X - Problems
Fall 13 - Spring 14

Odd numbered problems are from fall 2013 and even numbered are from spring 2014

[1] (30 points)EFFECTIVE RATES  Solution
Walter White plans to get a $100,000 10-year mortgage to buy a car wash and has three possible borrowing plans.
Plan A is equal monthly payments at an APR of 6%. Interest is compounded monthly.
Plan B is $36 a day (assume 360 days per year or 30 per month). Interest is compounded daily.
Plan C is $25 a day (360 days per year) plus a balloon payment at maturity of $50,000. Interest is compounded daily.

{a} For each loan, calculate the APR, EAR and total dollar amount repaid over the 10 years. Display all of the results in a chart.

{b} Explain which loan Walt should take.

{c} If the annual rate of deflation is 15%, by what uniform percentage rate do prices decline each month

 

[3] (35 points)TIME VALUE OF MONEY  Solution
On October 1, 2013 Jesse Pinkman makes a deposit of $D into an account that he expects to always pay 5% a year. He plans to also deposit D for 4 more years (2014, 15, 16 and 17), then skip 3 years and then finish with 3 more D deposits (2021, 22 and 23). Jesse's goal is to be able to withdraw $W annually for 10 years starting in 2028 and ending in 2037.

On October 1, 2028 Jesse realizes that two factors changed: in addition to the planned deposits, he actually did make deposits in 2018, 19 and 20 (total of 11 D’s) and also the interest rate increased on October 1, 2020 to 8% where it has stayed since and will continue to stay. Jesse calculates that he can now actually withdraw $1,000 a year in perpetuity starting October 1, 2028.

Calculate D and W. 


 

[5] (35 points)CAPITAL BUDGETING  Solution
Los Pollos Hermanos is already considering replacing a piece of equipment that it bought just last year. The existing equipment was purchased for $8,000 and is being depreciated using the straight-line method to a salvage value of $1,500 over a life of 13 years. It is one year old and can be sold today for $5,500.

The new equipment would cost $10,000 and be depreciated using straight-line to a salvage of $400 over a life of 12 years. Because of operating efficiencies, Los Pollos thinks the new equipment will save the company incrementally $400 annually for years 1 through 6 and $600 annually for years 8 through 12. In year 7 there will need to be a major overhaul so that incremental expenses will actually rise by $200 in that year. Additional net working capital of $300 would be required if the new equipment is purchased.

The firm’s tax rate is 40% and the firm uses a required return of 15% on this type of investment.

{a} Calculate the net-present-value of the replacement.

{b} Define net working capital and give two examples.

[7] (31 points)CAPITAL BUDGETING UNDER RISK  Solution
The Lincecum Company is contemplating the purchase of a new piece of equipment that would cost $1,600. The equipment would be depreciated over a life of 7 years to a salvage value of $200 using the straight-line method. Lincecum forecasts that annual sales will increase by $800 each year, but because of uncertainties in raw material costs and a new union labor contract, the firm forecasts that the annual increase in operating costs each year could be $200 or $100 or $50 (equal likelihood of each occurring).
The firm has a marginal tax rate of 40% and the new investment would require no additional net working capital. Assume there is a 40% chance that the equipment will actually last only 4 years with a scrap value of $450 and a 60% chance that it will last 12 years with a scrap value of zero. Take any remaining book value as a single depreciation charge in year 8.


Additional information:
σ / ΔCF 0 - .20.21 - .4.41 – 1.0 1.0+
k'13%15%17%20%

The risk-free rate of interest is 3%, the investment beta is 1.5 and the market's risk-premium above the risk-free rate is 6%.
{a} If the Lincecum Company 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.
{b} If the Lincecum Company 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.

 

 

[9] {a} (5 points) CERTAINTY EQUIVALENTS What is the meaning of a certainty equivalent coefficient?

{b} (8 points)OPERATING LEVERAGE How does the concept of operating leverage impact a firm’s decision on how it should pay its workers, i.e., fixed salary or a piece-rate basis? What effect do higher interest expenses have on operating leverage?

{c} (6 points) COST OF DEBT VS EQUITYWhat are the two main reasons why, for a given firm, debt is a cheaper source of funds than equity?

 

[11] (9 points) BOND VALUATION  Solution
A firm has some outstanding subordinated debentures: $1,000 face value, mature in 25 years, annual coupon rate of 6%, payable semi-annually. They are selling for $1,141.81. It also has some outstanding mortgage bonds: $1,000 face value, mature in 25 years, annual coupon rate of 2.5%, payable semi-annually. They are selling for $912.50. Calculate the risk premium expressed as an EAR to 4 decimal places. Explain the existence of the premium and how it changes as the outlook for the economy worsens.

 

[13] (15 points) BOND VALUATION  Solution
Today you buy a new 25-year $1,000 par value subordinated debenture that has an annual coupon of 7%, payable semiannually. The bond is initially priced with a yield to maturity of 9% per year, compounded semiannually. It is callable after 5 years at a price of $1,040 and is convertible into the company’s common stock at a price of $100 per share. {a} What price did you pay for the bond? {b} After holding it for 6 years the firm calls the bond. The price of the common stock is $98.50 a share. What IRR did you earn? Express your answer as an EAR to four decimal places. {c} Now assume part {b} never happened. After holding it for a total of 12 years the firm calls the bond. The price of the common stock is $112.50 a share. What IRR did you earn? Express your answer as an EAR to four decimal places.

 

[13.5] (25 points) BOND VALUATION  Solution
Draw and label an upward sloping yield curve. Assume this curve exists when answering the questions below. {a} Explain the concept of interest rate risk and how it shapes the term structure of interest rates. {b} What is the advantage to investors of buying long-term bonds? {c} What is the advantage to investors of buying short-term bonds? {d} Suppose a firm has an issue of 30-year mortgage bonds: $1000 par, 9% annual coupon rate payable semi-annually and currently selling for $757.58 and another issue of 3-year mortgage bonds: $1000 par, 9% annual coupon rate payable semi-annually and currently selling for $1,110.16. Calculate the risk-premium (EAR) between the bonds.

[15] (30 points) SUPERGROWTH  Solution
Today you buy a $1,000 par value convertible 25-year subordinated debenture. The yield to maturity is 5.8% a year, compounded semi-annually. The annual coupon is 6% payable semi-annually and it is callable at $1,030. It is convertible into the firm’s common stock at a conversion price of $40 a share. You hold the bond for 7 years and then convert it.
Yesterday the common stock paid a dividend of $0.80. It is forecasted that earnings and dividends will grow at 25% annually for 5 years and then at 20% for 5 years before reaching its terminal growth rate of 4%. Investors require a 15% return for stocks in the given risk class.
{a} Find the IRR you earned if all forecasts hold. Express your answer as both an APR and an EAR.
{b} Recalculate the IRR if you convert the bond at maturity.

[16] (30 points) SUPERGROWTH  Solution
(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?

 

[17] (70 points) COST OF CAPITAL  Solution
Lehigh Inc. 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.

Debt             $300,000,000
Preferred Stock             100,000,000
Common Stock $80,000,000
Retained Earnings520,000,000
Common Equity             600,000,000
TOTAL CLAIMS             $1,000,000,000

Yesterday the firm paid a dividend of $9.767 and four years ago it paid a dividend of $7.314. Assume this growth rate continues for the indefinite future. Lehigh’s common stock is currently selling for $100 a share. The firm’s marginal tax rate is 50%. The firm has $24,000,000 available from retained earnings for investment this year. New capital can be raised under the following conditions:
BONDS: Up to $12,000,000 of new $1,000 par perpetual carrying an 12% coupon (paid annually) can be sold at par. Flotation costs total $40.00 per bond. Another $15,000,000 of bonds can be sold at a before-tax cost of 2% higher than the first block’s before-tax cost. Any additional bonds would have a before-tax cost of 4% higher than the first block.
PREFERRED STOCK: Up to $9,000,000 in new $50 par preferred stock carrying a dividend rate of 14% can be sold at par. Flotation costs total $3.33 per share. Any shares beyond the first $9,000,000 would also be sold at par but the component cost would be 3% higher than the first block.
COMMON STOCK: The first $48,000,000 of new common stock can be sold at a cost 3% higher than the cost of retained earnings. An unlimited second block of common stock would cost 6% more than the cost of retained earnings.
The following is a list of potential investments that the firm is considering:
PROJECTOUTLAY ($millions) IRR%
A1519.8
B2016.0
C2015.0
G2017.0
W25??
X2014.0
Z2020.0

{a} Calculate the marginal cost of capital for each segment of the marginal cost schedule. Plot the cost of capital schedule on a CLEARLY LABELED graph.
{b} Calculate the IRR of project W assuming a life of 6 years and annual CF’s of $7.15 million.
{c} Add the IRR schedule to your cost of capital graph. Determine which projects are acceptable and compute the average cost of capital for the capital budget you are advocating.
{d} What is the total amount of flotation costs and underpricing associated with selling each share of the second block of common stock?
{e} Compute the NPV of project W.
{f} Draw the "saucer-shaped" approach to the optimal capital structure question. Be sure to label your graph. Suppose that Lehigh believes that after they raise the funds to finance this year's proposals, they will then be at the extreme right side of the flat part of the saucer. Explain fully how they should raise capital next year and why they might want to do this.

 

[18] (70 points) COST OF CAPITAL  Solution
(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:

ProjectOutlay ($millions)Life yrsUniform annual CF'sIRR
A2064,727,50011.0
B3067,504,60013.0
J1062,571,60014.0
X2064,659,60010.5
Z2065,427,800??

{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.