200488 CORPORATE FINANCIAL MANAGEMENT

Autumn 2009 Abbreviated Tutorial Exercise Solutions

Weeks 2-6

TUTORIAL WEEK 2 1. Find the interest earned over 3 years on an

investment of $3000 paying simple interest of 7.5% per annum (p.a.).

Answer: $675 2. For the following investments find the compound

amount (future value) and total interest earned. Assume no interest is withdrawn before the term of the investment is reached. (i) $10,000 over 6 years earning 5% p.a.

compounded annually.

( )96.400,3$earnedInterest

96.400,13$ 05.01000,10 66

=≈+=FV

(ii) $6,000 over 4 years and 6 months earning 9%

p.a. compounded quarterly.

52.955,8$ 409.01000,6

18

≈⎟⎠⎞

⎜⎝⎛ +=nFV

1

Interest earned = $2,955.52

(iii) $5000 over 2 years earning 10% p.a. compounded daily. (Assume 365 days per year)

85.106,1$ earnedInterest

85.106,6$ 365

1.01000,5730

2

=

≈⎟⎠⎞

⎜⎝⎛ +=FV

3. Find the present value of $8,000 due in 5 years’

time at 10% per annum compounded monthly.

31.862,4$12

1.01000,8)125(

=⎟⎠⎞

⎜⎝⎛ +=

×−

PV

4. An amount of $6,000 is invested for a period of 6

years and earns interest at a rate of 12% per annum compounded monthly. What is the effective annual rate of interest earned on the investment? Express your answer as a percentage rounded to 2 decimal places.

%)68.12(1268.011212.01

12

≈−⎟⎠⎞

⎜⎝⎛ +=EAR

2

5. Gitman, Juchau and Flanagan (GJF, i.e. the textbook), Problem 2-10 (p. 78).

“The balance sheet for Rogers Industries for 31 December 2006 is given below. Information relevant to Rogers Industries’ 2007 operations is given following the balance sheet. Using the data presented: (a) Prepare an income statement for Rogers

Industries for the year ended 31 December 2007. Be sure to show EPS.

(b) Prepare a balance sheet for Rogers Industries for 31 December 2007.

Balance sheet ($000) Rogers Industries 31 December 2006 Assets Liabilities and shareholders’ equity Cash Marketable securities Accounts receivable Inventories Total current assets Non-current assets Less Accumulated depn. Net non-current assets Total assets

$401080

100$230

$890 240$650$880

Accounts payable Notes payable Accruals Total current liabilities Non-current debt Preference shares Ordinary shares (80,00 shares) Retained earnings Total shareholders’ equity Total liabilities and shareholders’ equity

$5080

10$140$270

40320

110$470

$880

3

Relevant Information Rogers Industries 1. Sales in 2007 were $1.2 million. 2. Cost of goods sold equals 60% of sales. 3. Operating expenses equal 15% of sales. 4. Interest expense is 10% of the total beginning

balance of notes payable and non-current debts. 5. The firm pays 40% taxes on ordinary income. 6. Preference dividends of $4,000 were paid in

2007. 7. Cash and marketable securities are unchanged. 8. Accounts receivable equals 8% of sales. 9. Inventory equals 10% of sales. 10. The firm acquired $30,000 of additional non-

current assets in 2007. 11. Total depreciation expense in 2007 was

$20,000. 12. Accounts payable equals 5% of sales. 13. Notes payable, non-current debt and

shareholders’ equity were unchanged. 14. Accruals are unchanged. 15. Cash dividends of $119,000 were paid to

ordinary shareholders in 2007.”

4

(From solutions manual) (a)

Rogers Industries Income Statement

for the Year Ended 31 December 2007 Sales $1,200,000

Less: Cost of goods sold 720,000 Gross profit $ 480,000

Less: Operating expenses 180,000 Operating profits $ 300,000

Less: Interest expense 35,000 Net profits before taxes $ 265,000

Less: Taxes at 40% 106,000 Net profits after taxes $ 159,000

Less: Preference dividends 4,000 Earnings available to ordinary shareholders $155,000

Earnings per share (EPS) $1.9375

5

(b) Rogers Industries

Balance Sheet 31 December 2007

Assets Current assets:

Cash $ 40,000 Marketable securities 10,000 Accounts receivable 96,000 Inventories 120,000

Total current assets $ 266,000 Gross Non-Current assets $ 920,000

Less: Accumulated depreciation 260,000 Net assets $ 660,000 Total assets $ 926,000

6

Liabilities and shareholders' equity: Current liabilities:

Accounts payable $ 60,000 Notes payable 80,000 Accruals 10,000

Total current liabilities $150,000 Non-Current debt 270,000

Total liabilities $420,000 Shareholders' equity

Preference shares $ 40,000 Ordinary shares 320,000 Retained earnings 146,000 ($110,000+$155,000-$119,000)

Total shareholders' equity $506,000 Total liabilities and shareholders' equity $926,000 6. GJF, Problem 2-11 (p. 79)

“Hayes Enterprises began 2007 with a retained earnings balance of $928,000. During 2007 the firm earned $377,000 after taxes. From this amount, preference shareholders were paid $47,000 in dividends. At year-end 2007 the firm’s retained earnings totalled $1,048,000. The firm had 140,000 ordinary shares during 2007. (a) Calculate retained earnings for the year ended

31 December 2007 for Hayes Enterprises. (Note: Be sure to calculate and include the amount of ordinary dividends paid in 2007)

(b) Calculate the firm’s 2007 EPS.

7

(c) How large a per share cash dividend did the firm pay on ordinary shares during 2007?”

(From solutions manual) (a)

$210,000928,000) - (1,048,000 - 47,000 - 377,000

earnings retainedin change -dividends preference-safter taxeprofitsNet dividends Ord.

==

=

Hayes Enterprises

Statement of Retained Earnings for the Year Ended December 31, 2007

Retained earnings balance (January 1, 2007) $928,000

Plus:Net profits after taxes (for 2007) 377,000 Less:Cash dividends (paid during 2007)

Preference stock (47,000) Ordinary (210,000)

Retained earnings (December 31, 2007) $1,048,000 (b)

36.2$000,140

000,47000,377 shareper Earnings

=

−=

(c)

50.1$140,000

000,210 shareper dividendCash ==

8

TUTORIAL WEEK 3 1. To achieve a savings goal of $15,000 in 3 years’

time, an individual decides to make 6 equal deposits in a savings account at 6-monthly intervals starting now. If the interest rate is 9% per annum compounded semi-annually, what will each deposit be?

045.0=i

01.137,2$1)045.1(

045.0)045.01(

000,156 =⎥

⎦

⎤⎢⎣

⎡−+

=PMT

2. A firm currently has a debt of $120,000 that is to be

repaid by equal quarterly (3-monthly) payments at the end of each quarter for the next 3 years, with the first payment to be made one quarter from now. If the interest rate is 12% per annum compounded quarterly, answer the following: (a) What will be the quarterly payment? (b) What will be the principal outstanding

(amount owing) 2 years from now (i.e. immediately after the eighth quarterly payment is made)?

(a)

45.055,12$)03.1(1

)03.0(000,12012 =

−= −PMT

9

(b)

29.811,44$03.0

])03.1(1[45.055,12 4

=− −

3. A firm’s managers wish to have $300,000 available

in 3 years’ time from now to allow for a planned renovation of the firm’s factory at that time. To accumulate this amount, the firm’s managers decide to make equal monthly deposits into a fund over the next 3 years. The fund earns interest of 12% per annum compounded monthly. (a) Suppose 36 equal monthly deposits are made

into the fund, with the first deposit made immediately (i.e. at 0=t ). What should each deposit be if there is to be $300,000 in the fund in 3 years’ time? (No withdrawal is made from the fund over the 3-year period)

(b) Suppose that instead, only 30 equal monthly deposits are made into the fund, with the first deposit made in 7 months’ time. What should each deposit be now if there is still to be $300,000 in the fund in 3 years’ time from now? (Again no withdrawal is made from the fund until the end of 3 years from now).

10

(a)

34.895,6$01.0

)01.1](1)01.01[(000,30036

=

−+=

PMT

PMT

(b)

43.624,8$01.0

]1)01.01[(000,30030

=

−+=

PMT

PMT

4. A football association wishes to create a perpetual

prize of $50,000 each year for the ‘best and fairest’ player in its football competition by making an immediate investment. Supposing an interest rate of 8% per annum compounded annually, how much money will the association need to fund the annual prize now if the prize is first awarded: (a) in one year's time, (b) two years from now? (Assume that the prize will indeed be awarded at yearly intervals subsequent to the first award being made)

(a)

$625,000 08.0000,50

==∞PVA

(b)

( ) 70.703,578$ 08.1000,625 1 =−

11

5. In order to replace a machine in the future, a firm plans to deposit 10 equal amounts into a fund at yearly intervals so that the amount in the fund will be $30,000 when the 10th (last) deposit is made. Initially the fund earns 8% per annum compounded annually, however after 4 years the interest rate unexpectedly increases to 9% per annum compounded annually. If the firm reduces its annual deposit to take account of the higher interest rate, what will be the new annual payment for the last 6 years? (Hint: Proceed by first calculating the regular deposit amount under the initial conditions, then the amount in the fund once the fourth deposit is made, then the new deposit after four years)

Initial yearly payment 1PMT=

88.070,2$1)08.1(

)08.0(000,30]1)1[( 10

1

11 =

−=

−+×

= niiFVAPMT

Amount in the sinking fund after 4 years

1

4

62.331,9$08.0

]1)08.1[(88.070,2 FVA==−

=

2

6 06.650,15$)09.1(62.331,9 FVA== after 10 years Let

32 94.349,14$06.650,15000,30000,30 FVAFVA ==−=−

12

39.907,1$1)09.1(

)94.349,14(09.062 =−

=PMT

13

TUTORIAL WEEK 4 1. GJF, Review Question 5-7 (p. 218)

“When is the coefficient of variation preferred over the standard deviation for comparing asset risk?”

See text/lecture notes 2. GJF, Review Question 5-11 (p. 237)

“How are total risk, non-diversifiable risk and diversifiable risk related? Why is non-diversifiable risk the only relevant risk?”

See text/lecture notes 3. GJF, Problem 5-4 (p. 241)

“Sharon Smith, the financial manager for Barnett Corporation, wishes to evaluate three prospective investments –X, Y and Z. Currently the firm earns 12% on its investments, which have a risk index of 6%. The three investments under consideration are profiled below in terms of expected return and expected risk.

14

Investment Expected Return Expected risk

index X Y Z

14% 12 10

7% 8 9

(a) If Sharon were risk-indifferent, which

investments would she select? Why? (b) If Sharon were risk-averse, which investments

would she select? Why? (c) If Sharon were a risk-seeker, which

investments would she select? Why? (d) Given the traditional risk preference

behaviour exhibited by financial managers, which investments would be preferred? Why?

(From solutions manual) (a) The risk-indifferent manager would accept

Investments X and Y because these have the same or higher returns than the 12% required return and the risk doesn’t matter.

(b) The risk-averse manager would accept Investment X

because it provides the highest return and has the lowest amount of risk. Investment X offers an increase in return for taking on more risk than what the firm currently earns. (Although there is nothing in the question that allows us to assess whether this increase in return is sufficient to compensate for the increased risk)

15

(c) The risk-seeking manager would accept Investments Y

and Z because he or she is willing to take greater risk without an increase in return.

(d) Traditionally, financial managers are risk-averse and

would choose Investment X, since it provides the required increase in return for an increase in risk.

4. The numbers below represent the annual return in

% earned on shares held in a particular company for the 8 successive years. Considering these returns as a sample of returns on the shares, calculate the sample mean return and the sample standard deviation of the returns. Round your answer to 4 decimal places, if necessary.

4.5, 8, 9.6, 2.3, 0.5, 2.8, 4, 8.3

(Sample) mean return 5)( == k (Sample) standard deviation of returns

2663.31

)(1

2

≈−

−=σ

∑=

n

kkn

ii

k

16

5. In the following table, returns to two assets (A and B) are given for different states of nature with the stated probabilities of occurring. Calculate the expected (mean) return, standard deviation of returns and coefficient of variation of returns for each asset. Which asset would be considered more risky?

State of Nature Probability Return A Return B

(1) (2) (3) (4)

0.20 0.35 0.40 0.05

23% 11% 7%

19%

9% 6%

-3% -6%

For asset A:

%2.12=k For asset B:

%4.2=k For asset A:

%0795.696.36 ≈=σ For asset B:

%3329.544.28 ≈=σ For asset A:

4983.0≈Vc For asset B:

2220.2≈Vc

17

6. Given the same information as in question (5) above, calculate the expected return and standard deviation of the following two portfolios with weights as given. (Hint: Start by calculating the return to each portfolio under each state of nature)

Portfolio Asset A Weight Asset B Weight

X Y

0.40 0.64

0.60 0.36

For portfolio X:

%32.6)4.2(6.0)2.12(4.0 =+=pk For portfolio Y:

%672.8=pk Then, using the hint. State of nature Portfolio X

Return (%) Portfolio Y Return (%)

(1) (2) (3) (4)

14.60 8.00 1.00 4.00

17.96 9.20 3.40

10.00 pk (%) 6.32 8.672

pσ (%) 5.1273 5.3439

18

7. The following table shows the returns (in percent) on ordinary shares A and B in three possible states of nature, together with the probabilities of these states of nature occurring.

State of Nature

Probability Return on A (%)

Return on B (%)

Recession Normal Boom

0.2 0.4 0.4

4 6 8

12 5 2

With reference to the above table: (a) Calculate the expected return and standard

deviation of returns for A shares and for B shares (separately).

(b) If a risk averse investor had to choose between holding A shares and holding B shares, which would he/she choose. Give a reason for your answer.

(c) If an investor were to form a portfolio consisting of A and B shares, would it be possible for the portfolio to offer a lower standard deviation of returns than both A and B shares, and an expected return that is not lower than the expected returns of both shares? Give a reason for your answer (Hint: you should be able to give a reason for your answer without having to perform any further calculations)

19

(i)

4.6)8(4.0)6(4.0)4(2.0 =++=k 2.5)2(4.0)5(4.0)12(2.0 =++=Bk

%50.124.2)4.68(4.0)4.66(4.0)4.64(2.0 222 ≈=−+−+−=σ A %66.336.13)2.52(4.0)2.55(4.0)2.512(2.0 222 ≈=−+−+−=σB

(ii) A risk averse investor would prefer A shares. (iii) No it would not be possible to form a portfolio

consisting of the two assets that satisfies both requirements. Certainly, from the table of returns we see that the returns on the two shares are negatively correlated, which means that they may be combined to give a portfolio with a lower standard deviation of returns than that of the asset (share A) with the lower standard deviation of returns. However, the expected return on any portfolio consisting of positive amounts of both A and B shares will be between the expected returns on the individual shares, therefore it could not be lower than the expected returns of both shares.

20

TUTORIAL WEEK 5 1. GJF, Review Question 5-14 (p. 237)

See text/lecture notes 2. The expected return on a portfolio of shares is

8.9% per annum and the portfolio has a beta of 1.3. If the expected return on the market portfolio is 8 per annum and the assumptions of the capital asset pricing model hold, what is the annual risk free rate of interest? Also state what the market risk premium is.

From the security market line

%5)8(3.19.8

=−+=

F

FF

rrr

Market risk premium %3= 3. Suppose a share in CFM Incorporated is expected

to be worth $50 in three years’ time. The expected return on the market portfolio is 8% per annum, the risk free rate is 5% per annum, and the beta of UWS Incorporated shares is 1.75. Assuming the CAPM is valid and that no dividends are expected to be paid over the next three years, how much should you be willing to pay for one CFM Inc. share now?

21

From the security market line, the expected rate of return on the shares is

%)25.10(1025.0=jk You should be willing to pay (per share)

31.37$)1025.01(

5030 =

+=P

4. (a) State what is meant by the term structure of

interest rates and the yield curve. (b) Distinguish between interest rate risk and

default risk. See text/lecture notes 5. A particular issue of government bonds has a per

bond face value of $1,000, a coupon rate of 7.5%, and mature in 20 years’ time. If the current yield to maturity is 9.5% and the bonds pay interest annually, what is the current price of these bonds?

We have

75.823$)095.01(

000,1095.0

])095.01(1[7520

20

0

=+

++−

=−

B

22

6. The oldest issue of Auston Incorporated bonds mature in one year’s time when the final annual coupon of $60 will be paid together with the par (face) value of $1,000 per bond. (a) What is the current annual yield on these

bonds if their current price is $950? Express your answer as a percentage correct to two decimal places (as there is only one year involved, this can be calculated by hand).

(b) If instead the bonds paid semi-annual coupons but still had the same effective annual yield as in (i), what would be the bond’s annual yield quoted in the financial press? Express your answer as a percentage correct to two decimal places.

(i) We have

1158.01950

000,1601

11

0

0

=−+

=−+

=

++

+=

BMIk

kM

kIB

d

dd

or 11.58% (ii)

1158.01)21( 2 =−+ dk 1126.0=dk

or 11.26%

23

7. An opal mining company has known resources that are being depleted at a constant rate, resulting in a constant fall in earnings and dividends of 6% per annum. The company’s current dividend is $10 per share and investors require a return of 12% on the company’s shares. What is the current price of the firm’s shares?

We use the constant dividend growth (Gordon) model

22.52$)06.0(12.0

)06.01(100 =

−−−

=P

8. The ordinary share annual dividend of the ABC

Corporation is expected to grow by 4% per annum over the next 3 years and at a constant rate of 1% per annum thereafter. If the latest dividend (just paid) is $5 per share, what is the maximum amount an investor who has these expectations would be prepared to pay now for one of the firm’s ordinary shares if she requires a return of 8% per annum?

We use the variable dividend growth model:

34.78$01.008.0

)01.1()04.1(5)08.1(

1)08.1()04.1(5

)08.1()04.1(5

08.1)04.1(5 3

33

3

2

2

0

=

⎟⎠

⎞⎜⎝

⎛−

+++=P

24

TUTORIAL WEEK 6 1. A company involved in the production of HIV

(human immunodeficiency virus) blood tests is considering bringing in a new type of test that is slightly different from its currently marketed test. For the project involving introduction of the new test, which of the following costs are relevant for an analysis of whether the new test should be introduced? (a) $1.2 million spent last year on research and

development of the new test. (b) An increase in annual marketing costs of

$800,000 if the new test is introduced. (c) A drop in annual sales of the existing test of

$2.4 million if the new test is introduced. (d) Laboratory facilities already owned by the

company that could be used to produce the test and are currently valued at $1.5 million.

Only (b) and (c) would be included in the calculation of relevant incremental cash flows. 2. Give definitions of the following:

(a) Conventional projects (b) Incremental net cash flows

See text/lecture notes

25

3. GJF, Problem 8-18 (p. 376)

“Cushing Limited is considering the purchase of a new grading machine to replace the existing one. The existing machine was purchased three years ago at an installed cost of $20,000. It was being depreciated using the prime cost method with an effective life of five years. The existing machine is expected to have a usable life of at least five more years. The new machine costs $35,000 and requires $5,000 in installation costs. It will be depreciated using the prime cost method over five years. The existing machine can currently be sold for $25,000 without incurring any removal or clean-up costs. The firm pays 40% taxes on both ordinary income and capital gains. Calculate the initial investment associated with the proposed purchase of a new grading machine.”

(From solutions manual) Installed cost of new asset = =35,000 + 5,000 = $40,000 (depreciable value) Book value of existing machine =

$20,000 – ⎟⎠⎞

⎜⎝⎛ ×

5)3000,20($ = $8,000

26

From the sale of the existing machine, we would have: Recovered depreciation = 20,000 – 8,000 = $12,000 Capital gain = 25,000 – 20,000 = $5,000 Tax on recovered depreciation = $12,000 × (0.40) = 4,800 Tax on capital gain = 5,000 × (0.40) = 2,000 Total tax on sale of existing machine = 4,800 + 2,000= $6,800 Hence: After-tax proceeds from sale of old asset = = 25,000 - 6,800 = $18,200 Initial Investment = = 40,000 – 18,200 = $21,800 4. Suppose a company is considering an expansion

project requiring an initial investment of $1,500,000. The project has a life of 10 years and the initial investment amount would be depreciated fully over the life of 10 years using straight line (prime cost) depreciation. The firm faces a company tax rate of 30%. Based on the following information that relates exclusively to this project in year 4 of its life, calculate the relevant year 4 incremental after tax cash flow of this project for capital budgeting purposes.

27

Annual sales 50,000 units at $50 per unit Variable costs $12 per unit Fixed costs $350,000 per annum Interest expense $120,000 per annum

We have, for the fourth year: Sales (50,000×50) 2,500,000-Variable Costs (50,000×12) -600,000-Fixed Costs -350,000-Depreciation (0.1×1,500,000) -150,000Pre-Tax Income 1,400,000-Taxes (0.3×1,400,000) -420,000Net Operating Income 980,000Net Cash Flow 1,130,000 The relevant net cash flow is $1,130,000. 5. GJF, Problem 8-27 (p. 378)

“Russell Industries Limited is considering replacing a fully depreciated machine having a remaining useful life of 10 years with a newer, more sophisticated machine. The new machine will cost $200,000 and require $30,000 in installation costs. It will be depreciated using the prime cost method over an effective life of five years. A $25,000 increase in net working capital will be required to support the new machine. The firm plans to evaluate the potential replacement over a four-year period. They estimate that the old

28

machine could be sold at the end of four years to net $15,000 before taxes; the new machine at the end of four years will be worth $75,000 before taxes. Calculate the terminal cash flow relevant to the proposed purchase of the new machine. The firm is subject to a 40% tax rate.”

(From solutions manual) Book value of new machine after 4 years = $46,000 New Old Proceeds from sale $75,000 $15,000less Book value 46,000 0Profit on sale of asset 29,000 15,000Tax liability at 40% (11,600) (6,000) Proceeds from sale 75,000 15,000less Tax liability (11,600) (6,000)Terminal cash flow 63,400 9,000 Terminal cash flow (new machine) 63,400 less Terminal cash flow (old machine)

(9,000)

Plus recovery of working capital 25,000 Incremental terminal cash flow 79,400

29

6. Calculate the NPV of the following net cash flows if the cost of capital is 12% per annum. Also calculate the payback period (assuming cash inflows occur evenly each year).

Year Net Cash Flow ($)

0 1 2 3 4

-50,000 10,000 32,000 30,000 -5,000

59.614,2$=NPV

Payback period 27.23082 ≈+= years.

7. Briefly discuss the advantages and disadvantages

of the Net Present Value and Internal Rate of Return methods of project evaluation. Do these methods always lead to consistent recommendations? If not, why not?

See text/lecture notes

30

8. Mish Mash Pty. Ltd. wishes to choose between two mutually exclusive projects, A and B, each giving only one positive net cash flow at the end of one year, as per the following table.

Net Cash Flows Year 0 Year 1 Project A Project B

-400 -200

500 280

Determine the IRR for each project manually by equating the NPV to zero and solving for the discount rate. Determine the cost of capital at which the firm should be indifferent between the two projects and give a rough sketch of the NPV profiles of the projects. Under what circumstances will choosing the project with the higher IRR give the best outcome for the firm’s shareholders?

25.0

04001

500

=

=−+

IRRIRR

Thus the IRR for project A is 25%

40.0

02001

280

=

=−+

IRRIRR

Thus the IRR for project B is 40%

31

The cost of capital at which the firm should be indifferent between the two projects is the discount rate for which the NPVs are equal.

10.0

2001280400

1500

=

−+

=−+

kkk

This is the discount rate at which the projects’ NPV profiles will cross. Diagrammatically: NPV

32

100 Project A

80

Project B

0 10% 25% 40% Cost of Capital