[1] (10 points) RATIO ANALYSIS
A fundamental concept of finance is that as the perceived risk of an investment rises, an investor will require a higher rate of return (k’) on the investment to compensate. Assume that you use this homemade formula to determine your k’ : k’ = .08 + .1 x DR - 6 x TIE, where DR is the firm’s debt ratio and TIE is the firm’s times interest earned ratio. Explain why the sign of DR is positive and TIE is negative.
 

[2] (30 points) EFFECTIVE RATES  Solution
You’ve reached the age of 65 and have accumulated a nest egg of $500,000 in a retirement account. You estimate you will live an additional 20 years. You have two choices as to how to take your money out of the account. Plan A would provide an APR of 8%, compounded quarterly by allowing you to make equal quarterly withdrawals for the 20 years. Plan B would allow you to make monthly withdrawals of $4,182 for the 20 years. Assume the first withdrawal of each plan is at the end of the first period. For both plans, compute the APR and EAR. Calculate the total amount of money you will receive over a three-month period under both plans. Explain which plan you should choose and why.
 

[3] (30 points) EFFECTIVE RATES  Solution
To finance the purchase of a Zucchini GT, you need to borrow $50,000. The dealer offers you a choice of borrowing plans: With Plan A, they will lend you the money at an APR of 9.6%, compounded monthly for four years. With Plan B they will lend you the money and require 8 semi-annual payments of $7650. For both loans, calculate the APR, EAR and total payments over a six-month period. Which plan should you choose?
 

[4] (35 points) PV - FV  Solution
On October 1, 2001 you make the first of what you expect to be 8 equal annual deposits of $500 into an account that you expect will pay 10% annual interest (last deposit scheduled for October 1, 2008). You plan to use the funds in order to provide scholarships of $X a year for 10 years to Lehigh starting on October 1, 2015 and continuing through 2024. Assume you make the 8 $500 deposits as planned but on October 1, 2011 the interest rate changes to 15%. You decide with this good fortune to make your gift of $X a year a perpetuity still starting on October 1, 2015. You figure that in order to accomplish this, you will need to either add a lump-sum on October 1, 2011 or else be able to withdraw a lump-sum in case you have already given more than is necessary. Compute the amount you either must deposit or can withdraw on October 1, 2011.
 

[5] (35 points) PV - FV  Solution
On February 18, 2002 you make the first of 8 annual contributions into an investment that pays 10% interest. The contributions must be of sufficient size to enable you to make a lump-sum donation to Lehigh on February 18, 2014 that will enable the University to establish a scholarship fund that will generate $100,000 per year in perpetuity starting on February 18, 2015. Assume that you know that Lehigh can earn an annual return of only 8% on the funds you donate. You make the 8 deposits as planned. Then on February 18, 2011 you decide that since you can earn 2% more than the University can earn, it makes sense that you keep the funds rather than giving Lehigh the lump-sum check. You simultaneously decide to just endow only 15 years of $100,000 scholarships still starting on February 18, 2015 rather than the original perpetual gift. How much can you withdraw from the investment on February 18, 2011 if you go with the revised more moderate gift and keep the funds earning 10%?
 

[6] (35 points) CAPITAL BUDGETING  Solution
Melrose Inc. is thinking of replacing a piece of equipment with a new, larger model. The existing machinery was purchased three years ago for $90,000. It is being depreciated using the straight-line method to a salvage value of $10,000 over its original expected life of eight years. The new equipment would lower before-tax expenses each year but would not affect sales revenues. It costs $180,000, has a zero salvage value and would be depreciated over its expected life of five years using the straight-line method. The firm would require additional net-working-capital of $12,000 if the new machine is purchased. If the firm were to scrap the existing machine today, it would realize $15,000 from the sale. The firm's required rate of return is 15% and its marginal tax rate is 40%. What is the minimum annual reduction in before-tax expenses necessary for the replacement to become worthwhile?
 

[7] (30 points) CAPITAL BUDGETING  Solution
Melrose Manufacturing is considering replacing some outdated equipment and needs your advice. The existing equipment has a book value of $80,000 and is being depreciated over a remaining life of 9 years to a salvage value of $8,000 using the straight-line method. The firm could sell the old equipment today for $100,000. The firm has a marginal tax rate of 40%. The proposed new machine would cost $600,000 and would be depreciated over an expected life of 9 years to a salvage value of $60,000 also using the straight-line method. Because of greater efficiencies, the new equipment would lower Melrose’s operating expenses by $105,000 a year but would require additional net working capital of $20,000. Compute the IRR of the decision to replace the equipment.
 

[8] (40 points) CAPITAL BUDGETING UNDER RISK AND UNCERTAINTY  Solution
Bunky’s Burgers 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 forecasts that for each year of operation, the expected value of annual sales revenue is $300,000 and the expected value of annual operating expenses is $150,000. Bunky’s marginal tax rate is 40%. Vice-President Abbott pessimistically predicts that the machinery will last only 3 years and then be scrapped for $90,000, while Vice-President Costello optimistically predicts that it will actually last 12 years with a zero scrap value. Additional information: The appropriate certainty equivalent coefficient (a) for operating cash flows is .6 and for non-operating cash flows is 1.0, 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} Assume that Bunky’s is only in the fast food business. Only calculate the NPV if Abbott is correct. {b} Now assume that Bunky’s is in a wide-range of businesses. Only calculate the NPV if Costello is correct. {c} Fully explain why you chose the method for taking into account risk that you did for both parts {a} and {b}.
 

[9] (45 points) CAPITAL BUDGETING UNDER RISK AND UNCERTAINTY  Solution
The Krusty Krab 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 forecasts that for each year of operation, there is a 20% chance that the increase in sales less operating costs will be $70,000, a 50% chance the increase will be $150,000 and a 30% chance it will be $180,000. The Krusty Krab’s marginal tax rate is 40%. Vice-President Squidward pessimistically predicts that the machinery will last only 3 years and then be scrapped for $90,000, while Vice-President SpongeBob optimistically predicts that it will actually last 12 years with a zero scrap value. Additional information: The appropriate certainty equivalent coefficient (a) for operating cash flows is .6 and for non-operating cash flows is 1.0, 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} Assume that the Krusty Krab is only in the fast food business. Calculate the expected NPV assuming that there is a 50% chance that Squidward is correct and a 50% chance that SpongeBob is correct. {b} Now assume that Krusty Krab is in a diversified, wide-range of businesses. Calculate the expected NPV assuming that there is a 50% chance that Squidward is correct and a 50% chance that SpongeBob is correct. {c} Fully explain why you chose the method for taking into account risk that you did for both parts {a} and {b}.
 

[10] (30 points) CONVERTIBLE AND CALLABLE BONDS  Solution
{a} What happens to the yield differential between a pharmaceutical firm’s straight bonds and its convertible bonds as the prospect of FDA approval of its proposed “wonder-drug,” once considered a sure thing, becomes less and less likely? Why? {b} What happens to the yield differential between a firms’ subordinated debentures and its mortgage bonds if the outlook for the economy starts to worsen? Why? {c} Draw and label an upward sloping yield curve. What are the relative advantages for the borrower of issuing short-term bonds versus issuing long-term bonds? How do these advantages depend upon the expectations of future rates?
 

[11] (20 points) CONVERTIBLE AND CALLABLE BONDS  Solution
{a} What is likely to happen to the yield differential between a pharmaceutical firm’s straight bonds and its convertible bonds as the prospect of FDA approval of its proposed “wonder-drug,” once considered somewhat shaky, becomes more and more likely? Explain why how a yield differential is really a “risk premium”. {b} Draw and label an upward sloping yield curve. What are the relative advantages for the investor of buying short-term bonds and of buying long-term bonds? How do these advantages depend upon the expectations of future rates?
 

[12] (30 points) CONVERTIBLE AND CALLABLE BONDS  Solution
You purchase a subordinated debenture of Melrose, Inc. for $1,047.69. The $1,000 par value bond carries an annual coupon rate of 9%, payable semiannually and matures in 20 years. The bond is callable at $1,050 and is also convertible into Melrose common stock at a conversion price of $25 per share. {a} At the time of purchase, what is the bond’s yield to maturity? ASSUME THAT PARTS {b} AND {c} ARE INDEPENDENT OF EACH OTHER. {b} Calculate your IRR if you hold the bond for 8 years and then sell it at its market value. At the time of sale, the yield to maturity is 10% a year compounded semiannually on 12 year subordinated debentures and 11.5% on 20 year subordinated debentures. {c} Calculate your IRR if you hold the bond for 8 years and then convert it. At the time of conversion, Melrose’s stock is trading at $31 a share.
 

[13] (35 points) CONVERTIBLE AND CALLABLE BONDS  Solution
Dexter’s Laboratory issues new $1,000 par value subordinated debentures that mature in 30 years. The bonds have an annual coupon rate of 14%, payable semiannually. The bonds are callable at a price of $1070. {a} Suppose Emily buys a newly issued bond for the market price of $1,317.86. What was the yield to maturity on the bond at the time of issuance? Display your answer as the effective annual rate. {b} Assume that 10 years after issuance interest rates have declined to 7% a year, compounded semi-annually, on 20 year bonds and 8% a year, compounded semiannually, on 30 years bonds. Compute the rate of return earned by Emily over the 10 year period if Dexter’s calls the bond. Display your answer as the effective annual rate. {c} Compute the NPV of Dexter's decision to call the bonds after 10 years if it refinances with new 20 bonds sold at par. Investment bankers charge a fee of $20 per old bond to handle the transaction. To help you answer this part, think about the "outlay" of this decision and the incremental "savings" or "cash inflows" per period.

[14] (30 points) SUPER GROWTH EQUITY VALUATION  Solution
On November 27, 2001, Stuff Mart, Inc. paid a dividend of $3.00 on its common stock. Analysts forecast the firms’ earnings and dividends will decline by 10% per year for 8 years before growing at a positive 7% rate for the indefinite future. {a} If you buy the stock on November 28, 2004 and the forecasts still hold, what price did you pay if the market's required rate of return is 18%? {b} Suppose you sell the stock on November 28, 2024 and the original forecasts still hold. What price did you receive for the stock if the market's required rate of return is still 18%? {c} What rate of return did you earn over the 20 years? Think before proceeding on this one!!
 

[15] (25 points) SUPER GROWTH EQUITY VALUATION  Solution
You are contemplating purchasing 100 shares of Melrose, Inc. Yesterday the stock paid a dividend per share of $3.00. Earnings and dividends are expected to grow at a 25% rate for the next 2 years, a 20% rate for another 2 years, and then a 7% rate thereafter forever. You plan to buy the stock today and hold it for 8 years and then sell. The market requires a 15% annual rate of return on the stock. {a} Compute the purchase price today. {b} Compute the expected selling price in 8 years. {c} What IRR did you earn over the 8 years if all forecasts hold. Some careful thought and some efficient use of your financial calculator can make this a very quick problem!

[16] (70 points) COST OF CAPITAL  Solution
Melrose Industries is planning its 2002 capital budget and needs your advice. The firm believes that the capital relations shown below are optimal and will be maintained.
 

Debt $600,000,000
Preferred Stock 240,000,000
Common Equity 360,000,000
--------------
TOTAL CLAIMS $1,200,000,000
The firm has a marginal tax rate of 30% and has $6,000,000 of retained earnings available for investment this year. On November 27, 1998 Melrose paid a dividend of $7.626 on its common stock. Yesterday (November 27, 2001) it paid a dividend of $10.714. The stock is currently selling for $100 a share. Assume that this growth rate continues indefinitely. The firm can raise funds under these conditions:
 

BONDS: Up to $10,000,000 in new bonds can be sold at a before tax cost of 12%.
Beyond $10,000,000 the before tax cost jumps to 15%.
PREFERRED STOCK: Up to $8,000,000 in $100 par preferred stock with a dividend rate of 16% can be sold at $96 a share with flotation costs of $7.11.
Beyond $8,000,000 the flotation costs rise to $24.89 a share.
COMMON STOCK: Up to $6,000,000 in new common stock can be sold to net the firm $85.714 a share. Beyond $6,000,000 the net proceeds total only $75.00.
The firm is considering five potential projects with the following forecasted cash flows:

Project	Outlay	Annual CFs	Life in Years	IRR
A	10,000,000	2,912,800	5	14.0
J	12,000,000	3,837,300	5	18.0
P	10,000,000	3,343,800	5	20.0
R	8,000,000	2,414,800	5	15.5
Z	10,000,000	3,054,100	5	16.0

{a} Compute Melrose’s marginal cost of capital for each segment of the marginal cost schedule.
{b} 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} Explain the difference between the current common stock price of $100 and the $85.714 net proceeds from the sale of the first $6,000,000 of new stock.
{d} Compute the net-present value of Project J. Clearly indicate what discount rate you are using.
{e} Why is Melrose accepting a project whose IRR is less than the rate of return required by shareholders require? Even if you did not get this result, explain how it is possible.
{f} If the cost of equity is so much greater than the cost of debt, why does the firm still use so much equity?

[17] (75 points) COST OF CAPITAL  Solution
SpongeBob Industries is planning its 2002 capital budget and needs your advice. The firm believes that its capital structure relations shown below are optimal and will be maintained.
Debt $500,000,000
Preferred Stock 100,000,000
Common Equity 400,000,000
--------------
TOTAL CLAIMS $1,000,000,000
The firm has a marginal tax rate of 40% and has $10,000,000 of retained earnings available for investment this year. On April 28, 1997 SpongeBob paid a dividend of $3.151 on its common stock. Yesterday (April 28, 2002) it paid a dividend of $4.63. The stock is currently selling for $50 a share. Assume that this growth rate continues indefinitely. The firm can raise funds under these conditions:
BONDS: Up to $25,000,000 in new bonds can be sold at a before tax cost of 15%.
Beyond $25,000,000 the before tax cost jumps to 20%.
PREFERRED STOCK: Up to $2,500,000 of new preferred stock with a dividend rate of 10% can be sold at its par value of $100 a share with flotation costs of $16.67.
Beyond $2,500,000 the flotation costs rise to $28.57 a share.
COMMON STOCK: Up to $15,000,000 in new common stock can be sold at a cost equal to the cost of retained earnings plus 3%.
Beyond $15,000,000 the cost of the common stock is the cost of retained earnings plus 6%.
The firm is considering five potential projects with the following forecasted cash flows:

Project	Outlay	Annual CFs	Life in Years	IRR
A	10,000,000	2,983,200	5	15.0
M	20,000,000	5,755,800	5	13.5
X	20,000,000	6,108,200	5	16.0
Z	20,000,000	6,395,600	5	18.0

{a} Compute SpongeBob’s marginal cost of capital for each segment of the marginal cost schedule and display your results on a CLEARLY LABELED graph.
{b} On the same graph, plot the firm’s IRR schedule and indicate which projects are acceptable. Compute the average cost of capital for the capital budget you are advocating.
{c} Compute the total underpricing and flotation costs associated with selling the first $15,000,000 of new common stock.
{d} Compute the net-present value of Project X. Clearly indicate what discount rate you are using.
{e} If the cost of debt is so much less than the cost of equity, how can the firm think that using only 50% debt is “optimal.”

[2] (a) W = $12,580.35; EAR=8.24%; (b) i=.667%/mo, EAR=8.30%

[3] A: R=1,258.75, EAR=10.03%; B: i=.04724% EAR=9.67%

[4] X=1648.56, have=7610, need=7226.37

[5] D=67,869.82, need=571,456, have 939,143

[6] outlay = 159,000, DCF=.6DC+10,400, DC=-61,226

[7] outlay = 528,000 DCF=83,800, IRR=9.33%

[8] n=3, NPV_A=-166,637; n=12, k'=11%, NPV_B=217,864

[9] DCF=125.80, (a) cert equi, outlay=520, NPV₃=-173.63, NPV₁₂=82.48; (b) beta model, k'=11%, NPV₃=-99.98, NPV₁₂=45.31

[12] (a) i=8.50%/yr, (b) P₈=931.01 irr=7.55%/yr, (c) conv value=1240, irr=10.13%

[13] (a) i=5.25%/period, EAR = 10.78%; (b) r=4.73%/period, EAR=9.68%/yr; (c) NPV=657.43

[14] (a) P₀₄=10.71; (b) P₂₄=34.66; (c) r=18%

[15] (a) P₄=90.28, P₀=65.98; (b) P₈=118.34; (c) r=15%

[16] Breaks: 20(D&Eq), 40(P&Eq); k_e=24%, D₀₂=12.00, MCC₁=15.0, MCC₃=18.15, ACC₂₂=15.15, k_j=15.275, NPV_j=779,914

[17] Breaks: 25(P&Eq), 50(D), 62.5(Eq); MCC₁=12.9%, MCC₄=17.0%, ACC₅₀=13.6%, k_x=13.95%, NPV_x=995,169