[1] (30 points) EFFECTIVE RATES  Solution
{a} Your parents are contemplating buying a new home for $400,000 by putting 20% down and financing the remainder over 15 years. Loan A would require monthly payments and the bank would charge an APR 6%. Loan B would require quarterly payments of $8,000. Compute the EAR and total amount they would pay each year for both loans. Which one do you suggest they take and why?
{b} Today you buy some shares of preferred stock for $250. You expect to receive, starting in 3 months, quarterly dividend payments of $12.50 in perpetuity. What APR and EAR are you earning?
 

[2] (30 points) EFFECTIVE RATES  Solution
You are buying a new Hummer Mini for $25,000 by putting $5,000 down and financing the remainder over 3 years.

{a} The bank will lend you the $20,000 at an APR of 8%, compounded monthly. Compute the EAR and monthly payments.

{b} The Hummer dealer offers you quarterly payments of $1,900. Compute the EAR and APR.

{c} You’d like to borrow the money from the dealer to build some goodwill but you don’t want to pay his higher EAR. So you’d like to be able to tell him, “Reduce my quarterly payments down to $X so that you’ll have the same EAR as the bank and I’ll finance through you.” Calculate X.

{d} Explain why the dealer’s quarterly payment of X is higher than three of the bank’s monthly payments.
 

[3] (35 points) TIME VALUE OF MONEY  Solution
Starting 10 years ago you made 7 equal annual deposits (D). The deposits were of sufficient size to enable you to make 20 planned equal annual withdrawals (W) starting 2 years from today. You believed that the interest rate would remain at the initial 8% rate for the entire 31 years.

Today you discover a pleasant piece of news: unbeknownst to you, the interest rate had increased to 15% beginning 6 years ago. Assuming that the 15% rate continues for another 21 years, you calculate that because you now have a bigger balance than you had anticipated, you can withdraw $2,000 a year for 20 years still starting 2 years from today.

Find D and W.
 

[4] (35 points) TIME VALUE OF MONEY  Solution
On February 21, 2008 you make the first of 6 equal annual deposits to an account that you expect to earn 8% interest a year through February 21, 2012 and then 12% from then on. The last deposit is February 21, 2013. The deposits must be of sufficient size to enable you to withdraw $5,000 a year in perpetuity starting on February 21, 2020.
Assume that immediately after you make your 3rd $5,000 withdrawal on February 21, 2022, you learn that the interest rate that did not rise to 12% as you had expected but it had stayed 8%.

{a} What is your balance immediately following the 3rd withdrawal?

Assume parts {b} and {c} are independent of each other.

{b} How much can you withdraw now in perpetuity starting in 2023?

{c} Suppose you never did figure out that the interest rate didn’t change. How many full withdrawals of $5,000 (including the first three) can you make before the account goes dry.
 

[5] (35 points) CAPITAL BUDGETING  Solution
GEM Industries is contemplating replacing a piece of equipment with a newer model. The new machinery would cost $130 and be depreciated over an expected life of 5 years to a salvage value of $30 using the straight-line method. It is expected that the new equipment would increase annual sales by $40 and increase annual operating costs by $15. Additional net-working-capital of $27 would be required if the old machine is replaced. At the end of year 3 the firm would need to overhaul the machine at a cost of $60 (this is in addition to the additional operating costs of 15 and is a tax deductible expense).The firm has a marginal tax rate of 40% and a required hurdle rate of 15%.

The existing equipment has a current book value of $65 and is being depreciated using the straight-line method to a salvage value of $5 over a remaining life of 5 years. The firm could sell the old equipment today for $85.

Compute the NPV and IRR of the replacement.
 

[6] (35 points) CAPITAL BUDGETING  Solution
Mega Conglomerate, Inc. is considering replacing some existing equipment with a new model. The new equipment would cost $5,500 and be depreciated to a $500 salvage value over a 10 year expected life using the straight-line method. The firm expects as a result of replacing the old equipment to increase annual sales by $400 in years 1 through 6 and by $700 in years 7 through 10 and to increase annual operating expenses by $200 in years 1 through 6 and by $300 in years 7 through 10. Additional net working capital of $1,000 would be required.
The existing equipment was purchased 5 years ago for $4,200 and is being depreciated over a 15 year life using the straight-line method to a salvage value of $1,200. The existing equipment could be sold today for $1,600. The firm has a marginal tax rate of 30% and a required hurdle rate of 15%.

Compute the NPV of the decision to replace the equipment.
You must clearly indicate your work with equations and not a list of calculator buttons.
 

[7] (40 points) CAPITAL BUDGETING UNDER RISK  Solution
Wrobel Technology is considering purchasing a new piece of equipment for $600. It would be depreciated over a life of 6 years using the straight-line method to a zero salvage value. The equipment would require additional net working capital of $40. The firm forecasts the following for each year of operation:

[8] (35 points) CAPITAL BUDGETING UNDER RISK  Solution
Bunky’s Performance Products is involved only in the auto parts industry. It is thinking of investing in a new project that deals with the remanufacturing of fuel injection systems for import cars. T he cost of the project is $1,000; the equipment would be depreciated using the straight-line method to a zero salvage value over a life of 10 years. The firm's marginal tax rate is 45% and additional net-working-capital of $100 would be required.
Below are the forecasts of the expected change in sales revenues less expenses for each year:
60% Probability of $250 per year
40% Probability of $550 per year
The risk-free rate of interest is 4%. The project has a beta coefficient of 1.4. The market's risk premium is 5%. The firm also found the table below from an old copy of a Fin 225 exam that may or may not prove useful: If and when you use the table, apply you’re a to all cash flows, both operating and non-operating.

[9] (30 points) RISK PREMIUMS AND YIELD CURVE  Solution
{a} Explain what happens to the risk-premium 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 long-shot, becomes more and more likely. Why?
{b} Explain what happens to the risk-premium of a firm’s subordinated debentures relative to its mortgage bonds as the outlook for the economy starts to improve Why?
{c} Draw and label an inverted yield curve. What are the relative advantages and disadvantages for the investor of buying short-term bonds versus buying long-term bonds? How do these advantages depend upon the expectations of future rates suggested by the shape of the curve?
{d} Explain what happens to the risk-premium of a firm’s callable bonds relative to its non-callable bonds as leading indicators suggest that the trend of interest rates is upward. Why?

[10[ (30 points) RISK PREMIUMS AND YIELD CURVE  Solution
{a} Explain how buying stock on margin (borrowing some of the money from your broker) is an example of personal leverage. Illustrate with a numerical example if it will make your answer clearer.
{b} Define systematic risk and give a couple of examples. Define unsystematic risk and give a couple of examples. In the CAPM (“beta model”) explain which one is relevant and what happens to the other one.
{c} Draw and label an upward sloping term structure of interest rates. Explain the advantages and disadvantages to the investor of buying long-term securities? How do expectations of future interest rate movements impact your answer?
 

[11] (30 points) BOND VALUATION  Solution
You purchase a subordinated debenture of GEM, Inc. for $1,065.38. The $1,000 par value bond carries an annual coupon rate of 9%, payable semiannually and matures in 30 years. The bond is convertible into GEM common stock at a conversion price of $25 per share.
{a} At the time of purchase, what is the bond’s yield to maturity? Express your answer as an EAR.
ASSUME THAT PARTS {b} AND {c} ARE INDEPENDENT OF EACH OTHER.
{b} Calculate your IRR if you hold the bond for 12 years and then sell it at its market value. At the time of sale, the yield to maturity is 11.5% a year compounded semiannually on 18-year subordinated debentures and 13% on 30-year subordinated debentures. Express your answer as an EAR.
{c} Calculate your IRR if you hold the bond for 12 years and then convert it. At the time of conversion, GEM’s stock is trading at $32 a share. Express your answer as an EAR.
 

[12] (35 points)BOND VALUATION  Solution
Eight years ago you buy a newly issued $1,000 par value subordinated debenture of GEM Industries for $1,065.63. The bond carries a coupon rate of 7% per year, payable semiannually, and matures in 30 years.
{a} What are the main differences between a subordinated debenture and a mortgage bond of the same company?
{b} Calculate the yield to maturity on the bond (express your answer as an effective annual rate).
{c} Today you sell it in the open market. The yield to maturity on 30-year bonds is now 4.75% per year, payable semiannually and the yield to maturity on 22-year bonds is 4.25% per year, payable semiannually. Calculate the rate of return you earned over the 8-year period (express your answer as an effective annual rate).
{d} This part is independent of part {c}. Now suppose the bond is callable at $1,045 and is convertible into GEM’s common stock at a conversion price of $33.33 per share. The common stock is currently selling for $45 per share. GEM calls the bond and you take the better course of action. Calculate the return you earn over the 8-year period (express your answer as an effective annual rate).
{e} This part is independent of part {d}. The outstanding bond is not convertible but is callable at a price of $1.045. The firm is thinking of issuing new bonds at par and using the proceeds to call the outstanding bonds. The new bonds would have a par value of $1,000, mature in 22 year, and offer an annual coupon of 4.25%, payable semiannually. Calculate the IRR of the decision to refinance the bonds. Should the firm refinance the bonds?
 

[13] (30 points) SUPERGROWTH - EQUITY VALUATION  Solution
Today you buy a convertible bond of Bunky’s Burgers for $866.55. The bond has a par value of $1000, matures in 20 years and has annual coupon rate of 12%, payable semiannually. Yesterday Bunky’s common stock paid a dividend of $0.20. You forecast that Bunky’s earnings and dividends will grow at 25% for the next 12 years before declining to an annual rate of 6% for the indefinite future. The stock market requires a 16% rate of return on Bunky’s common stock.
{a} Assume your growth forecasts are accurate and you hold the bond for 8 years and then convert it to Bunky’s common stock. You earn an IRR over the 8-year holding period of 20% a year, compounded semiannually. Calculate the conversion price of the common stock THAT IS PRINTED ON THE BOND AT ISSUANCE.
{b} Assume your growth forecasts are accurate and you convert the bond at its maturity. What IRR did you earn over the 20-year period?

[14] (30 points) SUPERGROWTH - EQUITY VALUATION  Solution
Today you purchase a $1,000 par value convertible bond of GEM Industries. 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 GEM’s common stock at a conversion price of $100 a share.
You forecast that the earnings and dividends of GEM will grow at annual rates of 30% for the next 5 years and then 20% for another 5 years before declining to a 6% rate for the indefinite future. Yesterday the firm paid a dividend (D0) of $2.72. Stockholders require a return of 18% on stocks in GEM's risk class.
{a} You hold the bond for 7 years and then convert it. Assume that all your forecasts hold. What IRR did you earn over the 7 year period?
{b} If you hold the bond for 30 years and convert it the day before it matures, what rate of return did you earn if all the forecasts come true?

[15] (70 points) COST OF CAPITAL  Solution
Bill’s Khakis has the following capital structure that it believes is optimal and will be maintained:

Debt	$250,000,000
Preferred Stock	100,000,000
Common Equity	150,000,000
CLAIMS	$500,000,000

The firm is planning its capital budget for the coming year and needs your expertise. The firm's marginal tax rate is 45%, it has retained earnings available for investment of $9,000,000 and its common stock has a dividend yield of 7.5%. Earnings and dividends are expected to grow indefinitely at an 8% rate.
New securities can be sold under the following conditions:
DEBT: Up to $10,000,000 in new 30 year debentures with an 6% coupon (payable annually) can be sold for $934.71 with flotation costs of $58.80. An additional $5,000,000 could be sold at a before-tax cost of 2% higher than the first $10,000,000. Any additional debt could be issued at a before-tax cost of 4% higher than the first $10,000,000.
PREFERRED STOCK: Any size issue of new $50 par value preferred stock with a dividend rate of 10% can be sold to net the firm $33.33 a share. Flotation costs total $6.67 per share.
COMMON STOCK: Up to $6,000,000 in new common stock can be sold with under pricing and flotation costs equal to 25% of the common stock’s current price. Beyond $6,000,000 the under pricing and flotation costs total 37.5% of the stock’s price.
The following three investment projects have been proposed (outlay in $millions):

Project	Outlay	IRR
A	10	12.5%
B	10	10.0%
C	15	14.0%
D	10	11.9%
E	15	10.5%

{a} Compute the cost of capital for all segments of the cost of capital schedule. ACCURATELY display your results on a large, readable graph.
{b} On the same graph, draw the firm's IRR schedule. Which projects should the firm accept?
{c} Compute the average cost of capital for the amount of the capital budget you found in {b}.
{d} Calculate the investor’s yield on the preferred stock.
{e} Compute the NPV of project D. Assume uniform cash flows and a life of 4 years.
{f} If financing with debt is so much cheaper than financing with equity, why does the firm raise only 50% of its funds from debt?

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

Debt	$480,000,000
Preferred Stock	120,000,000
Common Equity	600,000,000
CLAIMS	$1,200,000,000

The firm has a marginal tax rate of 40% and has $8,000,000 of retained earnings available for investment this year. On April 20, 2001 Lehigh paid a dividend of $7.626 on its common stock. Yesterday it paid a dividend of $12.282. The stock is currently selling for $112.60 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 $3,600,000 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 $3,600,000 the flotation costs rise to $24.89 a share.
COMMON STOCK: Up to $10,000,000 in new common stock can be sold to net the firm $90.07 a share. Beyond $10,000,000 the net proceeds total only $75.06.
The firm is considering five potential projects with the following forecasted cash flows:

Project	Outlay	Life in Years	IRR
A	15	5	21.0%
J	10	5	18.0%
P	6	5	19.0%
B	10	5	17.5%

{a} Compute Lehigh’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 $112.60 and the $90.07 net proceeds from the sale of the first $10,000,000 of new stock.
{d} Compute the net-present value of Project J. Clearly indicate what discount rate you are using. Assume uniform annual cash flows.
{e} Why is Lehigh 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.

[1] (a) Loan A: payment = 2,700.34, EAR = 6.17%, total annual payments = $32,404; Loan B: i = 1.4395% per month, EAR = 5.88%, total annual payments = $32,000; Choose loan B with the lower EAR

[2] Bank: R = $626.73, EAR = 8.30%; Dealer APR = 8.303%, EAR = 8.57%; {c} i = 2.013%/quarter, X = $1,892.74

[3] Balance today = 10,885.79' D = 628.14 and W = 838.78

[4] D = $2,788.37, {a} balance = $24,658.24, {b} W = $1,972.66, {c} n = 14 full withdrawals, the 15th is less than 5000

[5] outlay = 80, DCF=18.2, NPV=-16.81, IRR = 7.81%

[6] outlay = 4420, DCF=230 for years 1-6 and 370 for years 7-10, NPV=-3,018.73

[7] DCF_1-8=172; DCF₉₊=132; cv=45.54/172; net proceeds yr 4 = 134; {a} NPV₄ = -69.92; NPV₁₄ = $440.97; {b} NPV₄ = 8.24; NPV₁₄ = 460

[8] DCF_1-10=248.5; DCF₁₁₊=203.5; cv=80.83/248.5; net proceeds yr 6 = 290; {a} NPV₆ = -133.46; NPV₁₅ = $509.87; {b} NPV₆ = 159.80; NPV₁₅ = 649.26

[11] i = 4.20%/period; EAR=8.58%; P₁₂ = 811.66; IRR=3.58%/period; conv value = 1280

[12] i = 3.25%/period; EAR=8.58%; P₈ = 1390.53; IRR=30.56%/period; conv value = 1350

[13] P₈ = 22.81; P₃₀ = 22.81; conversion value = 1824.79; conversion ratio = 80 shares : 1 bond; conversion price = $12.50

[14] P₃₀ = 711.92, IRR = 12.02% per year, comp sa

[15] Break points: Debt = $20 and $30; Equity = $30 and $50; Component costs: Debt = 3.9%, 5.0%, 6.1%; Pf'd stock = 15.0%; Equity = 15.5%, 18.0%, 20.0%; Accept C-A-D-E and raise $35 million at an ACC of 10.0%; yield on Pf'd Stock = 12.5%; Project D: CF = $3,285,413, k_D = 10.85%; NPV_D = $225,545

[16] Break points: Debt = $25; Preferred $36; Equity = $16 and $36; Component costs: Debt = 7.2%, 9.0%, Pf'd stock = 18% and 22.5; Equity = 22.0%, 25.0%, 28.0%; Accept A-P-J and raise $31 million at an ACC of 16.55%; Project J: CF = $3,197,778, k_J = 17.61%; NPV_J = $88,525