[1] (30 points) EFFECTIVE RATES  Solution
All three parts are independent of each other.
{a} Emily decides to finance the purchase of a car. She knows she can afford payments of $200 per month for 36 months. If the dealer charges her an APR of 6%,compounded monthly, find the maximum amount she can borrow from the dealer. What is the dealer’s EAR?
Now assume Emily can borrow the exact same amount from part {a} from the bank. The bank will require semi-annual payments of $1210 for 3 years. What is the bank’s EAR and APR?
Which lender requires the greater payments and which the greater EAR? From whom should Emily borrow the money and why?
{b} During September consumer prices rose by 1.6%. This is an annual rate of inflation of X? Find X.
{c} During September wholesale prices fell by .8%. This is an annual rate of deflation of Y? Find Y.
 

[2] (30 points) EFFECTIVE RATES  Solution
All three parts are independent of each other.
{a} Matt decides to finance the purchase of a car. He knows he can afford payments of $500 per month for 60 months. If the dealer charges him an APR of 8%, compounded monthly, find the maximum amount he can borrow from the dealer. What is the dealer’s EAR?
Now assume Matt can borrow the exact same amount from part {a} from his credit union. The credit union will require quarterly payments of $1,560 for 5 years. What is the credit union’s EAR and APR?
Which lender requires the greater payments and which the greater EAR? From whom should Matt borrow the money and why?
{b} During January consumer prices rose by X%. This is an annual rate of inflation of 12%. Find X.
{c} During January wholesale prices fell by Y%. This is an annual rate of deflation of 12%? Find Y.
{d} Explain why the absolute value of Y in {c} is bigger than the absolute value of X in {b}.
 

[3] (35 points) TIME VALUE OF MONEY  Solution
Starting today (September 28, 2006) Emily makes the first of 8 deposits of $10,000 into an account that will pay 10% annual interest through September 28, 2010 and then 15% annual interest from then on. The last $10,000 deposit is September 28, 2013. To augment her retirement benefits, Emily wants to be able to withdraw an equal amount each year for 20 years starting on September 28, 2018. In addition, Emily also wants to be able to leave her sister a lump sum of $100,000 on the day of the last withdrawal (September 28, 2037).
{a} Find the maximum amount Emily can withdraw for the 20 years and still be able to leave her sister the $100,000.
{b} Suppose that the sister wants to use the $100,000 to endow a perpetual scholarship to Lehigh starting on September 28, 2037. The first scholarship will be awarded the exact same day (September 28, 2037) that the spouse receives the money. Find the maximum amount of the annual, perpetual scholarship. Assume the interest rate still is at 15%.
 

[4] (35 points) TIME VALUE OF MONEY  Solution
On February 20, 2007 you make the first of 8 equal annual deposits to an investment that you expect to earn 15% interest a year indefinitely. The last deposit is February 20, 2014. You plan that the deposits must be of sufficient size to enable you to withdraw $10,000 a year for 25 years starting on February 20, 2021.
Assume that immediately after you make your 4th $10,000 withdrawal on February 20, 2024, you learn that the interest rate rose to 18% starting on February 20, 2012 and has remained at 18% ever since.
{a} What is the amount of your initial deposits?
{b} What is your balance immediately following the 4th withdrawal?
Assume parts {c} and {d} are independent of each other. {c} How much can you withdraw now in perpetuity starting in 2025?
{d} Suppose you were told on February 20, 2012 that the rate was increasing to 18%. How much smaller can the two remaining deposits be if you still just want to make the initially planned 25 withdrawals of $10,000? (The two remaining deposits may be negative, meaning that you could actually withdraw money).
 

[5] (35 points) CAPITAL BUDGETING  Solution
Emily’s Industries is considering replacing a piece of equipment with a newer model. The existing equipment was purchased 2 years ago for $510. It is being depreciated over an original life of 12 years to an expected salvage value of $30 using the straight-line method. Emily’s is unsure of what price it can get for the existing equipment in today’s market.
The proposed new machine has a purchase price of $620 and will be depreciated using the straight-line method to an expected salvage of $20 over a life of 10 years.
The replacement is expected to increase annual sales revenues by $85 and decrease annual operating costs by $15. Additional net working capital of $25 would be required if the new machine is purchased. Emily’s marginal tax rate is 40% and required rate of return is 10%.
{a} Calculate the minimum price that Emily’s needs to sell the existing equipment for if the firm is to make the replacement.
{b} Suppose that Emily’s actually sells the old machine for twice your answer to {a}. Calculate the expected IRR on the replacement.
 

[6] (35 points) CAPITAL BUDGETING  Solution
Bunky’s Burgers is considering replacing a piece of equipment with a more efficient model. The new equipment costs $1,600 and would be depreciated using straight-line to a 0 salvage value over an expected life of 8 years. The machine would lower annual operating expenses but have no effect on sales. Additional net-working capital of $500 would be required.
The existing equipment has a book value of $800 and is being depreciated using the straight-line method to a salvage value of $80 over a remaining life of 8 years. If Bunky’s sells the machine today, it would receive $950.
Assume a marginal tax rate of 40% and a required rate of return of 16%.
{a} Find the minimum reduction in annual operating expenses that the machine must produce for Bunky’s to want to make the replacement.
{b} Calculate the effect on NPV of including the additional NWC as both part of the outlay and as part of the cash inflow in the terminal year.
 

[7] (40 points) CAPITAL BUDGETING UNDER RISK  Solution
Bunky’s Performance Products is a conglomerate involved in many different industries including fast foods, ethical drugs, plastics, clothing, financial services, etc. It is thinking of venturing into the auto parts business by investing in a new project that deals with the remanufacturing of fuel injection systems for import cars. The cost of the project is $800 and 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 30% 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
Stealth Industries is considering the purchase of a new piece of equipment. It would cost $1,500 and be depreciated over a life of 10 years to a $500 salvage value using the straight-line method. If the purchase is made, Stealth estimates the following probability distribution of revenues over operating expenses for each year:

[9] (30 points) RISK PREMIUMS AND YIELD CURVE  Solution
{a} Explain the meaning of a risk premium. Explain why there is a risk premium for newly issued callable bonds relative to newly issued comparable non-callable bonds. Explain the expected size of this risk premium if the level of interest rates is close to its historical lows.
{b} Explain why there is a premium for a firm’s non-convertible bonds relative to its convertible bonds. Comment on how and why that premium is likely to change as the prospect for the firm’s future growth begins to decline.
{c} Draw and label a downward sloping yield curve. Explain why there is a premium between a firm’s short-term and long-term bonds. Explain the advantages and disadvantages to the investor of “going short” as opposed to “going long” if the market’s expectations do materialize.
 

[10[ (30 points) RISK PREMIUMS AND YIELD CURVE  Solution
You are spending your summer working as an intern for Joe Perella’s investment bank and one of his clients seeks your advice on several independent potential bond issues.
{a} The client is considering issuing either subordinated debentures or mortgage bonds. Explain the concept of a risk premium between the two issues. Explain how and why this risk premium is likely to change as the outlook for the economy begins to improve.
{b} The client is considering whether to add a callable feature to a potential new issue of long-term bonds. Explain the concept of a premium as it applies to callable versus non-callable bonds. Explain how and why this premium is likely to change as the outlook for the future course of interest rates begins to change. Clearly state any assumptions you are making.
{c} The client wants to know the advantages and disadvantages of investing in long-term versus short-term bonds. Assume an inverted, downward sloping yield curve. Draw and label your yield curve.
{d} What’s operating leverage?
 

[11] (30 points) BOND VALUATION  Solution
Today you buy a $1000 par value bond that matures in 25 years for $912. The coupon rate is 14% per year payable semi-annually. The bond is callable at $1080.
{a} Calculate the yield to maturity (APR and EAR to 4 decimal places) at the time of purchase.
{b} You hold the bond for 8 years and then sell it in the open market. The prevailing interest rate on comparable bonds is 17% per year, compounded semi-annually. Calculate your rate of return (APR and EAR to 4 decimal places) over the 8-year period.
{c} Now, independent of part {b}, the firm calls the bond at the end of the 8th year. Calculate your rate of return (APR and EAR to 4 decimal places) over the 8-year period.
{d} Now, independent of parts {b} and {c}, you convert the bond into the firm’s common stock when it is selling for $112.50 a share. The bond is convertible at a conversion price of $100 a share. Calculate your rate of return (APR and EAR to 4 decimal places) over the 8-year period.
{e} Find the maximum interest rate in year 8 for which the firm would want to call the bonds in part {c}. In other words, what is the highest market interest rate that the firm would find calling the bonds at $1080 profitable?
 

[12] (30 points)BOND VALUATION  Solution
GE issues new $1,000 par value debentures. The bonds mature in 30 years and have an annual coupon rate of 20, payable semiannually.
{a} If you pay $1,052.40 for a bond, what yield to maturity are you making?
{b} You hold the bond for 10 years and then sell it in the open market. At the time of sale, the interest rate is 17% a year, compounded semi-annually, on 20-year bonds and 19% on 30-year bonds. What IRR did you earn over the 10-year holding period? Express your answer as an EAR to four decimals.
{c} Now suppose the bonds had been callable at $1,100. Calculate the NPV per bond of GE’s decision to call the bonds at the end of the 10th year and replace them with new 20-year bonds issued at par. Assume information from part {b} still applies.
 

[13] (35 points) SUPERGROWTH - EQUITY VALUATION  Solution
Today you buy 100 shares of Eli Manufacturing, Inc. $100 par value convertible preferred stock. The preferred has an annual dividend rate of 12%, payable quarterly. At the time of your purchase, the stock is priced to yield 16% a year, compounded quarterly. The preferred stock is convertible into Eli’s common stock at a conversion price of $12.50 per share.
Yesterday Eli paid its annual common stock dividend of $0.34 per share. Eli’s earnings and common dividends are expected to grow at a rate of 25% for the next 10 years before declining to a growth rate of 5% for the indefinite future. Investors in Eli’s common stock require a return of 18% a year, compounded annually.
{a} Calculate the IRR that you earned if all of the forecasts hold and you convert the preferred after holding it for 7 years.
{b} Calculate the IRR that you earned if all of the forecasts hold and you convert the preferred after holding it for 20 years.
{c} Suppose you converted the preferred stock after holding it for 7 years. If you keep the shares of common stock you received in the conversion for another 13 years and then sell them, what IRR did you earn over the 13-year holding period? Assume all the original forecasts still hold. Think about this one before writing; no calculations are necessary.
 

[14] (35 points) SUPERGROWTH - EQUITY VALUATION  Solution
Today you buy a share of Bunky’s Burgers $50 par value preferred stock for $48.50. The preferred stock pays a dividend of 8% per year, compounded quarterly, and is convertible into the Bunky’s common stock at a price of $20 per share. Yesterday Bunky’s paid a dividend of $.75 on its common stock (assume common stock dividends are paid annually). Earnings and dividends are forecasted to grow at a 20% rate for the next 10 years before declining to a positive 5% rate for the indefinite future. Investors in Bunky’s common stock require a 15% annual return.
{a} What is the current yield on the preferred stock?
{b} If you hold the preferred stock for 6 years and convert it, what IRR did you earn over the 6-year holding period if all of the forecasts hold?
{c} If you hold the preferred stock for 12 years and convert it, what IRR did you earn over the 12-year holding period if all of the forecasts hold?
{d} Why is the answer to {c} more or less than the answer to {b}?
 

[15] (65 points) COST OF CAPITAL  Solution
Matty's Inc. is planning its 2007 capital budget and needs your advice. The firm's capital structure relations shown below are believed to be optimal and will be maintained.

[16] (65 points) COST OF CAPITAL  Solution
Matty's Inc. is planning its capital budget and needs your advice. The firm's capital structure relations shown below are believed to be optimal and will be maintained.

[1] (a) Max loan = $6,574.20; EAR_dealer = 6.17%; i = 2.911% per period; EAR_bank = 5.91%; (b) EAR = 20.98%; (c) EAR = 9.19%

[2] (a1) PV = $24,659.22; EAR = 8.30%; (a2) i = 2.353% per quarter, EAR = 9.75%; (b) x = .95%/month; (c) Y = 1.06%/month

[3] W = $34,671.61; S = $13,043.47

[4] at 2020 need $64,641.49 so D= 2,035.89; balance = $100,951.65; (c) $18,171.30; (d) $54,669.06

[5] DCF = 68; outlay = 473-.6MV; NPV=0 if MV=$82.31; if MV=$164.62, IRR = 12.95%

[6] DCF = .6DC + 44; outlay = 1210; NPV=0 if DC = -$341.80; (c) -$347.49

[7] s = 76.68 DCF=430; proceeds sale = 354; IRR = 40.89%; DCF = 406; IRR=47.61%

[8] k' = 15.6%; DCF = 196; s = 49.84; NPV₇ = -744.67; NPV₁₄ = -736.04; DCF = 206

[11] i = 7.69%/period; EAR=15.98%; APR = 15.39%; P₈ = $834.55; r_b = 7.38% per period; r_c = 8.27%; r_d = 8.42%/periods; i = 6.42%/periods; APR=12.83%

[12] i = 9.5%/period; P₁₀ = $1,169.72; IRR = 9.70%/period; NPV = $69.72

[13] P₇ = 21.03; conversion value = 168.24; r = 5.86%/period; P₂₀ = $41.66; r = 4.48%/period

[14] yield = 4/48.50= 8.25%, P_CS,6 = 37.85; P_CS,10 = 48.76; r = 4.3795% per quarter; r = 17.52%; P_CS,12 = 53.76;

[15] Break points: Debt = $50 and $150; Preferred = $75; Equity = $50; Component costs: Debt = 7.8%, 9.0%, 9.6%; Pf'd stock = 12.9% and 15.0%; Equity = 22.0%, 25%; Accept A & D and raise $100 million at an ACC of 1r4.95; Project D: CF = $16,099,245, k_D = 15.23% NPV_D = $5,095,068

[16] Break points: Debt = $30; Preferred = $50; Equity = $30 and $50; Component costs: Debt = 6.0%, 7.2%; Pf'd stock = 12.9%, 15.0%; Equity = 17%, 20.0%, 23.0%; Accept C-B-A and raise $45 million at an ACC of 10.03%; Project D: CF = $3,817,386, k_D = 11.655%; NPV=-802,443 NPV_D = $225,545; {a} Price of bonds = $795,60; {b} flotation costs = $17.50