviation of 25% p.a. Does the combination of the risk-free asset and Stock 3 dominate the combinations previously examined?

2



7 2pσ = 0.02292

15%, 46%, 39% Unit 6

1b: A & rf B & rf C & rf

0.6579:0.3421 1.67:-0.67

0.8929:0.1071 2a 2b 2d

2e

0.75:0.25 16.95% and 0.3186

1.593:-0.593 16.15% and 0.3186 17.74% and 0.3186

3


Unit 6: The Capital Asset Pricing Model 1. Assume the following data:

• the market risk premium is 7% p.a.

• the variance of the return on the market is 0.14, and

• the risk-free rate is 6% p.a.

Your task is to determine a discount rate appropriate for a single company, BHP. If the variance of BHP's return is 0.30 and its beta is 1.20, what is the expected return of BHP?

2. The risk-free rate is 7% p.a. The expected return on the market portfolio is 12% p.a., and the variance of this return ( )σ 2

m is 0.09.

You are examining two stocks: A and B. The standard deviations of the return on Stocks A and B are 50% p.a. and 20% p.a. respectively. The correlation between each stock and the market is: , ,0.90, 0.60A m B mρ ρ= = .

a. Calculate the beta of each stock.

b. Calculate the expected return of each stock.

c. You construct a portfolio with 60% of your money in Stock A and 40% in Stock B. What is the beta of this portfolio? What is the expected return of this portfolio?

Hint: The beta of Stock A is equal to its covariance with the market divided by the variance of the market:

( )( )

cov ,var

A mA

m

r rr

β = .

Hint: Covariance is a function of the standard deviation of each asset and the correlation between them.

3. In the following table, X, Y, and Z refer to stocks, while M refers to the market portfolio. The following partially complete information is available:

Standard Deviation

ExpectedReturn

Covariance between

Stock and Market X Y Z M

0.1 0.2 ?

0.1414

? ?

0.216 0.120

0.01 0.025 0.052 n/a

The correlation between Stocks X and Y is 0.60.

a. Calculate the betas of Stocks X and Y.

b. Calculate the beta of a new portfolio comprising 80% in X and 20% in Y.

c. What is the risk-free rate of return?

d. What is the expected return on the new portfolio in (b)?

4. In a small economy, the market portfolio comprises shares in only three companies: D, E and F. Details are set out in the table below.

Company name Shares issued Price per share Expected return D 1,000,000 $ 2.00 8% E 500,000 $ 8.00 10% F 1,600,000 $ 2.50 21%

There is also a risk-free asset that offers a return of 4%.

a. Calculate the expected return on the market portfolio.

b. Assuming that the capital asset pricing model applies in this market, calculate the beta (β) of company E.

c. Suppose you wished to invest $25,000. Which investments would you make to achieve the most efficient portfolio possible with a beta (β) of 0.6? Be specific in your answer, providing (for example) details as to which share(s) you would purchase and the number you would purchase.

5. You are currently planning an investment strategy designed to partially finance your eight-year-old child's education. You have $10,000 to invest and your child will begin university studies ten years from now. Your financial advisor recommends that you buy some Telstra shares. Telstra shares have a beta of 0.9 and the returns on Telstra shares have a standard deviation of 40% p.a. The riskless rate of interest is 5% p.a. and the market risk premium is 7% p.a. The standard deviation of the return on the market is 20% p.a.

a. If you follow the advice of your financial advisor, how much do you expect to have available when your child begins university?

2

b. You become aware that your bank is marketing an Australian Equities Index Fund. The goal of this fund is to exactly match the performance of the S&P ASX 300 Index (a broad stock market index). If you invest in this fund, rather than the Telstra shares, how much do you expect to have available when your child enters university?

c. Finally, a colleague suggests that you shouldn't limit yourself to choosing between investing everything in Telstra or everything in the index fund. He suggests that you can do even better by diversifying. In particular, he suggests an equally-weighted portfolio consisting of $5,000 invested in Telstra shares and $5,000 invested in the index fund. What do you think about your colleagues advice?

3

4


Question Answer 3 14.4% 4a 4b 4c

1.50 and 0.40 14.5% and 9% 1.06 and 12.3%

5a 5b 5c 5d

0.50 and 1.25 0.65 6%

9.9% 6a 6b

14% 0.6

7a 7b

$29,171 $31,059


Unit 7: Cost of Capital 1.

a. Calculate the WACC of Pippin Ltd, using the following information:

Balance sheet extract Liabilities 10% debentures ($100 par) $50,000,000 Shareholders’ funds Paid-up capital – ordinary shares ($1 par) $30,000,000

Additional information

Ordinary shares pay a dividend of 68 cents per year, and are expected to pay the same dividend amount indefinitely.

Commonwealth government bonds trade at 5%.

The return on the market portfolio is 13%

Pippin Ltd’s beta is 1.5.

Its debentures are priced at $106.

The current return on Pippin Ltd debentures is 2% above the government bond rate.

No company or personal taxes are levied.

The existing capital structure is unlikely to change.

b. Explain how and why Pippin Ltd might use the WACC you’ve just computed.

c. Ash Ltd, a privately held firm, is in the same industry as Pippin Ltd. Ash’s operations are primarily in rural and regional areas. Ash is computing its WACC, but feels that they should be using a higher beta than Pippin Ltd for the following reasons:

Ash faces a higher risk of bush fires

Due to it’s rural locations, storm damage is more likely to affect the company’s assets

In your opinion, is this reasoning valid? Explain

2. Big Company LTD is investigating whether or not to proceed with project X. It is considered that project X is of the same nature of business as all existing operations and as a result the firm present WACC can be used to calculate its viability.

The cash flows associated with the project are as follows:

Year 0 1 2 3 4 Net Cash Flow

-20,000 2000 5000 5000 15,000

Other information

BALANCE SHEET OF BIG COMPANY ($thousands) Current Assets 10,000 Current Liabilities 8,000 Net fixed Assets 25,000 Long-term debt 10,000 Investments 15,000 Deferred taxes 3,000

Shareholders' equity 30,000 Total 50,000 Total 50,000

Corporate Tax Rate 30% Number of shares on issue 10 million Current Share Price $ 7.25 Equity Beta 1.47 Expected Return on the Market 12% Risk Free Rate applicable 7%

Long Term Debt consists of "Junk" Bonds issued at a face value of $7 million. These pay interest semi-annually at a rate of 16% p.a. (compounding semi-annually). They have 3 years to maturity. Long Term Debt also includes a secured liability to Huge Company Ltd which currently sits in the books at $3 million. Interest is payable annually on this at a fixed rate of 10% p.a. (which is also the current market rate for this liability). The market yield on the junk bonds is 18%p.a. (compounding semi-annually)

Compute the WACC of Big Company and determine the project's NPV.

3. You are the Chief Financial Officer of Greg Normal Ltd (GN). GN runs a chain of miniature golf courses in the Melbourne metropolitan area and would like to expand to other capital cities. GN’s Property Department has located land for a new mini golf course in Brisbane. The land costs $5 million, and development costs for the mini golf course and attached entertainment complex are estimated at $130 million. GN’s Marketing Department has determined that the current mini golf fad will last 8 years. After that time, you anticipate that the net salvage value (after disposal costs) for the land and equipment will be $20 million ($5 million for the land and $15 million for the equipment). Net revenue (EBDITA) from the mini golf course is expected to be $37 million in the first year of operation, and should grow at a rate of 4% per year over the 8 years the course will be operational.

Should GN purchase and develop this land?

Additional Information:

2

• GN’s Balance sheet at 31 December 2002:

Book Values ($m) as of 31/12/02 Cash $35.20 Accounts Payable $68.20 Accounts Receivable $75.20 Bank Loans $98.30 Inventory $132.70 Debentures $175.00 Plant and Equipment $426.40 Contingent Liabilities $10.00 Accum Deprec -$182.70 Retained Earnings $105.30

Paid in capital $30.00

Total Assets $486.80 Total Liabilities & Equity $486.80

• Accounts payable consist of trade accounts payable within 30 days.

• Bank Loans consists entirely of a mortgage on GN’s current premises. The mortgage has a fixed interest rate of 6.7% p.a., compounded monthly, and has exactly 10 years remaining. The book value is equal to the remaining principal balance on the loan.

• Current bank loans with similar terms are offered at 8.2% p.a. compounded monthly.

• Debentures are on the books at their face value. They have 10 years remaining and pay coupons twice per year. The coupon rate is 5%, and similar bonds currently trade at a yield of 7.5%

• Goodwill relates to the purchase of one of GN’s properties in Melbourne, and will be amortised over the next 10 years.

• Paid in capital consists of 120 million ordinary shares issued at 25 cents per share.

• Based on similar traded companies, it is estimated that GN’s shares have a beta of 1.25.

• The current risk free interest rate is 5%, and the market risk premium is estimated at 8%.

• Ordinary shares just paid an annual dividend of 33 cents per share. It is expected that dividends will grow at a rate of 4% per year.

• The corporate tax rate is 30%.

3

4


Question Answer 1 WACC = 13.94% 2 WACC=13.99%

NPV=-2,137.38 3 WACC=11.3551%

NPV=43.668

Documents

FINM2401 Tutorial