[1] (30 points) EFFECTIVE RATES  Solution
You need to borrow $100,000 for a term of 5 years. First National Bank will lend you the funds at an APR of 18%. You would be required to make equal monthly payments plus a balloon payment of $30,000 at the end of the 5th year. Last National Bank will lend you the funds if you agree to make 10 semi-annual payments of $13,000 plus a balloon payment of $40,000 at the end of the 5th year.
For both loans, calculate the APR and EAR.
For both loans calculate the sum total of all the payments you’d make over the life of both loans. (Ignore the TVM on this part and just sum the payments).
Explain why one loan has a lower EAR than the other.
 

[2] (20 points) EFFECTIVE RATES  Solution
{a} The wholesale price index rose 1.5% in January. If this rate continues for the entire year, this would be an annual inflation rate of X.
Calculate X and explain why your answer is what it is.

{b} You borrow $50,000 for 6 years agreeing to make quarterly payments of $3,000. Calculate the APR and EAR.
 

[3] (35 points) TIME VALUE OF MONEY  Solution
On September 30, 2003 you make the first of 8 equal annual deposits to an account that you expect to earn 10% interest a year. The last deposit is September 30, 2010. The deposits must be of sufficient size to enable you to withdraw $10,000 a year for 20 years starting on September 30, 2014 and continuing through September 30, 2033. Assume that immediately after you make your 6th deposit on September 30, 2008, the interest rate that you can earn changes to and stays at 14% a year. The two scenarios below are independent of each other.
Scenario #1: You still want to make the originally planned $10,000 withdrawals starting on September 30, 2014. What equal amount can you withdraw (or else need to deposit) on September 30, 2009 and 10 in order to be able to still make the 20 withdrawals as originally planned?
Scenario #2: Instead of wanting to make the originally planned 20 withdrawals, you change your mind and decide you want to be able to withdraw $10,000 a year for ever, still starting on September 30, 2014. Now what equal amount can you withdraw (or else need to deposit) on September 30, 2009 and 10 in order to be able to make the withdrawals in perpetuity?
 

[4] (35 points) TIME VALUE OF MONEY  Solution
Today you deposit $50,000 into an account that pays 5% interest per year, compounded semiannually. You decide to make 7 equal semiannual withdrawals from this account starting 2 years from today and ending 5 years from today. Immediately after making each withdrawal you transfer that withdrawal into a different account that pays 12% interest per year, compounded semiannually.
{a} Calculate the maximum constant amount that you can semiannually withdraw in perpetuity from this second account starting 7 years from today?
{b} Calculate the EAR of the second account?
Suggestion: when drawing your time line(s), label the points using both a year and a period scale.
 

[5] (35 points) CAPITAL BUDGETING  Solution
Emily’s Catering is contemplating replacing a meat grinder with a new, improved model. The original equipment was purchased 3 years ago for $530,000. It is being depreciated over an original life of 8 years to a salvage value of $50,000. It can be sold today for $400,000. The new equipment costs $900,000 and would be depreciated over a life of 5 years to a salvage value of $100,000. Emily’s uses the straight-line method of depreciation and has a marginal tax rate of 40%. The new equipment would lower annual operating expenses but have no effect on sales revenues. The new equipment would require additional net-working-capital of $20,000.
If Emily’s required rate of return is 12%, find the minimum annual reduction in operating expenses necessary for the replacement to be acceptable.
 

[6] (35 points) CAPITAL BUDGETING  Solution
Bunky’s Burgers is considering replacing a piece of equipment with a newer, more efficient model. The existing equipment was purchased 3 years ago for $136 and is being depreciated using straight line to a salvage value of $4 over an originally expected life of 11 years. If Bunky’s sold it today, they would receive $105. The proposed new equipment would has a purchase price of $350 and would be depreciated using straight line to a salvage value of 110 over an expected life of 8 years. The new machine would require additional net working capital of $20. The firm has a marginal tax rate of 40% and a required rate of return of 16%. Bunky’s knows that due to greater efficiencies the new equipment would lower annual before-tax operating expenses but is not sure by how much. (Assume no change in sales revenues). Calculate the minimum change in annual before-tax operating expenses necessary for the firm to want to make the replacement.
 

[7] (40 points) CAPITAL BUDGETING UNDER RISK  Solution American Airlines is contemplating the purchase of new equipment that would cost $800. The equipment would be depreciated over a life of 10 years to a zero salvage value using the straight-line method. American forecasts the following probability distribution for revenues over operating expenses for each year:

Probability	DS-DC
20%	280
60%	380
20%	580

The firm has a marginal tax rate of 30% and the new investment would require additional net working capital of $20. Assume there is a 50% chance that the equipment will actually last only 6 years with a scrap value of $120 and a 50% chance that it will last 14 years with a scrap value of zero Additional information:

s / DCF	0 - .40	.41 - .8	.81 - 1.2	1.21+
k'	14%	16%	18%	20%

The risk-free rate of interest is 3%, the investment beta is 1.5 and the market's risk-premium over and above the risk-free rate is 6%. {a} If American is not diversified and the new equipment is for use in its 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 chosen method consider systematic and/or unsystematic risk? If so, why; if not, why not? {b} If American is a very diversified conglomerate with interests in many different industries besides air-travel, 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 chosen method consider systematic and/or unsystematic risk? If so, why; if not, why not?

[8] (50 points) CAPITAL BUDGETING UNDER RISK  Solution
MEG, Inc. is contemplating the purchase of a new piece of equipment that would cost $600. The equipment would be depreciated over a life of 5 years to a zero salvage value using the straight-line method. MEG forecasts the following probability distributions for revenues over operating expenses for each year:
 

The firm has a marginal tax rate of 30% and the new investment would require additional net working capital of $100. Assume there is a 30% chance that the equipment will actually last only 3 years with a scrap value of $100 and a 70% chance that it will last 10 years with a scrap value of zero. The standard deviation (s) of the after-tax cash flows is 87.06. Additional information:
 

The risk-free rate of interest is 6%, the investment beta is 2 and the market's risk-premium over and above the risk-free rate is 5.5%. 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 MEG 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? {b} If MEG 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?

[9] (20 points) BOND YIELDS
{a} GAB Industries has two issues of debentures outstanding that are alike in maturity. Bond C is convertible into GAB common stock and Bond N is not convertible. What happens to the differential between the two yields as the outlook for GAB’s profits and growth is revised upward by the financial press? Explain how (potential) investors in the two bonds may react to the news.
{b} Assume an upward sloping yield curve. From the issuing firm’s point of view, what the advantages and disadvantages of issuing long-term bonds? Draw and label your yield curve and clearly state any assumptions you are making.

[10] (15 points) BOND YIELDS
The following questions are independent of each other. {a} What happens to the risk premium that a firm’s subordinated debentures carry relative to its mortgage bonds as the outlook for the economy becomes bleaker? Explain fully your answer and any assumptions you are making.
{b} What happens to the premium that a drug company’s nonconvertible bonds carry relative to its convertible bonds as it becomes increasingly more probable that one of its key new wonder drugs will receive FDA approval? Explain fully your answer and any assumptions you are making.

[11] (40 points) BOND VALUATION  Solution
Southwest Airlines has some $1000 mortgage bonds outstanding that mature in 25 years. The bonds carry an annual coupon rate of 10%, payable semiannually. Emily buys a bond when the yield to maturity is 11% per year, compounded semi-annually.
{a} Calculate the price Emily paid.
Parts {b}, {c} and {d} are independent of each other.
{b} Assume that the bond is neither callable nor convertible and that she sells it in the open market 10 years later when the yield to maturity has fallen to 8.5% a year, compounded semi-annually. Compute Emily’s IRR over her holding period.
{c} Assume that the bond is convertible into Southwest’s common stock at a price of $40 a share. Emily converts her bond 10 years after purchase. At that time, Southwest is expected to pay a dividend (D1) of $4.40 a share. Its earnings and dividends are expected to grow at 8% per year for the indefinite future and the stock market requires an 18% return in Southwest stock. Compute Emily’s IRR over her holding period.
{d} Now assume that with 15 years left to maturity, Southwest decides to call the bonds and refinance with an equal number of new 15 year bonds. The old bonds will be called at $1050. The new bonds will be sold at par and the yield to maturity is 8.5% a year, compounded semi-annually. Compute the NPV of Southwest’s decision to refinance. You will need to find the “savings” per period and the “outlay” of the “project.” Ignore any tax effects.

[12] (35 points) BOND VALUATION  Solution
Gabby's Gadgets has some outstanding $1000 par value mortgage bonds that mature in 25 years. The bonds have an annual coupon rate of 14%, payable semiannually. Initially assume that the bonds are neither callable nor convertible.
{a} Suppose you buy a bond today when the market interest rate on similar bonds is 12% per year compounded semiannually. What price do you pay?
{b} Suppose you hold the bond for 6 years and then sell it in the open market. The yield to maturity 6 years from now is 10% a year compounded semiannually for 19-year bonds. Compute the annual rate of return you earned over the 6-year period.
{c} Now assume that the bond is callable at a price of $1070 and also convertible into Gabby's common stock at a price of $25 a share. Suppose that 6 years from today the stock is trading at $27.125 a share and the firm calls the bond. What rate of return did you earn over the 6-year period if you follow the better course of action?
{d} Now assume that the bonds are NOT convertible but are still callable at $1070. Suppose the firm is contemplating calling the bonds and refinancing with new 19-year bonds issued at par. The annual interest rate from {b} is still 10%, compounded semiannually. Compute the NPV per bond of the decision to refinance. (Hint: what is the “outlay” and what is the annual “savings” per bond of the decision to refinance?)

[13] (30 points) EQUITY VALUATION - SUPERGROWTH  Solution
Because of the patent of one of GAB Industries’ closest competitors, GAB’s earnings and dividends are expected to decline at a 20% annual rate for the next 4 years and then increase at a 3% annual rate for the following 2 years before stabilizing at positive annual growth rate of 8% for the indefinite future. Yesterday GAB paid a dividend of $2.00 a share.
{a} If stockholders require a return of 15% on GAB common stock, find P3 and P10.
{b} What rate of return did the investor earn if she bought the stock at your calculated P3 and sold it seven years later at your P10 assuming all of the forecasts come true?
 

[14] (30 points) EQUITY VALUATION - SUPERGROWTH  Solution
The earnings and dividends of MEG Industries are forecasted to grow at an annual rate of 40% for the next 2 years and then at an annual rate of 20% for another 2 years before leveling off at an annual rate of 8% for the indefinite future. Yesterday MEG paid a dividend of $3.00 a share. The market requires a return of 16% for a stock in MEG’s risk class.
{a} Assume the forecasts hold and you buy 100 shares of the stock one year from now. Calculate the price you pay.
{b} Suppose you hold your 100 shares from part {a} for 5 years and then sell them at a price of $155 a share. What annual IRR did you earn over the 5 year period?
 

[15] (70 points) COST OF CAPITAL  Solution
On January 1, 2004 Bunky's Burgers, Inc. is planning its yearly capital budget and is faced with a list of 5 potential independent proposals:

PROJECT	OUTLAY	IRR
A	8,000,000	14.0%
B	8,000,000	21.0%
C	10,000,000	19.0%
D	12,000,000	13.5%
E	12,000,000	16.0%

The firm's capital structure relations shown below are considered optimal and will be maintained:

Debt	$120,000,000
Preferred Stock	20,000,000
Common Stock	24,000,000
Retained Earnings	36,000,000
Common Equity	80,000,000
TOTAL CLAIMS	$200,000,000

The firm has a marginal tax rate of 35% and has $4,500,000 from internal sources of equity available for investment. Four years ago Bunky's paid a common stock dividend of $5.545 a share. Yesterday they paid a dividend of $7.00. Assume that this dividend growth rate continues for the indefinite future. The common stock is currently priced to produce a dividend yield (based on the next dividend) of 18%.
Bunky's can raise new funds under the following conditions:
BONDS: (Up to $24,000,000) New 20 year $1000 par value bonds carrying a coupon of 12 per cent (payable annually) are priced to yield the investor 10% a year. Flotation costs total $70.27 per bond.
(Beyond $24,000,000) A second issue of 20 year 12 per cent coupon bonds can be sold to yield the investor 14% a year. Flotation costs total $67.54.
PREFERRED STOCK: Any size issue of new preferred stock can be sold to yield the investor 16%. Underwriters charge a fee of 20% of the selling price.
COMMON STOCK: Issuing up to $7,500,000 of new common stock requires underpricing and flotation costs equal to 20% of the stock's price. Beyond $7,500,000 requires flotation costs equal to 30% of the selling price.
{a} Which projects should Bunky's accept? Your analysis must include the calculation of the marginal cost of capital along all of the various segments. CLEARLY display your MCC and IRR results on a CAREFULLY labeled LARGE graph. (Carry all calculations to four decimal places; e.g., .1234 or 12.34%).
{b} What is the weighted average cost of capital for the capital budget you are advocating in part {a}?
{c} Compute the NPV of project B. Assume uniform cash flows and a life of 6 years.
{d} If Bunky's cost of equity is so much more than its cost of debt, how can it think raising roughly half of its funds from equity is "optimal"? You are required to use either the “traditional” approach or the “saucer-shaped” approach as part of your answer.

[16] (70 points) COST OF CAPITAL  Solution
SquarePants, Inc. is planning its 2005 capital budget and needs your advice. The firm believes that the capital relations shown below are optimal and will be maintained.

The firm has a marginal tax rate of 40% and has $16,000,000 of retained earnings available for investment this year. On April 20, 2000 SquarePants paid a dividend of $13.151 on its common stock. Yesterday (April 20, 2004) it paid a dividend of $15.385. The stock is currently selling for $100 a share. Assume that this past growth rate continues indefinitely. The firm can raise funds under these conditions:
Up to $16,000,000 in new 30 year $1,000 par value bonds carrying an annual 9% coupon (paid semi-annually) can be sold for $950.62 with flotation costs of $45.27 per bond.
Beyond $16,000,000, the after-tax cost is 2% (or 200 basis points) higher than on the first $16,000,000.
PREFERRED STOCK: Up to $4,000,000 in $50 par preferred stock with a dividend rate of 16% can be sold at $60 a share with flotation costs of $6.67.
Beyond $4,000,000 the cost of preferred stock rises by 3% (or 300 basis points).
COMMON STOCK: An unlimited amount of new common stock can be sold at a cost 4% (400 basis points) higher than the cost of retained earnings.
The following is a list of potential investments that the firm is considering:

Assume that the projects are NOT divisible - each one is all or nothing. You can't build 3/4 of a chemical plant.
{a} Compute SquarePants’ 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} Compute the NPV for project A. Clearly indicate your choice of a discount rate.
{d} Why is SquarePants accepting a project whose IRR is less than the rate of return that shareholders require?

[1] (a) FNB: R= $2,227.54/month, EAR = 19.56%, total = $163,652; LNB: i = 9.06%/period, EAR = 18.95%, total = $170,000

[2] (a) EAR = 19.56%; (b) rate per period = 3.15%, APR = 12.60%, EAR = 13.20%

[3] D=$5,593.24; X(#1) = 5,317.91 withdrawal; X(#2) = $3,678.65 withdrawal

[4] W = 8,480.27; P = 5,086.73; EAR = 12.36%

[5] (a) outlay = 540,000; DCF = 40,000+.6X; X=-$164,637

[6] BV_old = 100; D_new = 30; D_old = 12; outlay = 267; DCF = -.6DC + 7.2; DC=-$75.7

[7]Expected DCF = 304; outlay = 820; s=68.59; k'=14% from table; {a}NPV₆ = 453.27;NPV₁₄ = 988.96; {b} k'=12%; NPV₆ = 531.19;NPV₁₄ = 1175.58;

[8] Expected DCF = 272.25; outlay = 700; a=.8 from table; {a}NPV₃ = 85.37;NPV₁₀ = 868.21; {b} k'=17%; NPV₃ = 52.66; NPV₁₀ = 536.58;

[11] P₀=915.34; {b} P₁₀= 1125.84; IRR=12.16%/ yr csa; {c}conv ratio=25 shares; P=$44/ share; IRR=12.02%/yr csa; {d} outlay=$50; NPV=$75.84

[12] P₀=1,157.62; {b} P₆= 1,337.36; IRR=13.84%/ yr csa; {c}conv ratio=40 shares; P=$27.125; conversion value=1085; IRR=11.34%/yr csa; {d} outlay=$70; savings=$20 per period; NPV=$267.36

[13] P₃ = $10.74; P₁₀ = $18.24

[14] P₁ = $88.97; IRR = 18.89%/yr

[15] See web supplementary notes

[16] Break points: Debt = $40,000,000; Equity = $40,000,000; Preferred stock = $20,000,000; Component costs: Debt = 6.0% and 8.0%; Pf'd = 15.0% and 18.0%; Equity = 20% and 24%; Marginal costs: 0 to $20 MC = 13.4%; $20 to $40 MC = 14.0%; $40+ MC = 16.4%; accept J-C-A raise $45 million at an ACC = 14.0%; NPV of C = $695,298 using a discounr rate of 14.80%;