[1] (30 points) EFFECTIVE RATES  Solution
{a} Suppose you borrow $50,000 today and agree to make monthly payments of $2,284.24 for 2 years. What is your APR and EAR?
{b} Now suppose that another bank would lend you the $50,000 for 2 years. It would let you pay back only $1,111 per month for the first 12 months but then $3,333 per month for the second 12 months. What is your APR and EAR? (This is not hard to solve with the calculator if you think about it.)
{c} While riding in your car listening to your cheap staticky radio, a news reporter say “A new government report says that ‘last month, prices rose by #@$!* per cent. This is an annual rate of inflation of 24 per cent.’” The interference made it impossible for you to hear the missing number. So you pull safely off the road, whip out your financial calculator, and compute the missing number as ????
 

[2] (31 points) EFFECTIVE RATES  Solution
Gabby is choosing between three different $10,000 – 3 year car loans. Loan A is designed to give a new college graduate a chance to get used to payments. It requires monthly payments of $120 for the first 12 months, followed by $360 payments for the next 12 months and ending with $600 payments for the remaining 12 months. Loan B requires 36 monthly payments of $350. Loan C requires 36 monthly payments of $240 plus a balloon payment of $4,600 at the end of the third year (same time as the last $240 payment).
For each of the three loans, calculate the APR and EAR and the total of all the payments you make. Explain fully which loan Gabby should take and how you decided. Did you recommend the loan with the lowest total payments; why or why not?
 

[3] (35 points) TIME VALUE OF MONEY  Solution
Today (October 2, 2008) you make the first of 8 equal annual deposits (last one on October 2, 2015) into a bank account that will pay 12% through October 2, 2011 and then 8% thereafter. The deposits must be of sufficient size to enable you to give Lehigh a gift of $2,000 a year in perpetuity starting on October 2, 2022.
{a} Calculate the amount of the deposits.
{b} and {c} are independent of each other.
{b} Suppose you discover (on October 2, 2021) that a bank teller stole your 4th deposit and never put it in your account. You change your mind about the perpetual gift and decide instead to give Lehigh a 50-year annuity still starting on October 2, 2022. How much can you give Lehigh each year?
{c} Now suppose you do not find out about the teller and the lost 4th deposit and you start your $2,000 annual gift as planned. How many FULL gifts of $2,000 can you give before you embarrassingly run out of funds.
 

[4] (35 points) TIME VALUE OF MONEY  Solution
Starting today (February 17, 2009) you plan to make 8 equal annual deposits over the next 9 years (you know you will have to skip 2013 because of your daughter’s wedding expenses). The interest rate is 8% a year. The 8 deposits must be of sufficient size to enable you to give Lehigh a gift of $5,000 a year in perpetuity; the first payment will be on February 17, 2023.
You make the 8 planned deposits. On the morning of February 17, 2023 you toy with the idea of making a bigger splash at Lehigh by giving $10,000 a year starting that afternoon.
{a} How many full $10,000 payments can you make?
{b} What will be your balance immediately after you make the last payment of part {a}?
{c} What was the amount of each of your original deposits?
 

[5] (35 points) CAPITAL BUDGETING  Solution
Lehi Beverages is thinking of replacing an existing bottler with a new, more efficient model. The existing equipment was purchased 3 years ago for $50. It is being depreciated over an original life of 7 years to an expected salvage value of $8 using the straight-line method. It could be sold today for $22. The firm’s marginal tax rate is 45%.

The proposed new machine would cost $100 and be depreciated over a 4-year life using the straight-line method to an expected salvage value of $12. Additional net-working-capital of $6.5 would be required. The new machine is not expected to change annual sales but it should decrease operating expenses due to less breakage and lower energy costs. If the firm has a required hurdle rate of 15%, find the minimum annual change in operating expenses necessary for the firm to want to make the replacement.
 

[6] (30 points) CAPITAL BUDGETING  Solution
Gabby and Co. is contemplating replacing an existing piece of equipment with an newer model. The existing machinery was purchased 2 years ago for $100. It is being depreciated over an original life of 10 years to a $10 salvage value. It can be sold today for $70. The new machinery would cost $150 and be depreciated over an 8-year life to a salvage value of $30. The new equipment would be expected to increase annual sales by $15 and also change annual operating expenses. The replacement would require additional net working capital of $14.8. Gabby uses the straight-line method, has a marginal tax rate of 40% and has a required hurdle rate of 12%.
{a} Calculate the minimum change in annual expenses for Gabby to want to make the replacement.
{b} Assuming a reinvestment rate of 15% per year, calculate the MIRR of the replacement.
 

[7] (40 points) CAPITAL BUDGETING UNDER RISK  Solution
Coyote, Inc. is a firm operating in a wide range of industries. It is thinking of purchasing a new piece of equipment. The cost of the project is $840 and the equipment would be depreciated using the straight-line method to a zero salvage value over a life of 7 years. The firm's marginal tax rate is 30% and additional net-working-capital of $250 would be required.

Below are the forecasts of the expected change in sales revenues less expenses for each year:

The risk-free rate of interest is 6%. The project has a beta coefficient of 2.5. The market's risk premium is 6%. 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 k’ for all years.

Read parts {a} and {b} before proceeding.
{a} Compute the NPV assuming the actual life is 4 years and the equipment can be scrapped at that time for $200. Repeat assuming an actual life of 10 years.
{b} Now repeat the two NPV calculations assuming that Coyote operates in a single line of business.
{c} Standard deviation of cash flows measures (total risk, just systematic or just unsystematic) risk. Circle the right one. Explain you choice.
 

[8] (35 points) CAPITAL BUDGETING UNDER RISK  Solution
You’re working as a summer intern for the Victorino Company, a well-diversified firm that is considering buying a new machine for $700. Your manager, Utley, has asked you to calculate the NPV of the acquisition given various assumptions. They would depreciate the equipment over a 6-year life to a $100 salvage value using the straight-line method. Additional net working capital of $150 would be required if the machine were purchased. The firm has a marginal tax rate of 40%. The firm has made the following forecasts of the annual change in sales minus costs:

Your boss also gives you the following information which may or may not be useful: the risk-free rate of interest is 4.0%; the project has a beta coefficient of 1.5; the market's risk premium is 5.8%; and the following table:

[9] (10 points) LEVERAGE  Solution
Suppose the 2008 World Champion Philadelphia Phillies decide to renegotiate the contracts of some of their star players. Explain the concept of operating leverage as it applies to their deciding whether to offer a given player a 4-year contract of [A] $8,000,000 per year, [B] $4,000,000 per year plus $2.00 per fan per year, or [C] just $4.00 per fan per year. Assume the Phillies draw an average attendance of 2,000,000 fans a year with a range of 1,100,000 to 3,000,000 over the last decade.
 

[10] (10 points) RISK PREMIUMS Solution
{a} What is a convertible subordinated debenture?
{b} From the borrower’s point of view, what is attractive about adding a convertible feature to an about-to-be issued debenture? What is unattractive?
 

[11] (5 points) ISSUING SECURITIES Solution
A firm whose common stock was selling at $55 a share issues a new block of common stock using an investment banking firm. The underwriter pays the firm $47 a share.
What are the two main reasons why 47 is less than 55 – in other words, why doesn’t the firm receive the current stock price when it issues additional shares?
 

[12A] (10 points) YIELD CURVE   Solution
Explain why there is normally a risk premium between a firm’s 25-year debentures and its 5-year debentures and how that premium behaves as the market’s expectations of future interest rate increases becomes stronger.
 

[12B] (20 points) RISK PREMIUMS AND YIELD CURVE Solution
Draw and label a downward sloping term structure. What securities are used to construct a term structure? From the borrowers’ perspective what are the advantages and disadvantages of long-term bonds? What is the solution to overcoming the major disadvantage? How would the borrower “pay” for this solution?
 

[12C] (10 points) PREFERRED STOCK VALUATION   Solution
You pay $90 for a share of $100 par value preferred stock that has an annual dividend rate of 16% payable quarterly. You hold it for 10 years and then sell it in the open market and earn an IRR of 18% per year, compounded quarterly. At what price did you sell it?
 

[13] (30 points) RISK PREMIUMS AND BOND VALUATION Solution
Today you purchase a 30-year bond for $979.35. The bond has a $1,000 par value and carries a 14% annual coupon rate (payable semiannually).
{a} Calculate the yield to maturity on the bond.
Parts {b}, {c} and {d} are independent of each other.
{b} You hold the bond for 8 years and then sell it in the open market. At the time of sale, the yield on 22-year bonds is 13.5% a year, compounded semiannually and on 30-year bonds is 14.5% a year, compounded semiannually. Calculate the IRR you earned over your holding period. Express your answer as an EAR.
{c} Now assume that the bond is convertible into the company’s stock at a conversion price of $100 per share. You convert the bond after holding it for 8 years when the stock price is $111 a share. Calculate the IRR you earned over your holding period. Express your answer as an EAR.
{d} Now assume that the bond is called 8 years after purchase at a premium of $70 over par. Calculate the IRR you earned over your holding period. Express your answer as an EAR.
{e} Assume the call of {d} was financed by issuing an equal number of new 22-year bonds at par (see part {b} for prevailing interest rates). When calling the bonds in {d}, the firm also incurred a flotation cost of $15 per bond. Calculate the NPV of the decision to call.
 

[14] (30 points)BOND VALUATION  Solution
Five years ago Slick, Inc. issued $1,000 par value bonds that were scheduled to mature in 30 years. The annual coupon rate was 9%, payable semiannually. You buy the bonds today, 5 years after issuance. The yield to maturity on the bonds today is 11% a year, compounded semiannually. You hold the bonds for 8.5 years and then
{a} you sell it in the open market when the yield to maturity is still 11% a year, compounded semiannually. Calculate your selling price and the IRR you earned over your holding period.
{b} Slick calls the bonds for $1,045. Calculate your holding period IRR. Assume this is independent of part {a}.
{c} you convert your bond to Slick’s common stock at a conversion price of $25 per share. Assume that Slick’s stock is trading at $28.75 a share and that this is independent of parts {a} and {b}.
{d} Suppose that when making the call in part {b}, Slick issued new 16.5 year bonds at par. The interest rate at the time was 8% a year, compounded semiannually and flotation costs totaled $25 per bond. Calculate the NPV of the call. Was it a good decision?
 

[15] (30 points) SUPERGROWTH - EQUITY VALUATION Solution
Today you buy 100 shares of Emmo, Inc. $100 par value convertible preferred stock. The preferred has an annual dividend rate of 6%, payable quarterly. At the time of your purchase, the stock is priced to yield 5% a year, compounded quarterly. The each share of the preferred stock is convertible into one share of Emmo’s common stock.

Yesterday Emmo paid its annual common stock dividend of $2.50 per share. Emmo’s earnings and common dividends are expected to grow at a rate of 40% for the next 3 years, then 25% for the following 5 years and then 8% thereafter. Investors in Emmo’s common stock require a return of 14% a year, compounded annually.
{a} Calculate the IRR that you earn if all of the forecasts hold and you convert the preferred after holding it for 5 years.
{b} Calculate the IRR that you earn if all of the forecasts hold and you convert the preferred after holding it for 20 years.
 

[16] (30 points) SUPERGROWTH - EQUITY VALUATION Solution
Today you buy 50 shares of Bunky’s Burgers $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 15% a year, compounded quarterly. Each share of the preferred stock is convertible into Bunky’s common stock at a conversion price of $33.33 per share.
Yesterday Bunky’s paid its annual common stock dividend of $2.10 per share. Bunky’s earnings and common dividends are expected to grow at a rate of 25% for the next 4 years, then only 5% for the following 4 years and then 8% thereafter. Investors in Bunky’s common stock require a return of 20% a year, compounded annually.
{a} Calculate the IRR (express as an EAR) that you earn if all of the forecasts hold and you convert the preferred after holding it for 5 years.
{b} Calculate the IRR (express as an EAR) that you earn if all of the forecasts hold and you convert the preferred after holding it for 12 years.
 

[17] (70 points) COST OF CAPITAL  Solution
Rawlings Inc. is planning its 2009 capital budget and needs your advice. The firm's capital structure relations shown below are believed to be optimal and will be maintained.
 

Yesterday the firm paid a dividend of $7.407 and six years ago it paid a dividend of $4.668. Assume this growth rate continues for the indefinite future. Rawlings’ marginal tax rate is 40% and its common stock is trading for $80 a share. The firm has $6,000,000 available from retained earnings for investment this year.
New capital can be raised under the following conditions:
BONDS: Up to $20,000,000 of new $1000 par 30-year bonds carrying a 10% coupon (paid annually) can be sold for $1035.50. Flotation costs total $35.50 per bond.
Any additional $1000 par 30-year bonds carrying a 16% coupon (paid annually) can be sold with the same $35.50 flotation costs. The after-tax component cost of these bonds is 2.4% higher than for the first $20 million block.
PREFERRED STOCK: Up to $8,000,000 of $100 par value preferred stock carrying a 12% dividend rate can be sold to yield the investor 13.5%. Flotation costs per share total $3.18.
Any additional preferred stock can be sold at a component cost of 2% higher than the first $8 million block.
COMMON EQUITY: Up to $12,000,000 in new common stock can sold to net the firm $61.54 per share. Any additional common can be sold at a component cost of 7% higher than the cost of retained earnings.
The following is a list of potential investments that the firm is considering (outlays are in millions):
 

{a} (5 points) Calculate the price paid by an investor for a bond in the second block of bonds.
{b} (40 points) Calculate the marginal cost of capital for each segment of the marginal cost schedule. 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} (15 points) Compute the NPV of project R assuming a life of 8 years and uniform annual cash flows.
{d} (10 points) Why is Rawlings accepting projects whose IRR is less than the rate of return required by stockholders?
 

[18] (70 points) COST OF CAPITAL  Solution
The Acme Company 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.

The firm has a marginal tax rate of 50%. It has $18 million dollars available from retained earnings. Investors in companies similar to Acme require a rate of return of 15%. Acme’s earnings and dividends are expected to grow at a 3% annual rate for the indefinite future.
New capital can be raised under the following conditions:
BONDS: Up to $15,000,000 of new $1000 par 30-year bonds carrying a 12% coupon (paid semi-annually) can be sold for a yield to maturity of 14% a year, compounded semi-annually. The bonds can be sold at an after-tax cost to the firm of 8% a year, compounded semi-annually. An additional $21 million of debt can be issued at an after-tax cost to the firm of 10% per year. Any additional debt would cost 13% per year. PREFERRED STOCK: The first $2.5 million of $50 par value) preferred stock would carry a 10% annual dividend and be sold at a cost to the firm of 12% a year. Any additional preferred would cost the firm 15%. COMMON EQUITY: Up to $18,000,000 in new common stock can sold at a cost to the firm of 18%. Any additional common stock can be sold at a cost of 24% to the firm. The following is a list of potential investments that the firm is considering (outlays are in millions):

Calculate the marginal cost of capital for each segment of the marginal cost schedule. 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.
{x1} If the flotation costs on the preferred are $3.33 a share, calculate the return earned by an investor in the first block of new shares.
{x2} Calculate the flotation costs per bond on the first $15 million of new bonds. Clearly show your work.
{x3} Calculate the percentage of the common stock price that is lost to flotation costs and under-pricing for the first block of new stock.
{x4} Calculate the NPV of Project B assuming a life of 6 years and uniform annual cash flows. Clearly show your work.
{x5} What if you were to graph the list of potential projects in ascending rather than descending order? It’s possible that now all six projects would have positive NPV’s. Why is this better or worse than what you hopefully did in your analysis – in other words, is the firm better off with this result? Why or why not?

[1]{a} i=.75%/month, APR=9.00% EAR = 9.38%; {b} i=.4188%/mo, APR=5.03%, EAR = 5.14%; {c} x=(1.24)^1/12 = 1.81%

[2] A: i=1.115%/mo, APR=13.38%, EAR = 14.23%, total = 12,960; B: i=1.307%/mo, APR=15.58%, EAR = 16.86%, total = 12,600; C: i=1.1896%/mo, APR= 14.27%, EAR = 15.25%, total = 13,240

[3]{a} D=$1,431.12, {b} Pot = 21,910.32, W=$1,791.01, {c} n=28 (but only 27 full) PV=22,102

[4] {a} Feb 2023 have $67,500; n=9 (actually 8+) so 9 full including 2023; {b} $62.21; {c} D = 3,822.79

[5] outlay = 80, DCF = -.55DC + .72, sale of old = 26.5, DC = -$34

[6] Outlay = 90; DCF = 11.4 - .6DC; DC = -$6.48/yr; {b} FV8 = 244.66, MIRR = 13.32%

[7] outlay = 1090, s = 159.01 DCF=547; proceeds sale = 248; NPV4 = 531.94, NPV10=1145.08; {b} k'=14%, NPV4 = 798.66, NPV10 = $1,797.25

[8] DCF_1-7=208, s=58.79, cv = .28, a=.5 and .6; k'=12.7%, NPV₄ = 6.88; DCF_8-12=216, net proceeds = 228, NPV₁₂ = 4.45.70; {b} NPV₄ = -149.37, NPV₁₂ = 306.34

[9] - [12B] no numerical answers

[12C] P₁₀ = 95.35

[13] {a}i =7.15%, EAR = 14.81%; {b} yield = 6.75%, P8 = $1,034.95, IRRb = 7.345period, EAR = 15.23%; {c} Conv value = $1,100, IRRc = 7.6025/period, EAR = 15.78%; {d} IRRd= 7.6025/per, EAR = 15.49%

[14] P0 = 830.68, {a} Psell=849.25, IRR = 11%/yr, EAR = 11.3%, {b} IRRb = 6.31%/period, EAR = 13.01%; {c} IRRc = 6.698%/per, EAR = 13.84%; {d} outlay = $70, savings = 5/period for 33 periods, NPV=20.74

[15] Ppf'd = 120, P5=293.12, P8=376.83, IRR=5.42%/period, IRR= 21.69%/yr, P20=$948.92, IRR = 12.77%/yr

[16]Ppf'd= $80/share, P5 = $44.90, P8 = 56.09, IRR= 5.67%/period, EAR = 24.70%/yr, P12=76.31, IRR = 4.80%/per, EAR=20.63%/yr

[17] Break points: Debt = $40; Preferred = $40, Equity = $20 and $60; Component costs: Debt = 6.0% and 8.4%; Pf'd stock = 14.0% and 16%; Equity = 18.0%, 21.0% and 25.0%; Accept A-K-R-J-C and raise $55 million at an ACC of 12.2%; Project R: CF = $4.7538, k_R = 12.50%; NPV_D = $3.208

[18] Break points: Debt = $25 and $60; Preferred = $25, Equity = $60 and $120; Component costs: Debt = 8.0%, 10% and 13%; Pf'd stock = 12.0% and 15%; Equity = 15, 18.0% and 24.0%; accept Z-A-B-Y and raise $105 at an ACC of 12.8%, Project B: CF = $8.14, k_B= 12.9%; NPV_B = $2.64