[1] (30 points) EFFECTIVE RATES  Solution
To finance the purchase of a Shelby 427 Cobra, you need to borrow $120,000. The dealer offers you a choice of borrowing plans: With Option A, they will lend you the money at an APR of 13.2%, compounded monthly for two years. With Option B they will lend you the money and require 4 semi-annual payments of $35,000. {a} For both loans, calculate the APR, EAR and total payments over a six-month period. Explain which plan you should choose and why. {b} Now suppose there is also an Option C: EAR of 13.08%, uniform monthly payments for 24 months plus a balloon payment of $10,000 at month 24. (Note, this $10,000 is in addition to the regular monthly payment that also occurs at month 24). Calculate the uniform monthly payment. Now which option do you choose?
 

[2] (30 points) EFFECTIVE RATES  Solution
To finance the purchase of a new SUV, you need to borrow $9,530. You can borrow the funds from the dealer who will lend you the money for four years if you agree to make 8 semi-annual payments of $1,700. As an alternative you can borrow the funds from your banker who will lend you the money for four years at an APR of 18%. You would make 48 equal monthly payments. For both loans, calculate the EAR and total payments over a six-month period. Where should get your loan? Explain fully what makes your choice the better alternative.
 

[3] (35 points) TIME VALUE OF MONEY  Solution
On October 1, 2002 you make the first of 5 planned equal annual deposits to an account that earns 8% interest. The last deposit is planned for October 1, 2006. The deposits must be of sufficient size to enable you to withdraw $4000 a year starting on October 1, 2011 and continuing through October 1, 2030. As luck would have it, you were able to make only the first 3 planned deposits. On October 1, 2011 you make the first $4000 withdrawal as planned. On that same day, you decide to try and continue to withdraw the annual $4000, not just until October 2030, but in perpetuity. Clearly earning 8% won’t cut it. So you decide to switch your funds that day to another higher yielding investment. What is the minimum annual rate of return the new investment must provide if you are to continue the $4000 withdrawals in perpetuity?
 

[4] (35 points) TIME VALUE OF MONEY  Solution
You want to save for your approaching retirement. Starting on February 17, 2003 you PLAN to make 5 consecutive equal annual deposits into an account that pays 12% interest. You intend to withdraw $80,000 each year starting on February 17, 2012 and continuing through February 17, 2031. {a} If all goes according to plan, what will be the amount left in the account as of February 18, 2030? As it turns out, you make only the first three planned deposits and skip the last two. On February 17, 2009 you decide to: [1] Make a deposit of X dollars that day and another one of 2X dollars on February 17, 2010 and [2] switch the planned withdrawals to $80,000 a year for ever still starting on February 17, 2012. {b} Find the minimum value of X.
 

[5] (35 points) CAPITAL BUDGETING  Solution
Sponge Bob 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 cost of the proposed new machine is negotiable but the machine would be depreciated over an expected life of 9 years to a salvage value of 10% of its cost also using the straight-line method. Because of greater efficiencies, the new equipment would lower Sponge Bob’s operating expenses by $112,000 a year but would require additional net working capital of $12,000. Assume a hurdle rate of 15%. What is the maximum price that Sponge Bob could be willing to pay for the new machine if the replacement is to just profitable?
 

[6] (35 points) CAPITAL BUDGETING  Solution
L&G Industries is contemplating the replacement of a piece of equipment that has a book value of 110. It is being depreciated straight-line to a salvage value of 10 over an expected remaining life of 10 years. The new equipment under consideration has a purchase price of 330 and would be depreciated straight-line to a salvage value of 30 over an expected life of 10 years. The new equipment is expected to increase annual sales by 60 and increase annual operating costs by 20. Additional net working capital of 5 would be required if the new equipment is purchased. The firm’s marginal tax rate is 40% and the required rate of return is 15%. The firm has no idea of how much the current equipment is worth now. {a} Find the minimum selling price that L&G would have to get for the old equipment for it to want to make the replacement. {b} How do the NPV and IRR methods differ with regard to the assumed reinvestment rate of the early cash flows?
 

[7] (45 points) CAPITAL BUDGETING UNDER RISK  Solution M&E Enterprises is considering the purchase of a new piece of equipment. It would cost $150 and be depreciated over a life of 5 years to a zero salvage value using the straight-line method. If the purchase is made, M&E estimates the following probability distribution of revenues less operating expenses for each year:
 

M&E has a marginal tax rate of 40% and the new investment would require additional net working capital of $50. You may assume that any non-operating terminal year cash flows are known with certainty, i. e., their certainty equivalent coefficients are equal to 1.0. Also for simplicity, you may use the same certainty equivalent coefficient for all operating cash flows for every year. The risk-free rate is 5%, the investment’s beta is 2 and the market’s risk-premium over and above the risk-free rate is 6.5%.
{a} Calculate the risk-adjusted NPV of the investment if there is a 50% chance the equipment will actually last only 4 years and be scrapped for $40 and a 50% chance it will actually last 12 years at which time its scrap value will be zero.
{b} Suppose that instead of using the certainty equivalents approach, M&E uses the “Beta Model” for selecting its hurdle rate. Calculate the NPV if the information in {a} still holds.
{c} Explain the circumstances under which M&E should use the Beta Model; i.e., must M&E be diversified or just in one or two lines of business? What is systematic risk and what is unsystematic risk? Which does beta account for and what happens to the other one?
 

[8] (45 points) CAPITAL BUDGETING UNDER RISK  Solution
Skywalker, Inc. is contemplating the purchase of a new piece of equipment that would cost $540. The equipment would be depreciated over a life of 9 years to a zero salvage value using the straight-line method. Skywalker forecasts the following probability distributions for revenues over operating expenses for each year:
 

The firm has a marginal tax rate of 40% and the new investment would require additional net working capital of $50. Assume there is a 40% chance that the equipment will actually last only 5 years with a scrap value of $80 and a 60% chance that it will last 15 years with a scrap value of zero. The standard deviation (s) of the after-tax cash flows is 60.67. Additional information:
 

The risk-free rate of interest is 4%, the investment beta is 1.5 and the market's risk-premium over and above the risk-free rate is 6%. The certainty equivalents coefficient, a, is selected from the above table. Assume that the a for all non-operating cash flows is 1.0.
{a} If Skywalker 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 explain why you chose your approach to account for risk. Clearly and completely explain why you chose your approach to account for risk. Does your method consider systematic and/or unsystematic risk? If so, why; if not, why not?
{b} If Skywalker 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 and completely explain why you chose your approach to account for risk. Does your method consider systematic and/or unsystematic risk? If so, why; if not, why not?

[9] (20 points) LEVERAGE  Solution
The Bohlin Company sells its only product, a sterling silver and gold belt buckle for $3,500 each. The production process is highly labor intensive with almost the entire buckle being hand engraved by a single craftsman. Currently the company’s very skilled craftsmen are paid on a finished item basis. Current variable costs (including labor) per buckle are $1600 and total fixed operating costs for the company are $3,500,000. Fixed interest charges are $500,000. Bohlin is contemplating a change in how it pays its craftsmen. If they are each paid a guaranteed fixed annual salary, total fixed operating costs will rise to $6,500,000 but variable costs per buckle will drop to only $600 a buckle.
{a} Compute the degree of operating leverage at a sales level of $10,000,000 under both the present pay system and the proposed new one.
{b} Explain why there is a difference between your two values in {a}.
{c} How does the forecasted volatility of future years’ sales impact Bohlin’s decision?

[10] (30 points) LONG-TERM DEBT  Solution
{a} From the issuer’s point of view, what are possible advantages and disadvantages of adding a conversion feature to its bonds when raising capital using long-term debt? Clearly state any assumptions you are making.
{b} From the issuer’s point of view, what are possible advantages and disadvantages of raising capital using long-term bonds versus issuing short-term bonds? Assume a downward sloping yield curve at the time of issuance. Clearly state any other assumptions you are making.
{c} From the issuer’s point of view, what are possible advantages and disadvantages of adding a call feature to its bonds when raising capital using long-term debt? Assume that interest rates are near their historical highs at the time of issuance. Clearly state any other assumptions you are making.
 

[11] (25 points) BOND VALUATION  Solution
Yesterday Dexter’s Laboratory paid a dividend of $2.00 a share on its common stock. The firm’s earnings and dividends are expected to grow indefinitely at 5%, and the market requires a 15% rate of return on Dexter’s common stock.
Ten years ago you purchased a convertible debenture of Dexter’s Lab. At that time, the bond had 15 years left to maturity and its yield to maturity was 14%, compounded semi-annually. The $1,000 par value bond pays an annual coupon of 12%, compounded semi-annually. The bond is convertible into Dexter’s common stock at a conversion price of $20 a share.
{a} What price did you pay for the bond?
{b} What annual rate of return did you earn over the last 10 years if you convert the bond today?
{c} What annual rate of return did you earn over the last 10 years if, instead of converting, you surrender the bond when it is called at $1,090?
 

[12] (35 points) BOND VALUATION  Solution
Bunky's Burgers has some outstanding $1000 par value subordinated debentures that mature in 30 years. The bonds have an annual coupon rate of 11%, payable semiannually. The debentures are neither callable nor convertible.
{a} Suppose you buy a bond today for the market price of $930. What is the bond's yield to maturity?
{b} Suppose you hold the bond for 12 years and then sell it in the open market. The yield to maturity 12 years from now is 9% for 18-year bonds and 13% for 30-year bonds. Compute the annual rate of return you earned over the 12-year period.
{c} Now assume that the bond is callable at a price of $1060 and also convertible into Bunky's common stock at a price of $40 a share. Suppose that 12 years from today the stock is trading at $51.80 a share and the firm calls the bond. What rate of return did you earn over the 12-year period if you follow the better course of action?

[13] (30 points) EQUITY VALUATION - SUPERGROWTH Solution
You are contemplating buying a convertible bond of M&E Enterprises, Inc. for $950. The $1,000 par value bond has an annual coupon rate of 16% payable semiannually. The bond matures in 20 years and is convertible into M&E common stock at a conversion price of $100 a share. Yesterday M&E paid a dividend of $2.00 a share. Analysts expect that M&E’s earnings and dividends will grow at a 30% rate for another 9 years before settling at a 6% growth rate for the indefinite future. Stockholders require a return of 15% compounded annually on stock of M&E’s risk.
Assume that you expect the forecasts to hold and that you would convert the bond at the prevailing market price 5 years from now. Using an annual discount rate of 13%, compounded semi-annually, calculate the NPV of the decision to buy the bond today.
 

[14] (30 points) EQUITY VALUATION - SUPERGROWTH Solution
You buy a convertible bond today for $1035. The bond is convertible into the company’s common stock at a conversion price of $100 a share. The annual coupon rate is 8% payable semi-annually. Yesterday the firm paid a dividend per share on its common stock of $2.00. Financial gurus forecast that the firm’s earnings and dividends will grow at a 40% rate for 8 years before declining to a normal rate of 8% for the indefinite future. Assume that: all of the growth forecasts come true, stockholders require an 18% return on the common stock, and you hold the bond for 6 years before converting it. Calculate the rate of return you earned on the investment over the 6-year period.

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

The firm is planning its capital budget for the coming year and needs your expertise. The firm's marginal tax rate is 40%, it has retained earnings available for investment of $9,000,000 and its common stock has a dividend yield of 10%. Earnings and dividends are expected to grow indefinitely at an 8% rate.
New securities can be sold under the following conditions:
DEBT: Up to $12,000,000 in new 30 year debentures with an 8% coupon (payable annually) can be sold for $852.48 with flotation costs of $41.02. Beyond $12,000,000 the flotation costs rise to $113.29 per bond.
PREFERRED STOCK: Up to $2,000,000 in new $100 par value preferred stock with a dividend rate of 8% can be sold to net the firm $66.67. Beyond $2,000,000 the dividend rate must be 10% and the firm nets $71.43.
COMMON STOCK: Up to $6,000,000 in new common stock can be sold with underpricing and flotation costs equal to 20% of the common stock’s current price. Beyond $6,000,000 the underpricing and flotation costs total 33.33% of the stock’s price. The following three investment projects have been proposed (outlay in $millions):
 

{a} Compute the cost of capital for all segments of the cost of capital schedule. ACCURATELY display your results on a 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} Compute the NPV of project C. Assume uniform cash flows and a life of 4 years.
{e} If financing with common equity is so expensive compared to financing with debt, why does the firm still obtain 30% of its funds from common equity?

[16] (70 points) COST OF CAPITAL  Solution
Ace, Inc. is planning its 2004 capital budget and needs your advice. The firm's capital structure relations shown below are believed to be optimal and will be maintained.

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. Ace’s marginal tax rate is 50%. 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 $32,000,000 of new $1000 par 20-year bonds carrying a 12% coupon (paid annually) can be sold for $950. Flotation costs total $27.00 per bond.
Any additional $1000 par 20-year bonds carrying a 14% coupon (paid annually) can be sold for $987 with flotation costs totaling $53.67.
PREFERRED STOCK: Any size issue of $50 par value preferred stock carrying an 8.8% dividend rate can be sold to yield the investor 11%. Flotation costs total $4.80.
COMMON EQUITY:The firm can sell up to $20,000,000 in new common stock at a cost to the firm of kn = 20%. Beyond that the cost to the firm rises to 24%. The cost of retained earnings is ke = 18%.
The following is a list of potential investments that the firm is considering:

{a} What is the total amount of flotation costs and under pricing per share associated with selling the first $20,000,000 of new common stock?
{b} 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} Compute the NPV of project Q assuming a life of 5 years and uniform annual cash flows.
{d) Hopefully you discovered that the firm is accepting a project whose IRR is less than the rate of return required by stockholders. Why is this?

[1] (a) Ra = 5,716.30; EARa = 14.03%

[2] Dealer: i=8.66%, EAR=18.07%; Banker payment = 279.94, EAR = 19.56%

[3] (a) D = $4,920.49; at 2011 have 23,376.40; i = 17.11%

[4] D=59,777.50, X=76,843.12

[5] (a) outlay = X - 80000; DCF = 64000 + .04X

[6] Outlay = 291-.6MV, DCF=32, MV=207.03

[7] DCF = 43.8; s=20.97; a=.75; outlay = 200; {a} NPV₄ = -12.76; NPV₁₂ = 78.20; {b} NPV₄ = -37.82; NPV₁₂ = -3.19

[8] DCF = 171; s=60.67; outlay = 590; {a} NPV₅ = 116.74; NPV₁₃ = 491.12; {b} a=.60; NPV₅ = 26.21; NPV₁₃ = 325.77

[9] Present: OL = 2.81; Proposed: OL = 4.64

[11] P_{stock 0} = 21.00; P_{bond 0} = 875.91; conversion value = 1050, IRR =n 14.64%/yr comp sa; called at 1090, IRR = 14.84%/yr comp sa

[12] (a) i = 5.93% per period; (b) P₁₂ = 1176.66; r = 6.41% per period or 12.82% per year compounded sa (c) conv value = 1295; r = 13.25% per year comp sa

[13] Conv ratio = 10 shares:1 bond; P₅=183.56; P₉ = 142.82; conv value = 1835.6; NPV = 602.98

[14] P₈ = 318.77; P₆ = 268.00; conv value = 2680; IRR = 21.81%/yr compounded sa;

[15] Break points: Debt = 20,000,000, Pf'd = 20,000,000, Equity = 30 and 50,000,000; Component costs: Debt = 6.0% and 6.6%, Pf'd = 12% and 14%; Retained Earnings = 18% (given) and New Common = 20.5% and 23.0%; MC₁ = .102, MC₂ = .108; MC₃ = .115, MC₄ = .123; ACC at 40,000,000 10.68% Accepting B & A only; NPV_C = -378,335, k_c = 11.90, Cash Flows of C = 6,446,527

[16] Break points: Debt = $80,000,000; Equity = $40,000,000 and $80,000,000; Component costs: Debt = 6.55% and 7.53%; Pf'd = 12.50%; Marginal costs: 0 to $40 MC = 12.87%; $40 to $80 MC = 13.87%; $80+ MC = 16.26%; accept Z-Q, raise $100 million at an ACC = 13.95%; NPV of Q = 2,633,419 using a discounr rate of 14.67%; Equity flotation costs = $7.49 since P = 48.64