[1] (10 points)
Briefly explain how the TIE coverage ratio is a measure of the firm's exposure to risk.
[2] (20 points)
In doing an analysis of a potential corporate acquisition, your supervisor discovers that many of the firm's ratios are poor relative to the industry norms. In checking his work, you, a bold summer intern, point out that the firm really is weak in only one area: very low inventory turnover. Explain how the firm's total asset turnover ratio, times interest earned ratio, current ratio and return on assets will be changed if the inventory problem is remedied. Assume that any reduction in inventory will be matched by an equal decrease in notes payable.
[3] (25 points)
You are buying a new car and need to borrow $15,000 for three years. The car dealer will lend you the money at an APR of 17.18%, compounded monthly. As an alternative, you can borrow the $15,000 from First National Bank and make six semi-annual payments of $3,324.88.
Calculate the total payments, APR and EAR for both loans. Which loan should you choose and why?
[4] (20 points)
On January 1, the Dow Jones Industrial Average stood at X. On February 1, it was 8200.00. On the February 1st 7:00 news the anchor man said, "The Dow rose M% during January. This is an annual rate of 34.5%. If this trend continues, by January 1st of next year the Dow should be at a level of D."
Calculate M, X and D.
[5] (30 points)
On February 23, 1999 you make what you anticipate to be the first of 8 equal annual deposits which will continue through February 23, 2006. The deposits should be of sufficient size to enable you to withdraw $2,000 a year forever starting on February 23, 2013. You anticipate an interest rate of 8% a year. You start to make these 8 deposits as planned.
As it turns out, you actually make a total of 10 equal deposits (the originally planned 8 plus an additional 2 in 2007 and 08). On February 23, 2010 the interest rate rises to and stays at 12%. How much can you withdraw from the account on February 23, 2010 and still be able to make the infinite $2,000 withdrawals starting on February 23, 2013?
[6] (35 points)
On October 2, 1998 Dale Falcinelli makes the first of what he expects to be five equal deposits of $1,000 ending on October 2, 2002. He wants to give Lehigh an endowment just sufficient to enable it to give an annual best dressed teacher award of $X starting on October 2, 2007 and continuing for ever. Assume that all funds earn 10% interest.
As it turns out, Mr. Falcinelli makes only the first three of the planned five deposits because he spent the rest of his money on his own clothes. Assume that Lehigh still awards $X to teachers on October 2, 2007 and 2008. Believing that Mr. Falcinelli does not intend to contribute any additional funds, Lehigh decides to give the award for only an additional 10 years, through 2018.
What is the maximum constant amount that Lehigh can award each of the remaining 10 years?
[7] (25 points)
Bunky's Burgers is contemplating replacing a piece of equipment with a new, more powerful model. The existing equipment was purchased 4 years ago for $110,000 and is being depreciated over an original life of 10 years to a salvage value of $10,000 using the straight-line method. The new model would cost $150,000 and be depreciated over a six year life to a zero salvage value using straight-line. The new model would be expected to increase annual sales by $10,000 and lower annual expenses by $5,000. The new model would require additional net-working-capital of $8,000. The firm's marginal tax rate is 30%. The firm is unsure how much it would receive today if it sold the existing machinery. What is the minimum amount they must receive in order to produce an IRR of 16%?
[8] (35 points)
Bunky's Burgers is contemplating replacing a machine with a newer version that would lower its operating costs each year. The existing machine has a book value of $55,000 and is being depreciated using the straight-line method to a salvage value of $5,000 over a remaining life of 5 years. If Bunky's were to sell the machine today, it would realize $70,000 from the sale.
The proposed new machine would cost $200,000 and lower annual operating costs by $52,400. The firm would depreciate it using the straight-line method to a zero salvage value over an expected life of 5 years. The new machine would require additional net-working-capital of $14,000.
The firm has a required rate of return of 15%.
Pending legislation in Congress make it difficult to predict the firm's tax rate over the next several years. What is the maximum tax rate that would cause the firm to want to make the replacement?
[9] (30 points)
MattMan Industries is considering purchasing a new piece of equipment for $500,000. It would be depreciated over a life of 5 years using the straight-line method to a zero salvage value. The equipment would require additional net-working-capital of $20,000. The firm estimates that equipment would produce annual revenues of $300,000 and require annual operating expenses of $150,000. The tax rate is 30% and the firm requires a return of 16%. One member of the division making the proposal thinks that the machinery will last only 3 years and then be scrapped for $80,000 while another knows of the similar equipment that has lasted for 10 years with a zero scrap value. Calculate the expected NPV if there is a 30% chance the first person is right and 70% that the second is.
[10] (40 points)
Rachel Mfg., Inc. is contemplating the purchase of a new piece of equipment that would cost $500,000. The equipment would be depreciated over a life of 8 years to a zero salvage value using the straight-line method. Rachel forecasts the following probability distributions for revenues over operating expenses for each year:
YEARS 1 - 8
| Probability | DS - DC |
| .1 | 150,000 |
| .8 | 300,000 |
| .1 | 400,000 |
YEARS 9+
| Probability | DS - DC |
| .3 | 150,000 |
| .3 | 300,000 |
| .4 | 400,000 |
The firm has a marginal tax rate of 40% and the new investment would require additional net working capital of $30,000. Assume there is a 30% chance that the equipment will actually last only 5 years with a scrap value of $50,000 and a 70% chance that it will last 15 years with a scrap value of zero.
Additional information:
| s / DCF | 0 - .2 | .21 - .7 | .71 - 1.2 | 1.21+ |
| k' | 10% | 12% | 14% | 17% |
The risk-free rate of interest is 4%, the investment beta is 1.4 and the market's risk-premium over and above the risk-free rate is 5%.
{a} If Rachel Mfg. is a very diversified conglomerate with interests in many different industries, calculate the expected value of the risk-adjusted NPV of the decision to buy the new equipment. Clearly show how you determined your discount rate(s).
{b} If Rachel Mfg. is not diversified and the new equipment is for use in the firm's only line of business, calculate the expected value of the risk-adjusted NPV of the decision to buy the new equipment. Clearly show how you determined your discount rate(s).
[11] (20 points)
One method that a firm can use to take into account risk in its capital budgeting decision is to use a risk-adjusted discount rate; i.e., adding a risk premium to the risk-free rate of interest. We discussed two ways of determining that risk premium: (1) making it a function of the given project's coefficient of variation of cash flows; and (2) making it equal to the project's estimated beta coefficient times the market's excess return.
(a) What is systematic risk? What is unsystematic risk? Give an example of each.
(b) Explain which risk(s) the coefficient of variation attempt to measure? Explain which risk(s) beta attempts to measure?
(c) MegaCorp is a large corporation with interests in many different lines of business. Feet 'R Us is a firm that sells only footwear. Both are considering entering the retail market for casual clothing. Which of the two methods should each firm use? What happens to unsystematic risk for both firms?
[12] (15 points)
A firm sells its only product at a price of $60 a unit. It has variable costs per unit of $25 and fixed operating costs of $400,000. The firm also has fixed interest expenses of $100,000.
{a} Compute the degree of operating leverage at 15,000 units.
{b} Compute the degree of operating leverage at 25,000 units.
{c} Explain briefly why the degree of operating leverage declines from {a} to {b}.
[13] (20 points)
The Alpha Watch Company sells its only product, a gold pocket watch for $1,000 each. The production process is highly labor intensive with almost the entire watch being hand-made by a single craftsman. Currently the company's very skilled watch makers are paid on a per finished watch basis. Current variable costs per watch are $700 and total fixed operating costs for the company are $1,500,000. Fixed interest charges are $200,000.
Alpha is contemplating a change in how it pays its watch makers. If they are each paid a guaranteed fixed salary, total fixed costs will jump to $5,100,000 but variable costs per watch will drop to only $100.
{a} Compute the degree of operating leverage at a sales level of $6,000,000 under both the present pay system and the proposed new.
{b} Why is there such a big difference?
{c} Explain how the forecasted volatility of future years' sales will impact Alpha's decision.
[14] (15 points)
Draw and label a downward sloping yield curve. Suppose MattMan Industries is contemplating issuing new bonds and faces a downward sloping curve. What are the pros and cons of issuing long-term bonds? Of issuing short-term bonds? How might the call feature be used and what would be the "cost" of using it?
[15] (30 points)
Bunky's Burgers issues new $1,000 par value subordinated debentures that mature in 30 years. The bonds have an annual coupon rate of 16%, payable semiannually. The bonds are callable at a price of $1080.
{a} Suppose Emily buys a newly issued bond for the market price of $1,140.39. What was the yield to maturity on the bond at the time of issuance?
{b} Assume that 10 years after issuance interest rates have declined to 10% a year, compounded semi-annually, on 20 year bonds and 12% a year, compounded semiannually, on 30 years bonds. Compute the rate of return earned by Emily over the 10 year period if Bunky's calls the bond.
{c} Compute the NPV of the Bunky's decision to call the bonds after 10 years if it refinances with new 20 bonds sold at par. To help you answer this part, think about the "outlay" of this decision and the incremental "savings" or "cash inflows" per period.
{d} Now suppose that parts {b} and {c} never happened and that the bonds are convertible into Bunky's common stock at a price of $100 a share. What rate of return did Emily earn if she holds the bond for 10 years and then converts when the stock is selling for $115 a share?
[16] (30 points)
Yesterday Bunky's Burgers issued new $1,000 par value subordinated debentures that mature in 20 years. The bonds have an annual coupon rate of 8%, payable semiannually. The bonds were priced to yield an annual rate of 8.5%, compounded semiannually. The bond is convertible into Bunky's common stock at a conversion price of $20 a share.
Speaking of common stock, yesterday Bunky's paid a dividend of $2.00 on its common stock. The firm's earnings and dividends are expected to grow indefinitely at a rate of 4% per year. Investors require a return of 14% on Bunky's common stock.
Suppose you buy a bond today and hold it for 10 years and then convert it.
{a} What price did you pay for the bond today?
{b} What will the common stock be selling for in 10 years if all the forecasts hold and the market still requires a return of 14%?
{c} What rate of return did you earn over the 10 year period?
[17] (30 points)
Yesterday Bunky's Burgers paid a dividend $2.25 per share and two years ago they paid a dividend of $4.00 per share. Assume that this rate of decline is expected to continue for another two years. After that dividends are expected to grow at +20% for another three years before settling at 5% for the indefinite future.
{a} If the market requires a rate of return of 14% for a stock in Bunky's risk class, calculate the expected price per share one year from today and 10 years from today.
{b} What is the dividend yield of the stock in year 10?
[18] (35 points) Solution
Today you purchase a $1,000 par value convertible bond of Bunky's Burgers. The bond matures in 30 years and has an annual coupon of 12%, payable semiannually. The yield to the maturity on the bond is 10% a year, compounded semiannually. The bond is convertible into Bunky's common stock at a conversion price of $50 a share. At the time of purchase, the conversion value of the bond is $800.
You forecast that the earnings and dividends of Bunky's will grow at an annual rate of 25% for the next 7 years before declining to a 6% rate for the indefinite future. Yesterday the firm paid a dividend of D0. Stockholders require a return of 16% on stocks in Bunky's risk class.
{a} Assume that the market agrees with your forecasts. To produce a current conversion value of $800, what was the dividend that Bunky's paid yesterday?
{b} If you hold the bond for 20 years and convert at the prevailing market price, what rate of return did you earn if all the forecasts come true?
[19] (65 points) Solution
Matty's Inc. is planning its 1999 capital budget and needs your advice. The firm's capital structure relations shown below are believed to be optimal and will be maintained.
| Debt | $600,000,000 | |
| Preferred Stock | 200,000,000 | |
| Common Stock | $80,000,000 | |
| Retained Earnings | 120,000,000 | |
| Common Equity | 200,000,000 | |
| TOTAL CLAIMS | $1,000,000,000 |
Yesterday the firm paid a dividend of $5.00 and five years ago it paid a dividend of $3.565. Assume this growth rate continues for the indefinite future. Matty's marginal tax rate is 40%. The firm has $20,000,000 available from retained earnings for investment this year. New capital can be raised under the following conditions:
BONDS: Up to $30,000,000 of new $1000 par perpetual bonds carrying a 12% coupon (paid annually) can be sold for $950. Flotation costs total $27.00 per bond.
An additional $30,000,000 new $1000 par perpetual bonds carrying a 14% coupon (paid annually) can be sold for $987 with flotation costs totaling $53.67.
Any additional $1000 par perpetual bonds carrying an 18% coupon (paid annually) can be sold for $1173 with flotation costs totaling $48.00.
PREFERRED STOCK: Any size issue of $50 par value preferred stock carrying an 8% dividend rate can be sold to yield the investor 12%. Flotation costs total $2.33.
COMMON EQUITY: The cost of retained earnings is ke = 18%. Any size issue of new stock can be sold at a cost to the firm of kn = 20%.
The following is a list of potential investments that the firm is considering:
| PROJECT | OUTLAY | IRR% |
| A | 60,000,000 | 11.0 |
| B | 40,000,000 | 12.0 |
| C | 40,000,000 | 14.0 |
{a} (10 points) What is the total amount of flotation costs and underpricing associated with selling each share of new common stock?
{b} (35 points) Calculate the marginal cost of capital for each segment of the marginal cost schedule. Clearly demonstrate using a CLEARLY LABELED graph which projects are acceptable and compute the average cost of capital for the capital budget you are advocating.
{c} (10 points) Compute the NPV of project B assuming a life of 8 years and uniform annual cash flows.
{d} (10 points) Draw the "saucer-shaped" approach to the optimal capital structure question. Suppose that Matty's believes that after they raise the funds to finance this year's proposals, they will still be at the extreme right side of the flat part of the saucer. Explain fully how they would raise capital next year if they wanted to move closer to the left side and why they might want to do this.
[20] (70 points)
Emmo's Inc. is planning its 2000 capital budget and needs your advice. The firm's capital structure relations shown below are believed to be optimal and will be maintained.
| Debt | $500,000,000 | |
| Preferred Stock | 200,000,000 | |
| Common Stock | $80,000,000 | |
| Retained Earnings | 220,000,000 | |
| Common Equity | 300,000,000 | |
| TOTAL CLAIMS | $1,000,000,000 |
Yesterday the firm paid a dividend of $6.00. Earnings and dividends are expected to grow at 8% for the indefinite future. Emmo's marginal tax rate is 40%. The firm has $18,000,000 available from retained earnings for investment this year. New capital can be raised under the following conditions:
BONDS: Up to $45,000,000 of new $1000 par 10 year bonds carrying a coupon of C% (paid annually) can be sold for $943.50. At that price, the investor makes 12% a year. Flotation costs total $52.03 per bond.
Any additional $1000 par 10 year bonds carrying the same coupon rate of C% (paid annually) can be sold to yield the investor 15%. Flotation costs total $78.77.
PREFERRED STOCK: Any size issue of $50 par value preferred stock carrying an 10% dividend rate can be sold to yield the investor 15%. Flotation costs total $5.56.
COMMON EQUITY: The cost of retained earnings is ke = 23%. Any size issue of new stock can be sold at a cost to the firm of kn = 26%.
The following is a list of potential investments that the firm is considering:
| PROJECT | OUTLAY | IRR% | |
| A | 20,000,000 | 16.0 | |
| K | 25,000,000 | 17.5 | |
| B | 25,000,000 | 14.8 | |
| J | 40,000,000 | 20.0 |
{a} (10 points) What is the total amount of flotation costs and underpricing associated with selling each share of new common stock?
{b} (40 points) Calculate the marginal cost of capital for each segment of the marginal cost schedule. Clearly demonstrate using a CLEARLY LABELED graph which projects are acceptable and compute the average cost of capital for the capital budget you are advocating.
{c} (10 points) Compute the NPV of project B assuming a life of 8 years and uniform annual cash flows.
{d} (10 points) Explain why the firm is accepting a project whose IRR is less than the rate of return required by stockholders.
LOTS OF ANSWERS TO MOST PROBLEMS
[3] Dealer: R = $536.14/month; EAR = 18.60%; Bank: APR = 17.62%;
EAR = 18.40%
[4] M = 2.50%; DJIA(now) = 8,000; DJIA(next year) = 10,759.93
[5] initial deposits = $1,481.13; withdrawal = $11,740.30
[6] X = $893.85; Award = $849.24
[7] outlay = 137,000 - .7MV, DCF = 15,000, MV = $117,928
[8] DCF = 52,400 - 22,400t; outlay = 144,000 + 15,000t; t = 40.1%
[9]DCF1-3 = 135,000, Sale of Old = 116,000, NPV3= -129,695 DCF6-10 = 105,000, NPV10 = 90,251
[10] {a} DCF = 202,000; k' = 11%; NPV(5) = $296,687; NPV(15) = $898,174; {b} s = 34.07; k' = 10%; NPV(5) = $319,563.
[12] OL(15,000) = 4.20; OL(25,000) = 1.84;
[13]OLold = 6x; OLnew = 18x
[15] {a} Yield = 14% a year csa; {b} IRR = 13.77% a year, csa; {c} NPV = $434.77; {d} IRR = 14.07% a year, csa
[16]P0 = $952.31, Pcs,10 = 30.79, conversion value = $1,539.45, r = 11.79%, comp sa
[17] P1 = $19.91; P10 = $32.56; yield = .09
[18] Conv ratio = 20 : 1; Price of common = $40 per share; D0= $1.46; P20= 157.18; P0=$1,189.20; IRR = 12.17% per year, comp sa.
[19] Breaks at $50,000,000 (D) and $100,000,000 (D and Eq). ki1=7.8%; ki2=9.0%; ki3=9.6%; kp=12.9%; ke=18%; flotation costs = $7.49 per share; accept C & B; raise $80 million; ACC = 11.13%
[20] Breaks at $60 and $90 million; MC1 = 14.4%; MC2 = 15.3%; MC3 = 16.5%; Flotation costs = $7.20 per share;