Odd numbered problems are from Fall 2015 and even numbered are from Spring 2016

[1] (20 points) EFFECTIVE RATES  Solution
You want to borrow $40,000 to buy a new Maxi Cooper and can choose between two 4-year loans: Loan A requires quarterly payments of $2,845 for 4 years. Loan B requires equal monthly payments and carries an EAR of 6.5%. For both loans, calculate the EAR, APR, and total amount paid over a 3-month period. Which is the better deal for you and why?

[1.1] (20 points) SMALL PROBLEMS  Solution

[a] (10 points) Here’s a problem that a former IBE Fin 125 student asked me for help on as part of his ISE 226 homework. How about if you help him and find the NPV today of the dam maintenance costs? Maintenance costs on a dam: $1,000 now, 300 end of years 1 & 2, 400 end of years 3 through 7, and 150 per year in perpetuity starting end of year 8. Interest rate is 10%.

[b] (5 points) Suppose you calculate the NPV of potential new equipment using straight-line depreciation. Then you recalculate the NPV of the same equipment using MACRS over the same expected life. Assume that in both cases you fully depreciate the new equipment. Compare the two NPV’s and explain why there is a difference or if they are the same.

[c] (5 points) If the Consumer Price Index (CPI) is 100 on January 1st and 101 on February 1st, and this same percentage rate of change occurs each month for the year, what will be the CPI on January 1st of the next year?

[2] (25 points)EFFECTIVE RATES  Solution
Karl Drogo needs to borrow $7,600 for 4 years. His banker offers him a choice of three different loans:

Plan A requires monthly payments of $200 for the 4 years.

Plan B requires constant quarterly payments with an APR of 12.00%.

Plan C requires monthly payments of $100 for the first 2 years and $320 for the last 2 years.

{a} Calculate the APR, EAR and total amount repaid over the 4 years for each of the three loans.

{b} Which loan should Drogo pick?

[3] (30 points)TIME VALUE OF MONEY  Solution

Today (September 29, 2015) you make the first of 13 anticipated annual deposits ending on September 29, 2027) into an account. The deposits are all of the same size with the one exception that you plan to double your deposit but only on September 29, 2019. You expect the investment to pay 10% interest through September 29, 2019 before becoming 20% through September 29, 2027 and then 8% thereafter. You want to withdraw $25,000 per year for 4 years starting September 29, 2027 and ending 2030.
{a} Calculate the size of your deposits.
{b} Suppose that when you get to September 29, 2027, you change your mind and decide to withdraw W’ in perpetuity starting that day. If all interest forecasts hold, calculate W’.

[4] (35 points)TIME VALUE OF MONEY  Solution
Jonny Snow is saving to augment his retirement by planning to make 10 equal annual deposits of $D starting today (March 1, 2016) into an investment fund that he is told will pay 8 percent interest per year through March 1, 2023 and then 12 percent thereafter. His goal is to be able to withdraw $W per year for 25 years. The first withdrawal would be March 1, 2034 and would continue through March 1, 2058.

On March 1, 2034, just as he’s about to make the first $W withdrawal, Jonny discovers two bad things have happened: he forgot that he didn’t make the last 3 planned deposits and the investment fund managers lied – the interest rate never increased to 12 percent but has stayed at the original 8 percent.

If the investment fund managers cave in to Jonny’s threat of a law suit and agree to raise the interest rate to 12 percent from that day (March 1, 2034) henceforth, Jonny calculates he now has exactly enough to begin withdrawing $5,000 a year in perpetuity starting that very day (March 1, 2034).

Find the amount D and W. 


[5] (35 points)CAPITAL BUDGETING  Solution
The OGQ Company is considering replacing some existing equipment with a new version. The new equipment has a purchase price of $650 and will be depreciated over an expected life of 10 years to a salvage value of $50. The new equipment is expected to increase annual sales by $40 and will also change annual operating expenses. Additional net working capital of $110 would be required if the new equipment is purchased.

The existing equipment has a current book value of $330 and is being depreciated over a remaining expected life of 10 years to a salvage value of $30. It can be sold to today for $230.

The firm has a marginal tax rate of 30% and a hurdle rate for projects of 16%.

OGQ engineers are uncertain as to how much annual operating expenses will change (up or down).

Calculate the minimum annual decrease (or maximum annual increase) in operating expenses necessary for the firm to want to make the replacement.

[6] (35 points)CAPITAL BUDGETING  Solution
Stark, Inc. is considering replacing a piece of existing equipment with a new improved model and needs your analysis. The old machine has a remaining book value of $2,100 and is being depreciated over a remaining life of 10 years using the straight-line method to a salvage value of $100. Stark could sell the equipment today for $1,800.

The new equipment has a purchase price of $6,000 and would be depreciated over an expected life of 10 years using the straight-line method to a zero salvage value. Stark forecasts that the new equipment would increase annual sales by $800 every year and increase annual operating expenses by $300 for the first 6 years and, due to higher maintenance costs, by $400 for the final 4 years. An additional $320 of net working capital would be needed.

The firm requires a 12 percent return on its replacement decisions and has a marginal tax rate of 40 percent.

{a} Write out an equation for the NPV of the replacement decision using the cash flow method.

{b} Write out an equation for the NPV of the replacement decision using the PMT annuity + FV etc. method.

{c} Choosing either method, calculate the NPV of the replacement.

[7] (40 points)CAPITAL BUDGETING UNDER RISK  Solution
The Cheesey Company is considering purchasing a new piece of equipment for $1,300. It would be depreciated over a life of 9 years to a salvage value of $400 using the straight-line method. The equipment would require additional net working capital of $140. The firm has a marginal tax rate of 40%. For each year, Cheesy forecasts the following increase in sales over and above costs:

The firm is not sure how long the equipment will actually last. For other firms, similar equipment has lasted as long as 16 years, but for others, the actual life was only 7 years. You may or may not find the following information useful:

σ / ΔCF	0 - .20	.21 - .40	.41 - .80	.81 - 1.4	1.41+
Risk-adjusted k'	15%	17%	20%	22%	25

The current risk-free rate of interest is 10% and the beta of the equipment is 1.8. Assume an historic market risk premium of 6.67%.

{a} Assume initially that the firm operates in many diverse industries. Calculate the NPV of the purchase for both possible actual lives. For the longer 16-year life, assume the remaining salvage value would be depreciated evenly over years 10 through 13, and the equipment would be worthless at the end of year 16. For the shorter 7-year life, assume the equipment would be sold for only $200 at the end of year 7.

{b} Now assume that the firm operates in only one industry. Repeat your NPV calculations.  

 

[8] (40 points)CAPITAL BUDGETING UNDER RISK  Solution
Rubik’s, Inc. is a firm that operates in only one industry. It is thinking of purchasing some new equipment. The cost of the project is $990 and the equipment would be depreciated using the straight-line method to a $190 salvage value over a life of 8 years. The firm's marginal tax rate is 40% and additional net-working-capital of $210 would be required. Below are the forecasts of the expected change in sales revenues less operating expenses for each year:

40% chance of $300 per year

40% chance of $600 per year

20% chance of $1000 per year

The project has a beta coefficient of 1.8. The market's risk premium is 6.5%. If and when you use the table below, apply your to all cash flows, both operating and non-operating.

Coeff of Variation of Cash Flows	0 - .30	.31 - .60	.61 – 1.0	1.0+
Certainty Equivalent Coeff	.9,	.7	.6	.5

{a} The Rubik’s CFO wants to know the NPV of the purchase. She pulls out her desk drawer, and (I lied in lecture) the graph on the next page actually is taped inside. She uses the graph and assumes an actual life of only 6 years. The equipment can be scrapped at the end of the 6th year for $200. Calculate her NPV.
{b} Summer intern, Joe Cool, also wants to know the NPV of the purchase. He uses the supplied certainty equivalents table and assumes an actual life of 18 years. Joe also uses the CFO’s graph for a needed key value. The $190 salvage value will be depreciated to 0 over the final 10 years using the straight-line method. Calculate Joe’s NPV. In the interest of time, you do NOT need to recalculate of the cash flows – continue to use the value from the 6-year life above.
{c} Now assume that Rubik’s is widely diversified. Calculate the CFO’s NPV of the purchase only for the actual life of 6 years.

 

[9] (5 points) RISK PREMIUMS Explain why you would expect to find a risk premium between a closed-ended mortgage bond and a similar open-ended mortgage bond of the same company. Be sure to explain how the bonds differ from each other.

[10] (10 points) LEVERAGE A firm sells its only product at $100 per unit with variable operating costs of $62.50 per unit. Fixed operating costs are $200,000 and fixed interest costs on debt are $50,000. {a} Calculate the degree of operating leverage at an output of 10,000 units. {b} Explain the meaning of this elasticity coefficient.

[11] (10 points) RISK PREMIUMS Give three examples of systematic and unsystematic risk. Explain why one of two cannot be diversified away. For the Cheesy of Problem 2 {b}, which risks (systematic and/or unsystematic) matter and why?

[13] (15 points) YIELD CURVE 
{a} Draw and label an upward sloping term structure. {b} Consider the given curve – what are the advantages and disadvantages to the lender of short-term and long-term bonds?

[14] (20 points) BOND VALUATION AND PREMIUMS  Solution

Bond C is a closed-ended $1,000 par value mortgage bond. It matures in 25 years and has a 4 percent annual coupon rate, payable semi-annually. Its current price is $987.65.
Bond O is an open-ended $1,000 par value mortgage bond. It matures in 25 years and has a 3 percent annual coupon rate, payable semi-annually.
{a} Calculate the yield to maturity of Bond C.
{b} There is a 1.5% (APR) risk premium between the bonds. Calculate the current price of Bond O.
{c} Explain the existence of the above risk premium – include in your explanation what it means to be open-ended and closed-ended?
{d} Now assume that bond O is called at the end of year 12 at a price of $1,020. Calculate the IRR earned over the 12-year holding period by the investor who bought it at your price in {b}. Express your answer as an EAR.

[15] (30 points) BOND VALUATION  Solution
Today you buy some Lehigh Company $1,000 par value subordinated debentures. The bonds mature in 25 years and have an annual coupon rate of 6% payable semi-annually. They are callable at $1,035 and are convertible into Lehigh’s common stock at a conversion price of $20 a share. The current yield to maturity on the bonds is 7.5% per year, compounded semi-annually.
Assume parts {a}, {b} and {c} are independent of each other. Express each of your IRR's as an EAR.
{a} You hold the bonds for 8 years and then sell them in the open market. Assume at that time the yield to maturity is 8.5% a year compounded semi-annually. Calculate the IRR you earned.
{b} The bonds are called in 8 years. Calculate the IRR you earned.
{c} You convert the bonds after 8 years when Lehigh’s common stock is priced at $24 per share. Calculate the IRR you earned.
{d} Now back to part {b}. Assume the firm refinances by calling the existing bonds at $1,035 and issuing new 17-year bonds at par. The yield to maturity of similar 17-year bonds is 4.5% per year compounded semi-annually, and the investment banker charges a fee of $15 per new bond. Calculate the NPV of the decision to call and refinance.

[16] (20 points) BOND VALUATION AND PREMIUMS  Solution

(a) Bond X is a 30-year straight, nonconvertible bond with a $1,000 par value and an annual coupon rate of 7%, payable semi-annually. It’s currently selling for $1,111.11.
Bond Y is a 30-year convertible bond of the same company with a $1,000 par value and an annual coupon rate of 7%, payable semi-annually.
{a} Find the yield to maturity of Bond X.
{b} Assume there is a risk premium of 3% (APR) between the two bonds. Find the price of Bond Y.
{c} Explain what would likely happen to the risk premium if the long-term outlook for some of the company’s main products improved.
{d} Now assume that Bond Y is convertible into the firm’s common stock at a price of $100 a share. Calculate the IRR earned by an investor who buys Bond Y at the price in {b} and then converts it 8 years later when the stock price is $225 per share. Express your IRR as an EAR.

[17] (30 points) SUPERGROWTH  Solution
Today you buy shares $100 par value preferred stock of Gumby, Inc. for $81 a share. The preferred stock pays an annual dividend of $7.00. The preferred stock is convertible into Gumby’s common stock at a conversion price of $25 a share.
Yesterday Gumby’s common stock paid a dividend of $0.65 per share. The firm forecasts that its earnings and dividends will increase at 40% a year for the next 3 years, and then increase at 20% a year for the another 4 years and before stabilizing at an annual 8% growth rate for the indefinite future.
{a} If common stock investors require an 18% return and you expect the forecasts to hold, calculate the IRR of your investment if you expect to convert the preferred stock in 4 years.
{b} If the forecasts still hold and instead of converting after 4 years, you keep the preferred stock for 20 years and then convert, what is your IRR?

[18] (30 points) SUPERGROWTH  Solution
You buy a debenture of Mance Rayder, Incorporated (MRI) today. The bond has a par value of $1,000, an annual coupon rate of 7% payable semi-annually and an annual yield to maturity of 6.5%, compounded semi-annually. It matures in 25 years and is convertible into MRI common stock at a conversion price of $25 a share.

Yesterday MRI paid a common stock dividend of $4.00 a share. Stockholders require a rate of return of 20% on stocks of similar risk. It is forecasted that because of fierce competition, MRI’s dividend will decline at an annual rate of 10% for the next 4 years but then increase at an annual rate of 15% for the following 5 years before stabilizing at an annual rate of 8% for the indefinite future.

{a} If you hold the bond for 6 years and then convert it and all of the forecasts hold, what IRR did you earn over the 6-year period?
{b} If you hold the bond until it matures and then convert it and all of the forecasts hold, what IRR did you earn over the 25-year period?

[19] (70 points) COST OF CAPITAL  Solution

Northeast Industries is planning its forthcoming capital budget and needs your advice. The firm believes that the capital structure relations shown below are optimal and will be maintained.

Debt	100,000,000
Preferred Stock	50,000,000
Common Equity	100,000,000
TOTAL CLAIMS	250,000,000

The firm has a marginal tax rate of 40% and has $24,000,000 of retained earnings available for investment this year. Three years ago Northeast paid a common stock dividend of $5.513 per share and yesterday it paid one of $6.944. Assume this rate of growth continues for the indefinite future. The common stock is currently trading for $75 a share.

The firm can raise funds under these conditions:

BONDS: Up to $24 million in new 25-year $1,000 par bonds can be issued with an annual yield to maturity of 10.32%, compounded semiannually. The annual coupon rate is 12%, payable semiannually. Flotation costs would be $64.98 per bond. Any additional bonds would have an annual after-tax cost of 1.8% higher than the first $24 million.

PREFERRED STOCK: New $50 par value preferred stock can be issued with an annual dividend of 16% to produce an annual yield of 12%. The first $28 million requires flotation costs of $9.53 and anything beyond that requires flotation costs of $19.61 per share.

COMMON STOCK: Up to $32 million can be sold with flotation costs of $25 a share. Any additional shares would require flotation costs of $30.82.

The firm is considering five potential projects with the following forecasted cash flows (assume a 5-year life for all projects):

Project	Outlay ($millions)	IRR%
A	25	18.0
B	35	14.0
C	25	???
D	35	13.0
E	50	17.0

{a} Compute Northeast’s marginal cost of capital for each segment of the marginal cost schedule and display your results on a CLEARLY LABELED graph.

{b} For project C, assume uniform annual cash flows of $8.36 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} Calculate the NPV of project E. Clearly indicate your discount rate.

(e) Why did Northeast accept project E even though its IRR is less than the rate of return required by the stockholders on their investment? Explain why this is possible even if you did not get this result.

{f} As the new fiscal year approaches, a firm finds itself on the left hand side of the “saucer” of the curve drawn in the last lecture. How should it raise most of its funds in the coming year? Why? Draw and label the curve.

[20] (70 points) COST OF CAPITAL  Solution

Hodor Industries has the following capital structure that it believes is optimal and will be maintained:

Debt	600,000,000
Preferred Stock	100,000,000
Common Equity	300,000,000
TOTAL CLAIMS	1,000,000,000

The firm is planning its capital budget for the coming year and needs your expertise. The firm's marginal tax rate is 35%; it has retained earnings available for investment of $12,000,000. Hodor’s common stock is currently selling for $80 a share. Five years ago the common stock paid a dividend of $6.05 and yesterday it paid a dividend of $8.89. Assume that this growth rate continues for the indefinite future
New securities can be sold under the following conditions:
DEBT: Up to $12,000,000 in new 30-year $1,000 par value debentures with an 8% coupon (payable annually) can be sold for $852.48 with flotation costs of $41.02. Beyond $12,000,000 the flotation costs rise to $113.29 per bond.
PREFERRED STOCK: Up to $7,000,000 in new $100 par value preferred stock with a dividend rate of 10% can be sold to net the firm $66.67. Beyond $7,000,000 the dividend rate must be 12% and the firm nets $70.59.
COMMON STOCK: Up to $9,000,000 in new common stock can be sold with under pricing and flotation costs equal to 20% of the common stock’s current price. Beyond $9,000,000 the under pricing and flotation costs total 33.33% of the stock’s price.
The following five investment projects have been proposed (outlay in $millions):

Project	Outlay ($millions)	IRR%
A	15	12.2%
B	20	15.0%
C	10	11.6%
E	15	14.2%
F	20	13.0%

{a} Compute the cost of capital for all segments of the cost of capital schedule. ACCURATELY display your results on a graph.
{b} On the same graph, draw the firm's IRR schedule. Which projects should the firm accept?
{c} Compute the average cost of capital for the amount of the capital budget you found in {b}.
{d} Compute the NPV of project F. Assume uniform cash flows and a life of 5 years.
{e} Explain how it’s possible for the firm to reject project A even if its IRR exceeds the average cost of capital of part {c}?