Odd numbered problems are from fall 2012 and even numbered are from spring 2013
[1] (25 points)EFFECTIVE RATES Solution
To finance the purchase of a Zucchini GT, you need to borrow $240,000. 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 $70,000. {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 $20,000 at month 24. (Note, this $20,000 is in addition to the regular monthly payment that also occurs at month 24). Calculate the uniform monthly payment. Now which option do you choose?
[2] (25 points)EFFECTIVE RATES Solution
{a} On the nightly news, the business reporter states that “During January prices rose by 1.5%, and this is an annual inflation rate of X$&@! percent.” Calculate the garbled number.
{b} On another nightly news in a different year, the business reporter states that “During January prices fell by #&@#! percent, and this is an annual deflation rate of 19.56%.” Calculate the garbled number.
{c} Clearly explain why the absolute value of the monthly rate in {b} is larger or smaller than in {a}.
[3] (35 points)TIME VALUE OF MONEY Solution
On October 2, 2012 you make the first of 5 planned equal annual deposits to an account that earns 8% interest. The last deposit is planned for October 2, 2016. The deposits must be of sufficient size to enable you to withdraw $8,000 a year starting on October 2, 2021 and continuing through October 2, 2040. As luck would have it, you were able to make only the first 3 planned deposits. On October 2, 2021 you make the first $8,000 withdrawal as planned. On that same day, you decide to try and continue to withdraw the annual $8,000, not just until October 2040, 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 $8,000 withdrawals in perpetuity?
[4] (35 points)TIME VALUE OF MONEY Solution
Today, February 19, 2013, you make the first of what you expect to be 8 annual equal deposits (last one is February 19, 2020) into an account that pays 12% a year. Your goal is to be able to make 4 equal withdrawals starting on February 19, 2025 and ending on February 21, 2028.
On February 19, 2025, just as you are about to make your first withdrawal you discover that you have a lot less in the account than you had planned because you skipped making deposits in 2017 and 2018. But you realize that you do have exactly enough to start making $200 withdrawals in perpetuity starting that day (February 19, 2025).
{a} Calculate the value of the originally planned withdrawals and the amount of the deposits.
{b} Suppose on February 19, 2025 you are stubborn and still want to make the 4 originally planned withdrawals on the originally planned dates (starting February 19, 2025) even though you know your account is a lot smaller than you planned. So you make the first one as planned and then you take the remainder of your funds and invest them in the Bernie Madoff – Ponzi Fund. What super return would you need from BMPF to fulfill your original plans?
[5] (30 points)CAPITAL BUDGETING Solution
Sponge Bob is considering replacing some outdated equipment and needs your advice. The existing equipment has a book value of $160,000 and is being depreciated over a remaining life of 9 years to a salvage value of $16,000 using the straight-line method. The firm could sell the old equipment today for $200,000. 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 $224,000 a year but would require additional net working capital of $24,000. 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?
[5.5] (30 points) CAPITAL BUDGETING
Why do firms prefer accelerated depreciation over straight-line?
[6] (35 points)CAPITAL BUDGETING Solution
The company you work for is considering replacing an existing machine with a new one and your boss asks you to provide an analysis.
The new machine has a purchase price of $4,000 and would be depreciated over an expected 10-year life to a salvage value of 500 using the straight-line method. It is expected to reduce annual operating expenses by 800 over each of the first 4 years and then by only 600 over the remaining 6 years. Annual sales would be unaffected. Going with the new machine would require additional net working capital of 340.
The old machine has a current book value of 2,100 and is being depreciated over a remaining life of 10 year to a salvage value of 100 using he straight-line method. It can be sold to day for 500. The firm’s marginal tax-rate is 40% and its required rate of return is 15%.
Calculate the net-present-value of the replacement.
Provide your boss with two final versions of the NPV method: one using the CFj, etc. notation and the other using the PMT & PVIFa etc. notation. Which one you use to solve for the numerical answer is your choice but you need to provide both equations.
[7] (50 points)CAPITAL BUDGETING UNDER RISK Solution
Al's Stuff, Inc. is contemplating the purchase of a new piece of equipment that would cost $500. The equipment would be depreciated over a life of 8 years to a zero salvage value using the straight-line method. Al's forecasts the following probability distribution for revenues minus operating expenses for each year
| Probability | ΔS - ΔC |
| 50% | >150 |
| 30% | >300 |
| 20% | >400 |
| σ / ΔCF | 0 - .15 | .16 - .3 | .31 - .45 | .46+ |
| α | ? | ? | ? | ? |
[8] (40 points)CAPITAL BUDGETING UNDER RISK Solution
Gabby's Stuff, Inc. is contemplating the purchase of a new piece of equipment that would cost $640. The equipment would be depreciated over a life of 8 years to a zero salvage value using the straight-line method. Gabby's forecasts the following probability distribution for revenues minus operating expenses for each year:
| Probability | ΔS - ΔC |
| 50% | 250 |
| 30% | 500 |
| 20% | 800 |
The firm has a marginal tax rate of 40% and the new investment would require additional net working capital of $70. Assume there is a 30% chance that the equipment will actually last only 5 years with a scrap value of $100 and a 70% chance that it will last 14 years with a scrap value of zero.
Additional information:
| σ / ΔCF | 0 - .15 | .16 - .3 | .31 - .60 | .61 - .9 | .91+ |
| α | ? | ? | .6 | ? | ? |
[9] (9 points) RISK PREMIUMS
In deriving the Capital Asset Pricing Model (CAPM) or “Beta Model” explain the meaning of the term “market’s risk-premium” and the term “security j’s risk-premium”. Why do both of them exist? What role does beta play?
[9.5] (9 points) INVESTMENT BANKERS
Explain the roles of an investment banker in the issue of a firm’s common stock. How is the risk borne by the underwriters? What are the two reasons for the net proceeds per share received by the firm being less than the current price?
[10] (10 points) The owners of the 2010 and 2012 World Champion San Francisco Giants are negotiating contracts with some of their players. Plan A calls for the group of players to receive combined salaries of $180,000,000 plus $10 per fan attending the home games. Plan B calls for the group to receive combined salaries of $100,000,000 plus $50 per fan. Plan C calls for $50,000,000 + $75 per fan. Assume for simplicity that the Giants’ “product” is a seat at the ballpark, the seat costs each fan $150, there are no variable costs other than the per fan costs above and there are no other fixed costs besides the players’ salaries. Calculate the degree of operating leverage at an annual attendance of 2,000,000 for all three plans. Explain your results and the risk associated with the three plans.
[10.5] (5 points) When a firm is going to issue additional shares of common stock it hires an investment banker. The investment banker tells the firm that the firm will receive from the investment banker an amount per share that will be less than the current stock price. What are the two main reasons why this is this so?
[11] (9 points) RISK PREMIUMS
Explain the existence of a risk premium between a firm’s mortgage bonds and its subordinated debentures? How would the premium be expected to change as the outlook for the economy begins to improve? Why?
[12] (10 points) According to this March 12, 2013 article in the Morning Call, two factors contributed to Dick’s Sporting Goods having a not-so-great quarter. For each factor, explain whether it was unsystematic or systematic risk. Assume that the market had a positive excess return over the same period. Draw and label the characteristic line graph and plot Dick’s point for the period.
[13] (25 points) BOND VALUATION Solution
Today you buy a new 30-year $1,000 par value subordinated debenture that has an annual coupon of 11%, payable semiannually. The bond is priced to initially yield 12% per year, compounded semiannually. It is neither callable nor convertible.
{a} What price did you pay?
{b} Assume that you hold for bond for 8 years and then sell if for $1234.56. What is the yield to maturity at the time of sale?
{c} What IRR did you earn over your holding period? Express your answer as an effective annual rate.
{d} Now assume that the bond is convertible into the firm’s common stock at a price of $100 a share and callable at $1,060. Calculate your IRR over the 8-year holding period if instead of selling it in the open market in part {b}, you take the better course of action when the firm calls it and the stock is selling at $118 a share. Express your answer as an annual percentage rate.
[14] (35 points) BOND VALUATION Solution
10 years ago the Gabby Company issued new 25-year, $1,000 par value debentures at a price of $951.66. The annual coupon rate is 12%, payable semi-annually. Today the interest rate on similar 15-year bonds is 8% a year, compounded semi-annually. The bonds do not have a call feature.
[15] (30 points) SUPERGROWTH Solution [16] (30 points) SUPERGROWTH Solution [17] (70 points) COST OF CAPITAL Solution [18] (70 points) COST OF CAPITAL Solution
{a} Calculate the yield to maturity at the time of issuance.
{b} Calculate the current market price of Gabby’s bonds.
Now assume that the firm decides to refinance the original bonds by replacing them with new 15-year bonds issued at par.
{c} Calculate the NPV of the decision to refinance if the firm were to buy up the old bonds at their current price.
{d} Calculate the NPV of the decision to refinance now assuming that the bonds are callable at $1,060.
{e} Based upon your answers to {c} and {d}, explain why investors like or do not like the call feature.
{f} Calculate the IRR that an investor would earn over the past 10 years if she bought one of the bonds and then converted it into Gabby’s common stock (assume a conversion ratio of 25:1 and a stock price of $44 per share.
Today you buy 100 shares of Knutson’s Roundball, Inc.'s convertible preferred stock for $97 per share. The preferred stock has a par value of $100, a dividend rate of 8% per year and is convertible into Knutson’s common stock at a conversion price of $50 a share.
At the time of purchase, the company's earnings and common dividends are expected to grow at 30% for the next two years and then 20% for an additional three years before stabilizing at 5% for the indefinite future. Investors require a return of 15% on the common stock. Yesterday the firm paid a dividend on its common stock of $2.00 per share.
{a} Assuming the forecasts hold and that you convert to the common stock after three years, what IRR did you earn over the period?
{b} Suppose you had waited until the end of the tenth year to convert. What rate of return did you earn over the ten years?
(Test date April 18, 2013) Bunky's Burgers pays its dividend on April 17 of each year. Yesterday it was 2.00 a share and for the next several years it is forecasted to be: 2014 2.00, 2015 2.20, 2016 2.40, 2017 2.80, 2018 3.00, 2005 4.50.
Thereafter, the dividend will grow at 6% for the indefinite future.
{a} If the market requires a rate of return of 15%, find the predicted value of Bunky's stock on April 18, 2014 and April 18, 2021 if the dividend forecasts hold.
{b} Find the rate of return earned by the person who buys it on April 18, 2021 and who sells it on April 18, 2024 for $80. Again assume that the dividend forecasts hold.
{c} Evidently what is the market's new required rate of return on April, 2024 in order to produce a price of $80 assuming the original future dividend forecasts still hold?
Bunky's Burgers, Inc. is planning its 2013 capital budgeting and financing decisions and needs your expert assistance. The firm has a marginal tax rate of 40%, its common stock is currently selling for $100 a share, its earnings and dividends are expected to grow at 9% for the indefinite future, the stock's dividend yield (based on D1) is 9% and the firm has $9 million dollars available from internal sources for investment this year.
The firm's capital structure shown below is thought to be optimal and will be maintained:
Debt $60,000,000
Preferred stock 10,000,000
Common Stock $10,000,000
Retained Earnings 20,000,000
Common equity 30,000,000
TOTAL CLAIMS $100,000,000
New securities can be sold under the following conditions:
BONDS: Up to $9,000,000 in new bonds can be sold to the public at par with flotation costs of $91.29. The bonds have a face value of $1000, mature in 20 years and carry a coupon of 8%, paid annually. Beyond $9,000,000 the coupon rate will be 10% and the bonds can be sold for $1091.29 with flotation costs of $91.29.
PREFERRED STOCK: Up to $3,000,000 in new $100 par value stock with a dividend of 15% can be sold to the public for $125 with the firm netting $115.38. Beyond $3,000,000 the price of $125 still holds but the net proceeds fall to $107.14.
COMMON STOCK: Up to $6,000,000 in new common stock can be sold at a cost of 20%. Beyond $6,000,000 the cost to the firm rises to 24%.
Bunky's is considering the following projects:
PROJECT OUTLAY LIFE IRR
A 10,000,000 6 16.0% D 10,000,000 5 10.0% M 10,000,000 6 14.3% P 10,000,000 4 15.3% W 10,000,000 8 11.3% Z 20,000,000 6 11.6%
{a} Calculate the flotation costs and underpricing associated with the first $6,000,000 in new common stock.
{b} Accurately plot Bunky's marginal cost of capital schedule for $0 to $70,000,000.
{c} On the same graph plot Bunky's Internal Rate of Return schedule. Which projects should the firm accept? Calculate the average cost of capital for the total capital budget you are advocating.
{d} Suppose that the firm is able to obtain $9,000,000 (instead of $6,000,000) in new common stock at a cost of 20%. Clearly fix your graph. Does this affect your conclusion to {c}? You need not recalculate the average cost of capital if your conclusion has changed.
{e} Calculate the NPV of project P (assume uniform annual cash flows).
{f} Explain how the stockholders easily make their required return of roughly 20% by accepting project P with an IRR of only 15.3%.
(Test date April 18, 2013) WileCoyote.com is planning its 2014 capital budget and needs your advice. The firm believes that the capital relations shown below are optimal and will be maintained.
Debt $700,000,000
Preferred stock 50,000,000
Common Equit 250,000,000
TOTAL CLAIMS $1,000,000,000
The firm has a marginal tax rate of 40% and has $12,500,000 of retained earnings available for investment this year. On April 15, 2010 WileCoyote paid a dividend of $7.108 on its common stock. Yesterday it paid a dividend of $7.767. The stock is currently selling for $50 a share. Assume that this growth rate continues indefinitely. The firm can raise funds under these conditions:
BONDS: Up to $14,000,000 in new $1,000 par value perpetual bonds carrying a 10% coupon (paid annually) can be sold to net the firm $1,111.11. An additional $21,000,000 of perpetual bonds carrying an 11% coupon can be sold to net the firm $1,000. Any additional bonds would carry a coupon of 12% and the net proceeds would total $857.14.
PREFERRED STOCK: Any size issue of preferred stock can be sold to yield the investor 13.5% a year. Flotation and underwriting fees are equal to 10% of the market price.
COMMON STOCK: Up to $10,000,000 in new common stock can be sold with underpricing and flotation costs of $5.56 a share. Any additional shares can be sold with underpricing and flotation costs of $11.90 a share.
The firm is considering five potential projects with the following forecasted cash flows:
Project Outlay ($millions) Life yrs Uniform annual CF's IRR A 20 6 4,727,500 11.0 B 30 6 7,504,600 13.0 J 10 6 2,571,600 14.0 X 20 6 4,659,600 10.5 Z 20 6 5,427,800 ??
{a} Compute WileCoyote’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. How much of the capital budget will be financed by new common stock?
{c} Calculate the IRR of project Z.
{d} Why is WileCoyote accepting a project whose IRR is less than the rate of return that shareholders require?
{e} Calculate the NPV of project B. Clearly indicate your analysis – what numbers are you using and why?
{f} Suppose the firm finds itself at the right hand side of the saucer (flat range) of the optimal capital structure graph (Tuesday’s lecture). From what source(s) should the firm obtain new capital – explain your choice.