Odd numbered problems are from fall 2014 and even numbered are from spring 2015

[1] (30 points)EFFECTIVE RATES  Solution
{a} You are choosing between two 4-year loans of $5,000: Loan A requires monthly payments of $67 for the first year, $117 for the second and third years, and $167 for the final year. Loan B requires quarterly payments of $200 for the first year, $350 for the second and third years, and $500 for the final year. For both loans calculate the APR and EAR. If you are the borrower, which loan do you select?

{b} If prices rose by .5% last month and this rate continues for a year, by how much will they rise over the year?

[2] (30 points)EFFECTIVE RATES  Solution
{a} First National Bank, Second National Bank and Third National Bank are on three corners of the same intersection and compete for customers. On their savings accounts, FNB offers an APR of 5 percent, compounded quarterly while SNB offers an APR of 4.95 percent, compounded monthly. TNB wants to exactly match the true rate of the higher of FNB and SNB. If TNB compounds its interest only semi-annually, what APR must it offer? To receive full credit your answer must be correct to 5 decimal places (or 3 after the percent sign).

{b} Two plans to borrow $20,000 for 5 years: Plan A requires monthly payments of $300 plus a balloon payment of $6,000 at maturity. Plan B requires monthly payments of $600 for the first 2.5 years and $150 for the second 2.5 years. Calculate the APR, EAR and total amount repaid for both loans. Which loan should you choose?

[3] (35 points)TIME VALUE OF MONEY  Solution

Starting on September 30, 2014, you make the first of 18 annual deposits: The first 6 will be D, the next 6 will be 2D and the last 6 will be 4D. The last one is September 30, 2031. You anticipate being able to make 6 annual withdrawals of $10,000 starting on September 30, 2031. Assume an interest rate of 8% a year through September 30, 2020 and then 20% thereafter.

{a} Calculate the minimum value of D necessary to make the six $10,000 withdrawals.

{b} Suppose that instead of the six $10,000 withdrawals, you decide on September 30, 2031 to withdraw a constant amount in perpetuity still starting that day. Calculate the maximum withdrawal amount possible.

{c} For this part, assume you actually make only the first 7 planned deposits (six D’s and one 2D, ending September 30, 2020) and the last 2 planned deposits (4D September 30, 2030 and 31) and skip all the others. Calculate the revised maximum perpetual withdrawal still starting on September 30, 2031.

[4] (35 points)TIME VALUE OF MONEY  Solution
Dexter Morgan is saving for his retirement by planning to make 10 equal annual deposits starting today (February 24, 2015) into an account that he thinks will always pay 15 percent per year. He wants to be able to withdraw $20,000 per year for 20 years starting on February 24, 2030 and continuing through 2049. He makes the 10 planned deposits but when he is about to make the first planned withdrawal he checks his account and makes two wonderful discoveries: his employer matched his annual contribution on February 24, 2019, 2020 and 2021 and the account upped its interest rate to 20% starting on February 24, 2020 and it is expected to remain at that level in perpetuity. He quickly calculates that instead of the planned $20,000 withdrawals, he has exactly enough money to withdraw W each year in perpetuity starting on February 24, 2030. Find the amount of the deposits and W. 


[5] (35 points)CAPITAL BUDGETING  Solution
Baron’s, Inc. is contemplating replacing some existing equipment with some new hardware. The existing equipment, carried on the books at $800, is being depreciated using the straight-line method to a salvage value of $80 over its remaining life of 8 years. Baron's could scrap the equipment today for $900.

The new machinery would also be depreciated using the straight-line method to a salvage value of 20% of its purchase price over an expected life of 8 years. The new equipment would be expected to lower annual operating expenses by $750. The new machinery would require additional net-working-capital of $160. Baron's has a required return of 12% and a marginal tax rate of 40%.

Find the maximum amount that the firm would be willing to pay for the new equipment if replacement is to be worthwhile.

[6] (35 points)CAPITAL BUDGETING  Solution
Big Company is considering replacing a piece of existing equipment with a new improved model but is unsure of how much it would receive today from selling the existing equipment. The existing equipment has a book value of $1,000 and is being depreciated over a remaining 10-year life to a salvage value of $100 using the straight-line method. The firm requires a 15 percent return on its replacement decisions and has a marginal tax rate of 40 percent. The proposed new equipment costs $4,000 and would be depreciated over a 10-year life to a salvage value of $400 using the straight-line method. The firm forecasts that the new equipment would increase annual sales by $250 and lower annual expenses by $750. Additional net-working-capital of $200 would be required to support the new purchase.

{a} Calculate the minimum amount that the firm would need to realize today from the sale of the existing equipment for it to want to make the replacement.

{b} Explain briefly how the MIRR attempts to remedy the short-coming of the IRR method. A numerical example is NOT necessary.

[7] (40 points)CAPITAL BUDGETING UNDER RISK  Solution
Gert, 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. Gert forecasts the following probability distributions for revenues over operating expenses for each year:

[8] (40 points)CAPITAL BUDGETING UNDER RISK  Solution
Baron, 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 operating expenses for each year:

20% chance of $380 per year
40% chance of $580 per year
40% chance of $1080 per year

The risk-free rate of interest is 3%. The project has a beta coefficient of 1.8. The market's risk premium is 5%. The firm also found the table below from an old copy of a Fin 125 exam that may or may not prove useful: If and when you use the table, apply your α to only the operating cash flows and assume an α = 1 for any non-operating cash flows.

[9] (5 points) RISK PREMIUMS For each of the two events mentioned by the newscaster in the comic below, explain whether the event is an example of systematic or unsystematic risk and whether it is diversifiable or not.
Why would the second event have a positive effect on the market?

[11] (10 points) RISK PREMIUMS In the equation that results from the Capital Asset Pricing Model (“CAP-M”), explain the existence of the two risk-premiums and the role of the beta coefficient.

[12] (20 points) BOND VALUATION AND PREMIUMS Solution
Bond S is a subordinated debenture that matures in 30 years. Its annual coupon rate is 9%, payable semi-annually, and it is currently selling for $905.
Bond M is a mortgage bond that also matures in 30 years. Its annual coupon rate is 12%, payable semi-annually, and it is currently selling for $1,624.
{a} Calculate the annual risk premium between Bond S and Bond M; both bonds have a par value of $1,000.
{b} 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 above example?
{c} Explain what is likely to happen to the premium as the outlook for the economy begins to worsen and why.

[13] (15 points) YIELD CURVE  Solution
{a} Draw and label a downward sloping term structure of interest rates.
{b} Faced with this curve, explain what the advantages and disadvantages to the borrower are of using new short-term and long-term securities?
{c} What can the borrower do to reduce the disadvantage of using the long-term bonds? Explain why this comes at a “cost”.

[14] (25 points) BOND VALUATION AND PREMIUMS  Solution
Bond N is a 10-year straight, nonconvertible bond with a $1,000 par value and an annual coupon rate of 12%, payable semi-annually. It’s currently selling for $1,060.
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) risk 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 $32 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) BOND VALUATION  Solution
Bumgarner Enterprises 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 Bumgarner’s common stock at a price of $40 a share. Emily converts her bond 10 years after purchase when the stock is trading at $44 a share. Compute Emily’s IRR over her holding period.
{d} Now assume that with 15 years left to maturity, Bumgarner 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.Assume a flotation cstt of $20 per new bond. Compute the NPV of Bumgarner’s decision to refinance. You will need to find the “savings” per period and the “outlay” of the “project”. Ignore any tax effects.

[16] (10 points)YIELD CURVE 
(a) Draw and label an upward sloping term structure.
(b) The shape of the curve suggests that interest rates are expected to rise or fall?
(c) Assuming an upward sloping term structure, what is major disadvantage for an investor who buys a 25-year bond?

[17] (70 points) SUPERGROWTH  Solution
Today you buy a convertible bond of Oops, Inc. The $1,000 par value bond matures in 15 years, has an annual coupon rate of 4%, payable semi-annually, and is priced to yield 4.5% a year, compounded semi-annually. The bond is convertible into Oops’s common stock at a conversion price of $100 a share. Yesterday Oops paid a dividend of $3.00. You forecast that Oops’s dividends will grow at 25% for the next 5 years and then at 20% for an additional 3 years before stabilizing at 6% thereafter. Assume the stock market requires a 14% annual return on Oops’s common stock.
{a} If you hold the bond for 4 years and then convert it, what IRR did you earn?
{b} Assume all growth forecasts are accurate and you convert the bond at its maturity. What IRR did you earn?

[18] (30 points) SUPERGROWTH  Solution
Today you buy 100 shares of the Acme Company’s $100 par value convertible preferred stock. The preferred stock pays an annual dividend of 6% and is convertible into Acme’s common stock at a conversion price of $25 per share. The preferred is priced to yield 5% a year.
Acme’s common stock dividends are expected to grow at 30% for the next 5 years and then at 20% for another 6 years before stabilizing at a 4% rate for the indefinite future. Yesterday Acme paid a 40 cents common stock dividend. Investors require a return of 15% on common stock of Acme’s risk-class.
{a} Calculate the IRR you earn if all forecasts hold and you convert your preferred stock after 8 years.
{b} Calculate the IRR you earn if all forecasts hold and you convert your preferred stock after 20 years.
{c} What is Acme’s cost of retained earnings?

[19] (70 points) COST OF CAPITAL  Solution
Los Pollos Hermanos is planning its 2015 capital budget and needs your financial expertise. The firm believes that the capital structure relations shown below are optimal and will be maintained.

{a} Compute Los Pollos’s marginal cost of capital for each segment of the marginal cost schedule and display your results on a CLEARLY LABELED NEAT graph.
{b} For project E, assume a life of 6 years and uniform annual cash flows of $6.43 million. Calculate its IRR.
{c} On the same graph, plot the firm’s IRR schedule and indicate which projects are acceptable. Compute the average cost of capital for the capital budget you are advocating.
{d} For the preferred stock, calculate the flotation costs charged by the underwriters.
{e} Calculate the NPV of project A (assume a life of 6 years and uniform annual cash flows). Clearly indicate your discount rate.
{f} Did Los Pollos accept projects whose IRR is less than the required rate of return on their common stock? CLEARLY explain why or why not.

[20] (70 points) COST OF CAPITAL  Solution
Benchmark, Inc. has the following capital structure that it believes is optimal and will be maintained: