[1] (30 points) EFFECTIVE RATES  Solution
Gabby needs to borrow $50,000 for 5 years immediately and she has three choices: First National Bank charges an APR of 6% a year and requires equal monthly payments for 5 years. The local loan shark requires daily payments of $31 (assume no leap years) for 5 years. Her father requires only a single payment at the end of the fifth year.
{a} Compute the monthly bank payment and its EAR.
{b} Compute the APR and EAR of the loan shark.
{c} Compute the father’s lump-sum payment if he requires the same EAR as the loan shark.
 

[2] (25 points) EFFECTIVE RATES  Solution
George needs to borrow $60,000 for 5 years to buy a new Lincoln and the dealer gives him three borrowing plans: A requires an APR of 6% with equal monthly payments; B requires quarterly payments of $3,485; and C requires monthly payments of $500 and a balloon payment of $50,000 at the end of year 5.
{a} Calculate Plan A’s monthly payment and its EAR.
{b} Calculate the APR and EAR of Plans B and C.
{c} Calculate the total amount George would pay each year (ignore TVM) for plans A and B.
{d} EXPLAIN which plan George should choose and why.
 

[3] (35 points) TIME VALUE OF MONEY  Solution
Starting today (October 2, 2007) Gabby makes the first of 6 deposits of $D into an account that is expected to pay 20% annual interest through October 2, 2009 before declining to 10% and remaining there indefinitely. The last $D deposit is October 2, 2012. Gabby wants to be able to withdraw $T each year for four years for college starting on October 2, 2018. On October 2, 2015, Gabby learns that the interest never did decline and is still at 20% and is expected to remain at that level indefinitely. Gabby figures out that she can now either make four equal tuition withdrawals of $30,000 starting on October 2, 2018 and ending on October 2, 2021 or instead, she can give a gift of $X a year in perpetuity still starting on October 2, 2018.
{a} Find the value of X.
{b} Find the value of D.
{c} Find the value of T.
 

[4] (35 points) TIME VALUE OF MONEY  Solution
Starting today (February 19, 2008) Abe makes the first of 8 deposits of $D into an account that is expected to pay 6% annual interest through February 19, 2015. After he makes the last deposit on February 19, 2015 he transfers all of the funds to a different investment account that pays 8% interest for ever. Abe wants to be able to withdraw $60,000 annually for his retirement for 20 years starting on February 19, 2019 and ending on February 19, 2038. He also wants to leave his family $200,000 on February 19, 2039. On February 19, 2028, Abe learns that the interest rate of the original account declined from 6% to 3% on February 19, 2012. He had still moved his funds to the 8% account as planned and also had made the first 10 of the planned $60,000 withdrawals.
{a} Find the amount of the initial deposits.

Parts {b} and {c} are independent of each other.

{b} Abe wants to know on February 19, 2028 if he can still take out the 10 remaining planned $60,000 withdrawals if he’s willing to completely eliminate the gift to his family. Can he or can’t he? How big a surplus or deficit does he have in 2028?
{c} If Abe still wants to leave his family the planned $200,000, by how much must he reduce his remaining 10 planned equal withdrawals?
 

[5] (35 points) CAPITAL BUDGETING  Solution
Gabby’s Industries is considering replacing a piece of equipment with a newer model. The existing equipment has a remaining life of 5 years and has a current book value of $16. It is being depreciated over its remaining life to an expected salvage value of $6 using the straight-line method. Gabby’s can sell the existing equipment today for $20. The proposed new equipment is forecasted to increase annual sales revenue by $15 and to increase annual operating expenses by $5. Additional net-working-capital of $6.8 would be required if the new equipment is purchased. Gabby’s has recently adopted a policy of depreciating this type of equipment over a 5-year life to a salvage value of 20% of the equipment’s purchase price. Gabby’s marginal tax rate is 30% and required rate of return is 15%.
{a} Calculate the maximum price that Gabby’s would be willing to pay for the new equipment for it to want to make the replacement.
{b} Suppose that Gabby’s is able to buy the new machine for half of your answer to {a}. Calculate the expected IRR on the replacement.
 

[6] (30 points) CAPITAL BUDGETING  Solution
Steve and Co. is considering replacing a piece of equipment with a newer model. The existing equipment has a remaining life of 5 years and has a current book value of $30. It is being depreciated over its remaining life to an expected salvage value of $5 using the straight-line method. Steve and Co. can sell the existing equipment today for $20.
The proposed new equipment would cost $80 and be depreciated over an expected life of 5 years to a salvage value of $15. The equipment is expected to increase annual sales revenue by $50 and to increase annual operating expenses by $12. Additional net-working-capital of $10 would be required if the new equipment is purchased. Steve and Co. has a required rate of return of 15%. The decision to replace is complicated by a possible new tax law being discussed in Congress.

Calculate the maximum marginal tax rate Steve and Co. could be subjected to for it to still want to make the replacement.
 

[6.5] (10 points) CAPITAL BUDGETING 
Suppose that the firm where you are interning this summer is considering the purchase of a new piece of equipment and they need your advice. They ask you to compute the NPV and IRR first using the straight-line method of depreciation and then again using an accelerated method such as double declining balance or MACRS. Explain why both methods give the same NPV and IRR or why one of the methods gives higher values than the other.
 

[7] (40 points) CAPITAL BUDGETING UNDER RISK  Solution
Coyote, Inc. is a firm operating in a single line of business. It is thinking of purchasing a new piece of equipment. The cost of the project is $750 and the equipment would be depreciated using the straight-line method to a $50 salvage value over a life of 5 years. Assume that the $50 salvage value is depreciated in year 6. The firm's marginal tax rate is 40% 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:

[8] (40 points) CAPITAL BUDGETING UNDER RISK  Solution
The Acme Company is a firm operating in a wide variety of different industries. It is thinking of purchasing a new piece of equipment. The cost of the equipment is $800 and it would be depreciated using the straight-line method to an $80 salvage value over a life of 8 years. The firm's marginal tax rate is 30% and additional net-working-capital of $200 would be required.
Below are the forecasts of the expected change in sales revenues less expenses for each year:

[9A] (15 points) LEVERAGE 
Explain the concept of leverage and how it relates to the decision of whether to pay your employees a fixed salary or on a piece-rate (i.e., so much per unit of output). Is leverage a good thing?
 

[9B] (15 points) YIELD CURVE 
Draw and label an upward-sloping term structure of interest rates. From the point of view of the investor, what are the advantages and disadvantages of buying short-term bonds? How do market expectations of future interest rates impact your answer?
 

[10A] (20 points) RISK PREMIUMS AND YIELD CURVE  Solution
{a} Plot and clearly label the yield curve that results from the given data. Indicate the position of all four bonds on the curve. All bonds have a face value of $1,000 and interest is paid semi-annually.

[10B] (10 points) RISK PREMIUMS 
Explain how the risk-premium between a pharmaceutical firm’s non-convertible and similar convertible bonds would be expected to behave as the likelihood of the government’s approval of its new wonder drug seems to be increasing. List any assumptions you are making.
 

[11] (20 points) RISK PREMIUMS AND BOND VALUATION  Solution
Explain the concept of a risk premium as it applies to a firm’s long-term subordinated debentures vs. its long-term mortgage bonds. Why does the premium exist in the example that follows below?
Calculate the risk premium between Bond S and Bond M; both bonds have a par value of $1,000.
Bond S is a subordinated debenture that matures in 25 years. Its annual coupon rate is 10%, payable semi-annually, and it is currently selling for $942.
Bond M is a mortgage bond that also matures in 25 years. Its annual coupon rate is 11%, payable semi-annually, and it is currently selling for $1,108.
Explain what is likely to happen to the premium as the outlook for the economy begins to improve and why.
 

[12] (30 points)BOND VALUATION  Solution
MEG Industries issues new subordinated debentures. The $1,000 par value bonds mature in 15 years and are priced to yield 10.5% per year, compounded semi-annually. The annual coupon rate is 11%, payable semi-annually. Initially assume the bonds are neither convertible nor callable.
{a} You buy the newly issued bonds at the market price and hold for 7 years. What IRR did you earn over the 7-year period if you sell the bonds in the open market when the yield to maturity on 8-year bonds is 8.5% and on 15-year bonds is 9%?
{b} Now assume that the bonds are convertible into GEM”s common stock at a conversion price of $25 a share. At the end of the 7th year the stock is selling for $28 a share. Calculate the IRR you earn over the 7-year holding period if you convert.
{c} Now assume the bonds are not convertible but they are callable at a call premium of $55. Calculate the 7-year holding period IRR if the firm exercises its option to call.
{d} To finance the call of part {c}, the firm issues new 8-year bonds at par. Assume the interest rates of part {a} are in effect and the investment banker charges $20 per bond flotation costs. Calculate the NPV of the decision to call.
 

[13] (25 points) RISK PREMIUMS AND BOND VALUATION  Solution
Bond N is a 10-year straight, nonconvertible bond with a $1,000 par value and an annual coupon rate of 14%, payable semi-annually. It’s currently selling for $974.02.
Bond C is a 10-year convertible bond of the same company with a $1,000 par value and an annual coupon rate of 8%, compounded semi-annually. It is convertible into the company’s common stock at a conversion price of $25 per share.
{a} Calculate Bond N’s yield to maturity.

{b} Suppose the (annual) yield premium between bonds C and N is currently 3.5%. Calculate the current price of bond C.

{c} Calculate your IRR (expressed as an EAR) if you buy bond C at its current price and convert it 4 years later when the price of the stock is $30 per share.

{d} Explain what would likely happen to the yield premium if the long-term outlook for some of the company’s main products became gloomier.
 

[15] (30 points) SUPERGROWTH - EQUITY VALUATION  Solution
Today you buy a convertible bond of MattMan Industries that is convertible into the firm’s common stock at a conversion price of $50 per share. The $1,000 face value bond carries an annual coupon rate of 7%, payable semi-annually, and matures in 15 years. At the time of purchase the yield to maturity is 9% per year, compounded semi-annually. Also today you read a forecast that MattMan is expected to pay a dividend of $3.00 per share in 4 years and that its earnings and dividends are expected to grow annually at 30% for 4 years starting 4 years from today. Thereafter the growth rate will drop to 8% a year for the indefinite future. Assume the growth and dividend forecasts hold and stockholders of the firm require an annual rate of return of 20%.

Calculate the IRR you earn if you convert the bond after holding it for 6 years.
 

[16] (35 points) SUPERGROWTH - EQUITY VALUATION Solution
The earnings and dividends of Bunky’s Burgers are expected to grow at a 40% rate for the next 8 years before declining to 8% for the indefinite future. Yesterday the firm paid a dividend of $3.00 per share and stockholders require a 15% rate of return on this type of investment.
{a} If you buy the stock at the end of year 4, calculate the price you pay if all forecasts hold. What is the dividend yield when you buy it?
{b} If you sell the stock at the end of year 8, calculate the price you receive if all forecasts hold. What is the dividend yield when you sell it? Explain why the yield changed from part {a} to {b}?
{c} What IRR did you earn over the 4-year holding period? NO calculations are needed – but the numerical answer and an explanation are needed.
{d} What IRR did you earn over the 4-year holding period if you can sell it for $1,000 a share at the end of year 8? Calculations are needed and so is the numerical answer. YOU MUST SHOW CALCULATOR BUTTONS ON THIS ONE.
 

[17] (70 points) COST OF CAPITAL  Solution
G&E Enterprises is formulating its 2008 investment and financing plans and needs your advice. The firm has the following capital structure which it believes to optimal and will be maintained:

Long-term Debt			30,000,000
Preferred Stock			10,000,000
	Common Stock	20,000,000
	Retained Earnings	40,000,000
Common Equity			60,000,000
	TOTAL CLAIMS		100,000,000

The following slate of potential projects has been put forth:

Project	Life (years)	Outlay ($millions)	IRR
A	5	10	13.0%
J	5	10	14.0%
Q	5	15	13.5%
S	5	?	16.0%
Z	5	?	18.0%

Assume that all projects have an expected life of 5 years and uniform annual cash flows.
Six years ago G&E’s common stock paid a dividend per share of $2.334 and yesterday it paid a dividend of $3.704. Assume that this growth rate continues for the indefinite future. The common stock is currently selling for $40. G&E has $12,000,000 available from retained earnings for investment this coming year. The firm's marginal tax rate is 40%.
New securities can be sold under the following conditions:
BONDS: Up to $19,500,000 in new 20 year, $1,000 par value debentures can be sold at par with flotation costs of $115.57 per bond. The coupon rate is 5% and is paid semi-annually. Beyond $19,500,000 the coupon rate is 7% and the firm nets $901.04 per bond. Convert your answers to EAR’s before putting into your table.
PREFERRED STOCK: Any size issue of preferred stock can be sold at a yield to the investor of 11.5%. Flotation costs are 4% of the price paid.
COMMON STOCK: Up to $15,000,000 in new common stock can be sold with per share flotation costs of $6.667. An additional $12,000,000 can be sold with flotation costs of $11.429. Any more additional stock can be sold with flotation costs of $16.471.
{a} Calculate the marginal cost of capital above and below each break point in the cost of capital schedule. Display your results accurately with a graph.
{b} On the same graph, plot the IRR schedule. Assume the annual cash flows of projects S and Z are $9.162 million and $3.198 million, respectively.
{c} Which projects should the firm accept? Clearly indicate your analysis and display on the graph.
{d} Calculate the average cost of capital for the capital budget you are recommending in {c}.
{e} Compute the NPV of project J.
{f} A disgruntled investor at the annual shareholders’ meeting stands up and states that you are telling the firm to accept a project whose IRR is less than the stockholders’ required rate of return. How do you respond?
{g} Later at the same meeting you make the point that the firm is now to the left of the flat region of the “saucer-shaped” optimal capital structure. Therefore, you advocate that in the future they do what? Why?
 

[18] (70 points) COST OF CAPITAL  Solution
Wile E. Coyote Industries is planning its 2009 capital budget and needs your advice. The firm believes that its capital structure relations shown below are optimal and will be maintained.

[1] {a} Bank: R = $966.64, EAR = 6.17%; {b} Shark: i = .0138% or .000138/day, APR = 5.045%, EAR = 5.17%; {c} Dad: 50,000(1.0517)⁵ = 64,345.92

[2] A: R = $1,159.97, EAR = 6.17%; B: i = 1.472%, APR = 5.89%, EAR = 6.02%; C: .60187%, APR = 7.22%, EAR = 7.47%

[3] (a) X = $15,532.41 per year for ever; {b} D = $3,143.09; {c} Original T = $13,022.51

[4] D = $50,434.88, has $399,668.76 but needs $402,604.88 so is short $2,936.13

[5] DD=.16P - 2; DCF = 6.4 + .048P; outlay = P - 12; sale of old = 18.8; terminal CF = .2P + .8; assume NPV = 0; P = $45.76; CHECK: DCF = 8.60; outlay = 33.76; terminal CF = 9.952; {b} Price = 22.88; IRR = 66.04%

[6] outlay = 70 - 10t; DCF = 38 - 30t; t = 74.34% for NPV to be 0

[7] DCF_1-5 = 464, s=176.64, cv = .38; (b) a = .6, NPV₅ = 510.46, DCF_7-12 = 408, NPV₁₂ = 1,507.56 (c) k' = 14%, NPV₅ = 914.34, NPV₁₂ = 1681.52

[8] DCF_1-8=195, s=71.73, cv = .37, a=.7; k'=11%, NPV₃ = -143.26; DCF₉= 192, DCF_10-12=168, net proceeds = 320, NPV₁₂ = 296.21; {b} R_f, NPV₃ = -142.26, NPV₁₂ = $438

[10A] annual yields = 5%, 7%, 9%, 10.5%; risk premium = 2%

[11] i_S = 5.33%/per, 10.67%/yr; i_M = 9.83%/yr; premium = .84%

[12] P₀ = 1,037.36; P₇ = 1,143.00; IRR = 11.59%, {b} conv value = 1,120, IRR = 11.38%; {c} IRR if called 10.77%; {d} NPV= $68.00

[13] (a) i_N = 14.50%/yr; (b) i_C = 11%/yr, P_C = 820.74; (c) r = 9.06%/per, EAR= 18.9%

[15] P₆ = 65.00; conversion value = $1,300; P_{0 (bond)} = 837.11; r = 14.46%

[16] P₄ = 467.77; P₈ = 683.08; IRR_C = 15%; IRR_D = 25.25%

[17] Breaks: debt 65, equity 20, 45 and 65; k_i = 3.7 and 4.9; k_e = 18, 20 and 22; outlay_S = 30 million; accept Z and S raise $40 at and AC/C of 13.7%; NPV_J = -212,560

[18] Breaks: debt 40, preferred 25, equity 25 and 62.5; k_i = 7.8% and 10.8%, k_p = 12% and 14%, k_eq = 18%, 22% and 26%; accept Z - X - A; NPV_X = 1,642,912