Master in Management of International Projects

CORPORATE FINANCE

Problem bank

1. Here are simplified financial statements of Phone Corporation from a recent year:

INCOME STATEMENT (figures in millions of dollars)Net sales 13,194Cost of goods sold 4,060Other expenses 4,049Depreciation 2,518EBIT 2,566Interest expenses 685Income before tax 1,881Taxes 570Net income (EAT) 1,311Dividends 856

BALANCE SHEET (figures in millions of dollars)End of year Start of year

Assets Cash and marketable securities 89 158 Receivables 2,382 2,490 Inventories 187 238 Other current assets 867 932 Total current assets 3,525 3,818 Net property, plant and equipment 19,973 19,915 Other long-term assets 4,216 3,770 Total assets 27,714 27,503

Liabilities and shareholders’ equity Payables 2,564 3,040 Short-term debt 1,419 1,573 Other current liabilities 811 787 Total current liabilities 4,794 5,400 Long-term debt and leases 7,018 6,833 Other long-term liabilities 6,178 6,149 Shareholders’ equity 9,724 9,121 Total liabilities and shareholders’ equity 27,714 27,503

a) Calculate the following financial ratios: Debt ratio Debt-equity ratio Times interest earned Current ratio Quick ratio Net profit margin Days in inventory Average collection period Return on equity Return on assets Payout ratio

b) Suppose that Phone Corporation shut down its operations. For how many days could it pay its bills?c) If the market value of Phone Corp. stock was $17.2 billion at the end of the year, what was the market-to-book ratio? If there were 205 million shares outstanding, what were earnings per share? The price-earnings ratio?

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Solution

a)

b) We compute the average payables period:

c)

2. Keller Cosmetics maintains a profit margin of 5% and asset turnover ratio of 3.a) What is its ROA?b) If its debt-equity ratio is 1.0, its interest payments and taxes are each 8,000, and EBIT is 20,000, what

is its ROE?

Solutiona) ROA = Profit margin x Asset turnover ratio = 5% x 3 = 15%

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b)

3. As the fast-food analyst for a major brokerage firm, you have collected the following information on McDonald’s, Wendy’s and Church’s Friend Chicken for the last three years. Use the Du Pont system to compare the three companies. What can you say about their relative standing and activity through time?

Wendy (in thousand $)Year 3 Year 2 Year 1

Sales 944,768 720,383 606,964Net income 68,707 55,220 44,102Assets 613,636 506,713 453,561

Church’s (in thousands $)Year 3 Year 2 Year 1

Sales 533,208 454,490 413,144Net income 42,595 31,552 41,598Assets 334,068 302,155 277,562

McDonald’s (in thousands $)Year 3 Year 2 Year 1

Sales 3,414,798 3,062,822 2,770,000Net income 389,089 342,640 301,000Assets 4,229,638 3,727,307 3,263,000

Solution:Du Pont analysis:

(Net income/Sales) × (Sales/Assets) = Net income/Total assets = Return on assets

Wendy (in thousand $)Year 3 Year 2 Year 1

Sales 944,768.00 720,383.00 606,964.00Net income 68,707.00 55,220.00 44,102.00

Assets 613,636.00 506,713.00 453,561.00Profit margin 7.27% 7.67% 7.27%Assets turnover 1.5396 1.4217 1.3382ROA 11.20% 10.90% 9.72%Church’s (in thousands $)

Year 3 Year 2 Year 1

Sales 533,208.00 454,490.00 413,144.00Net income 42,595.00 31,552.00 41,598.00

Assets 334,068.00 302,155.00 277,562.00Profit margin 7.99% 6.94% 10.07%Assets turnover 1.5961 1.5042 1.4885ROA 12.75% 10.44% 14.99%McDonald’s (in thousands $)

Year 3 Year 2 Year 1

Sales 3,414,798.00 3,062,822.00 2,770,000.00

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Net income 389,089.00 342,640.00 301,000.00

Assets 4,229,638.00 3,727,307.00 3,263,000.00Profit margin 11.39% 11.19% 10.87%Assets turnover 0.8073 0.8217 0.8489ROA 9.20% 9.19% 9.22%

Wendy's appears to be on profitability up trend, which is characteristic of a growth firm. On the contrary, McDonald's, which is a mature firm, has been maintaining a constant return. Church's profitability is erratic, which also is characteristic of a growth firm. They probably ran into problems in year two that were unique to them because the other two firms in the industry show an upward or constant trend in year two.

4. During the year 2002, the Terri-Yung Company had sales of $1,000, cost of goods sold of $400, depreciation of $100, and interest paid of $150.

a) If the tax rate is 34% what is net income?b) Assume the Terri-Yung Company has 100 shares of common stock outstanding at the end of 2002.

Total dividends paid were $120. Compute earnings per share (EPS) and dividends per share (DPS).c) At year-end 2001 Terri-Yung had notes payable of $1,200, accounts payable pf $2,400, and long-

term debt of $3,000. Corresponding entries for 2002: $1,600, $2,000, and $2,800. Assets for 2001 and 2002 are shown below. Prepare the company’s balance sheet for the end of 2001 and 2002, respectively.

Solutiona)

TERRI-YUNG COMPANY, INC.2002 Income Statement

1. Net sales 1,0002. Cost of goods sold 4003. Depreciation 1004. Earnings before interest and taxes (1-2-3) 5005. Interest paid 1506. Earnings before taxes (4-5) 3507. Taxes (34%) 1198. Net income 231

b) EPS = (231/100) = $2.31. Dividends per share equals (120/100) = $1.20.c)

TERRI-YUNG COMPANY, INC.Balance sheets as of December 21, 2001 and 2002

2001 2002 2001 2002Assets Liabilities and owners’ equity Current assets Current liabilities Cash 800 500 Accounts payable 2,400 2,000 Marketable securities 400 300 Notes payable 1,200 1,600 Accounts receivable 900 800 Total 3,600 3,600 Inventory 1,800 3,600

Total 3,900 3,600 Long-term debt 3,000 2,800

Net fixed assets 6,000 8,000 Owners’ equity 3,300 5,200 Total assets 9,900 11,600 Total liabilities and owners’

equity9,900 11,600

5. Imagine an economy in which there are just three individuals: A, B and C. Each has money to invest and a number of possible investment projects, each of which would require $1,000. A has $2,000 to invest and two projects with returns of 11% and one project with a return of 7%. B has $1,000 to invest and has projects yielding 11% and 7%. C has $1,000 to invest and has projects offering 15% and 12% percent returns.a. What projects will be undertaken if there is no lending and borrowing?b. If they do borrow from and lend to each other, what projects will be undertaken and what will the

interest rates be?

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Solutiona) In the absence of lending and borrowing, A will undertake the two projects with 11% return, B will

undertake the project with 11% return and C will undertake the 15% project.b) C will borrow from either A or B to undertake the 12% project in addition to the 15% project. One of

the 11% projects will be dropped. The rate of interest will be 11%.

6. Calculate the NPV and rate of return on each of the following investments. The opportunity cost of capital is 20% for all four investments.

Investment Initial cash flow, C0 Cash flow in year 1, C1

1 -10,000 +20,0002 -5,000 +12,0003 -5,000 +5,5004 -2,000 +5,000

a) Which investment in most valuable?b) Suppose each investment would require use of the same parcel of land. Therefore you can take only

one. Which one?

Solutiona) NPV1 = -10,000 + (20,000/1.20) = -10,000 + 16,666.7 = +6,666.7 Rate of return1 = (20,000 – 10,000)/10,000 = 1 or 100% NPV2 = -5,000 + (12,000/1.20) = -5,000 + 10,000 = +5,000 Rate of return2 = (12,000 – 5,000)/5,000 = 1.4 or 140%

NPV3 = -5,000 + (5,500/1.20) = -5,000 + 4,583.3 = +416.7 Rate of return3 = (5,500 – 5,000)/5,000 = 0.1 or 10%

NPV4 = -2,000 + (5,000/1.20) = =2,000 + 4,166.7 = + 2,166.7 Rate of return4 = (5,000 – 2,000)/2,000 = 1.50 or 150%

Investment 1 is the most valuable, because it has the highest NPV.b) Investment 1, because it maximizes shareholders’ wealth.

7. Mary Jane has already saved $10,000 in a mutual fund account and expects to save an additional $9,000 for each of the next 2 years. She expects to pay $12,000 each at the end of 2 years and 3 years for her son's college education. How much can she afford to spend now on a vacation if she expects to earn 7% on her mutual fund account?

SolutionThe amount she can afford to spend on her vacation is the difference between the present values of her savings and the college education costs. First calculate the PV of Mary Jane's savings for the next two years (an annuity with two payments) and add this to her current savings of $10,000.

PV of 2 year annuity = $16,272.16Total PV of savings = $16,272.16 + $10,000 = $26,272.16PV of education costs = 12,000/1.072 + 12,000/1.073 = 20,276.83

Amount she can spend on vacation = $26,272.16 - 20,276.83 = $5,999.33

8. A store offers the following credit terms on a color television set "slashed" to a price of only $320: only $20 down and 18 monthly payments of $20.

(a) Is this an attractive proposition if you can borrow at 1% per month?(b) What monthly interest rate is being charged?(c) What annual rate is being charged?

Solutiona) You are taking a loan of $320 - $20 = $300, If your interest rate is 1% per month, your payment will

be $300 divided by the annuity factor for 18 periods and 1%, which equals 16.40. Monthly payment for your loan = $300/16.40 = $18.29. Since you are required to pay more than this amount, this is not an attractive proposition.

b) For payment of $20 per month, the annuity factor has to be $300/$20 = 15. This is very close to the factor for 18 periods and 2 percent (14.99). So the effective interest being charged is 2% per month.

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c) Effective annual rate = (1.02)12 – 1 =26.82%

9. Tom has invested his lump sum retirement pension of $300,000 in an account that guarantees him a 9 percent return. He wishes to make annual withdrawals of $40,000 beginning at the end of this year.a) How long will it be until Tom exhausts his account?b) Suppose Tom waits ten years until he starts making withdrawals. How long will it be until he

exhausts his account?

Solution:a) We want to find the value of n such that PVA = $300,000 = $40,000 × PVAF(9,n), or PVAF(9,n) = 300/40

= 7.5. From tables we know that PVAF(9,13) = 7.4869. The value of n is then slightly larger than 13, actually 13.04 years.

b) In this case, Tom’s $300,000 lump sum pension will have grown to $710,209.10 ($300,000 × 1.0910). A 9% return on this amount will yield Tom $63,918.82 annually. The result is that if Tom withdraws no more than this amount, he will never exhaust the principal amount of his pension. Given that $40,000 is less than $63,918.82, Tom will never exhaust his account if he waits 10 years before he begins drawing on his account.

10. Kangaroo Auto is offering free credit on a new $10,000 car. You pay $1,000 down and then $300 a month for the next 30 months. Turtle Motors next door does not offer free credit, but will give you $1,000 off the list price. If the rate of interest is 10 percent a year, which company is offering the better deal?

SolutionThe fact that Kangaroo Autos is offering “free credit” tells us what the cash payments are; it does not change the fact that money has time value. A 10 percent annual rate of interest is equivalent to a monthly rate of 0.83 percent.

rmonthly = rannual / 12 = 0.10 / 12 rmonthly = 0.0083

The present value of the payments to Kangaroo Autos is:

$1000 + 300 [Annuity factor, .83%, t = 30]

Because this interest rate is not in our tables, we must use the formula to find the annuity factor:

$1000 = 300 { [1 / .0083] - [1 / .0083 (1.0083)30] } = $8,938

A car from Turtle Motors costs $9,000 cash. Therefore, Kangaroo Autos offers the better deal, i.e., the lower present value of cost.

11. You own an oil pipeline, which will generate a $2 million cash return over the coming year. The pipeline’s operating costs are negligible, and it is expected to last for a very long time. Unfortunately, the volume of oil shipped is declining, and cash flows are expected to decline by 4 percent per year. The discount rate is 10%.What is the NPV of the pipeline’s cash flows if its cash flows are assumed to last forever?

SolutionThis calls for the growing perpetuity formula with a negative growth rate, g  =  -.04:

PV =

12. Norman Gerrymander has just received a $2 million gift. How should he invest it? There are four immediate alternatives:

(a) Investment in one-year U.S. government securities yielding 5 percent.(b) A loan to Norman’s nephew Gerald, who has four years aspired to open a big Cajun restaurant in

Duluth. Gerald had arranged a one-year bank loan for $900,000, at 10 percent, but asks for a loan from Norman at 7 percent.

(c) Investment in the stock market. The expected rate of return is 12 percent.(d) Investment in local real estate, which Norman judges is about as risky as the stock market. The

opportunity at hand would cost $1 million and is forecasted to be worth $1.1 million after one year.Which of these investments have positive NPVs? Which would you advise Norman to take?

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Solution(a) NPV = -$2,000,000 + [$2,000,000 (1.05) ] / (1.05) = $0(b) NPV = -$ 900,000 + [$900,000 (1.07)] / (1.10) = -$24,545.45The correct discount rate is 10% because this represents the appropriate risk of Norman’s nephew’s restaurant. The NPV is negative because Norman will not earn enough to offset the risk.(c) NPV = -$2,000,000 + [$2,000,000 (1.12) ] / (1.12) = $0(d)NPV = -$1,000,000 + ($1,100,000) / (1.12) = -$17,857.14Norman should invest in either the risk-free government securities or the risky stock market based upon his tolerance for risk. Correctly priced securities always have an NPV = 0.

13. Consider the following projects:

Project Cash flows ($)C0 C1 C2 C3 C4 C5

A -1,000 +1,000 0 0 0 0B -2,000 +1,000 +1,000 +4,000 +1,000 +1,000C -3,000 +1,000 +1,000 0 +1,000 +1,000

(a) If the opportunity cost of capital is 10%, which projects have a positive NPV?(b) Calculate the payback period for each project. (c) Which project(s) would a firm using the payback rule accept if the cutoff period were three years?

Solution(a)

(b) PaybackA = 1 year; PaybackB = 2 years; PaybackC = 4 years(c) A and B.

14. Star Corp. has an opportunity cost of capital of 10% and the following projects.

Projects Cash flow in thousands $Year 0 Year 1 Year 2 Year 3 IRR, %

Project A -112 40 50 60 15Project B 45 60 -70 -70 16Project C -100 -26 80 80 11Project D 146 -70 -60 -50 12Project E -100 450 -550 175 29

a) Assuming theses to be independent projects, select the best project(s) for the company. Explain why all the projects will not be selected.

b) How would your decision change if the projects were not independent projects?

Solutiona) The NPVs for the projects are as follows:

Project A = $10,765; Project B = -$10,898; Project C = $2,585; Project D = -$4,789; Project E = -$13,974.Only projects A and C have positive NPVs. The others are really "financing" projects and should not be selected, as the cost of borrowing (IRR) is higher than the opportunity cost of capital.

b) If the projects were mutually exclusive, one would select project A, as it has the highest NPV.

15. Mickey Minn Corp. is considering the following projects. The company is facing resource constraints and can invest only $800 this year. Advice the company.

Projects Investment NPV IRR, %A 100 8 13.9B 400 43 14.4

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C 300 25 16.0D 200 23 14.1E 200 21 16.1F 200 19 15.7

SolutionThe profitability index and ranking based on PI for the different projects are:

Projects PI RankingA 1.080 6B 1.108 2C 1.083 5D 1.115 1E 1.105 3F 1.095 4

Projects D, B, and E should be selected to invest the $800. Their combined NPV is the highest of all possible combinations, $87.

16. The firm for which you work must choose between the following two mutually exclusive projects. The appropriate discount rate for the projects is 10%.

C0 C1 C2 PI NPVA -1,000 1,000 500 1.21 421B -500 500 400 1.62 301

The firm chose to undertake A. At a luncheon for shareholders, the manager of a pension fund that owns a substantial amount of the firm's stock asked why the firm chose project A instead of project B when B is more profitable. How would you justify your firm's action? Are there any circumstances under which the pension fund manager's argument could be correct?

SolutionAlthough the profitability index is higher for project B than for project A, the NPV is the increase in the value of the company that will occur if a particular project is undertaken. Thus, the project with the higher NPV should be chosen because it increases the value of the firm at most. Only in the case of capital rationing could the pension fund manager be correct.

17. Radio Hut, a discount consumer electronics retail chain, is considering two different strategies for expanding into the eastern United States. One strategy (plan A) is to open stores in the center of three major cities (New York, Boston, Philadelphia); the other strategy (plan B) is to open several stores in suburban shopping malls. The projected cash flows ($000) are listed below:

Plan Investment Year 1 2 3 4 5

AB

$2,0001,000

$550250

$550300

$600400

$650350

$700300

a) With a cost of capital of 12 percent, which plan, A or B, should Radio Hut adopt under the NPV method?

b) Which plan should be adopted under the IRR method?c) An executive on the board of directors argues that B should be chosen because it gives more return

for its smaller investment. How would you answer?

Solution:a) NPV(000's) of Plan A = $166.88. NPV(000's) of Plan B = $139.74 Plan A is preferred.b) IRR of Plan A = 15.17%, and IRR of Plan B = 17.26%. Under the IRR criterion, Plan B is preferred.c) "True, B offers a higher return per dollar of investment, but would you rather earn 25% on a $1

investment or 24% on a $10,000 investment? The NPV criterion measures wealth creation; Plan A adds more value to the firm.". Another way of answering is to compute incremental cash flows, incremental IRR and incremental NPV.

Incremental CFs (A-B) Investment Year 1 2 3 4 5

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A - B $1,000 $300 $250 $200 $300 $400

Incremental NPV at 12% = 27.14 (= 166.88 – 139.74) > 0 project A should be chosenIncremental IRR = 13.03% > 12% project A should also be chosen.

18. The Fast Food chain is trying to introduce its new Hot and Spicy line of hamburgers. One plan (S) will include a big media campaign but less in-house production capability. The other plan (L) will concentrate on a more gradual rollout of the project but will involve more investment in personnel training and so forth. The cost of capital is 12 percent. The cash flows ($000) are listed below. The initial investment for each is $400,000.

Plan Year 1 2 3 4 5

SL

$250200

$250125

$150200

$100250

$60100

a) Construct the NPV profiles for plans S and L. Which has the higher IRR?b) Which plan should Fast Food choose using the NPV method?c) Which plan (S or L) should Fast Food choose? Why?d) At what cost of capital will the NPV and the IRR rankings conflict?

Solution:a) The NPVs for different discount rates and the NPV profiles are below. Project S has the greater IRR:

IRR(S) = 39.63% and IRR(L) = 34.37%.

0% 6% 12% 18% 24% 30% 36% 42%NPV(S) 410.00 308.34 226.88 160.51 105.64 59.68 20.75 -12.59NPV(L) 475.00 340.60 236.20 153.65 87.34 33.31 -11.28 -48.51

b)At a 12% cost of capital, NPV for S is lower than NPV for L L should be chosen.c) Fast Food should choose the plan with the highest NPV at a given cost of capital this is L.d)We can see from the graph that S and L have the same NPV at a cost of capital between 10% and

20%. This COC is the incremental IRR, which makes the incremental NPV to be zero. At any COC lower than incremental IRR, project L will be preferred, but at any COC higher than incremental IRR, project S will be preferred ( but not at a COC higher than its IRR). Using Excel or financial calculator, we find incremental IRR = 15.20%. It means that for any COC < 15.20% Fast Food will prefer L, and for any COC between 15.20% and 39.63% project S will be preferred. Also, if COC is higher than 39.63%, no project can be chosen, since their NPVs are negative.

19. The following table tracks the main components of working capital over the life of a four-year project.

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2000 2001 2002 2003 2004Accounts receivable 0 150,000 225,000 190,000 0Inventory 75,000 130,000 130,000 95,000 0Accounts payable 25,000 50,000 50,000 35,000 0

Calculate net working capital and the cash inflows and outflows due to investment in working capital.

Solution2000 2001 2002 2003 2004

Net Working Capital 50,000 230,000 305,000 250,000 0Cash Inflows (Outflows) -50,000 -180,000 -75,000 55,000 250,000

20. Bensonhurst Breweries, Inc., plans to open a new brewery in southern Florida. The plant is expected to produce 500,000 six-packs of beer a year. The beer sells for $2.00 a pack this year and is expected to increase by 2 percent a year. The operating costs of the plant this year (year zero) are $500,000 in fixed and variable costs. These costs are expected to grow at 3 percent a year. The plant will cost $800,000 to build and will be depreciated straight-line over its 6-year life. Given a required rate of return of 10 percent and tax rate of 40 percent, what is the NPV of the brewery?

Solution:Projected first-year sales are $1,020,000 (500,000 six-packs x $2.04 per six-pack), a 2% increase over the previous year; the 2% growth rate continues to be applied to sales for the next 5 years. First year projected costs are $515,000, a 3% increase over last year. Costs continue to increase at 3% per year. The $800,000 building is depreciated straight-line over its assumed 6-year life.

Project cash flows are below:Y0 Y1 Y2 Y3 Y4 Y5 Y6

1. Packs of beer produced 500,000.00 500,000.00 500,000.00 500,000.00 500,000.00 500,000.00

2. Price per pack 2.00 2.04 2.08 2.12 2.16 2.21 2.25

3. Total sales 1,020,000.00 1,040,400.00 1,061,208.00 1,082,432.16 1,104,080.80 1,126,162.42

4. Operating costs 500,000.00 515,000.00 530,450.00 546,363.50 562,754.41 579,637.04 597,026.15

5. EBITDA (3-5) 505,000.00 509,950.00 514,844.50 519,677.76 524,443.77 529,136.27

6. Depreciation 133,333.33 80,000.00 80,000.00 80,000.00 80,000.00 80,000.00

7. EBIT 371,666.67 429,950.00 434,844.50 439,677.76 444,443.77 449,136.27

8. Taxes (40%) 148,666.67 171,980.00 173,937.80 175,871.10 177,777.51 179,654.51

9. EAT (7-8) 223,000.00 257,970.00 260,906.70 263,806.65 266,666.26 269,481.7610. Operating cash flows 356,333.33 337,970.00 340,906.70 343,806.65 346,666.26 349,481.76

11. Investment 800,000.00

12. Project cash flows -800,000.00 356,333.33 337,970.00 340,906.70 343,806.65 346,666.26 349,481.76

NPV = $706,732.08 > 0 The brewery should be built.

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