F301 Problem Set 3
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Spring 2012
Each question is worth 3 points. Total points possible = 39.
Please follow the submission guidelines provided by your instructor.
Unless otherwise noted, any method of solving the problem is allowable, but you must show your work to receive
credit.
This Problem Set is due no later than the beginning of class on Wednesday April 11, 2012.
1. Suppose you initiate a seven-year project, which requires an initial capital expenditure on fixed
assets of $2,245,000. The fixed assets will be depreciated using 7-year MACRS. You estimate
these fixed assets will have a market value of $55,000 when the project is terminated at the end
of Year 7. If your marginal tax rate is 40%, what is your best estimate of the Terminal Cash
Flow in Year 7 for these capital expenditure items?
2. Refer to the project in Question 1, above. If the project each year generates $3,500,000 in
incremental annual sales revenue, and $2,750,000 in incremental annual costs, what is OCF in
years 4, 5 and 6?
3. Consider a three-year project with an initial investment in capital expenditures of $840,000.
This machinery will be depreciated straight-line to zero, over a depreciable lifetime of five
years. At the end of Year 3, the machinery will have a market value of $20,000. Unit price =
$32.85, variable cost/unit = $21.95 and fixed costs = $204,000 per year. Unit volume is
anticipated to be 90,000 units each year, and the tax rate is 40%. If your firm’s required rate of
return is 10%, should you proceed with the project? Show the appropriate calculation to justify
your answer.
4. Refer to the project in Question 3, above. Often financial managers are more concerned with
breakeven analysis than NPV analysis. This is particularly true of Unit Volume, since it is one
of the greatest sources of uncertainty in forecasting. Given the data in Question 3, at what
predicted Unit Volume (or above) would you recommend proceeding with the project? (In
other words, what Unit Volume is required to achieve NPV = 0?)
5. Suppose a five-year project under consideration has the following expected sales volumes (in
thousands):
Year
Cash Flow
1
$290
2
$310
3
$330
4
$400
5
$300
You estimate an initial infusion of Net Working Capital of $15,000 will be required (at Time
Zero) to get the project running and that Net Working Capital will need to be maintained at 7%
of sales thereafter. Thus, you will need to invest in or liquidate Net Working Capital in each
year according to the ups and downs of sales volume. Assume full recovery of Net Working
Capital at the end of Year 5. Compute the cash flow for Net Working Capital in each year
F301 Spring 2012
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(including Time Zero). NOTE: In order to receive full credit, you must show USES OF CASH
(outflows) with a negative sign and SOURCES OF CASH (inflows) with a positive sign.
6. A hedge fund manager bought a stock three months ago at a price of $40.00 per share. Today,
after three months, the price has risen to $40.80 per share. What has been the rate of return on
this stock on an annual basis? That is, what is the EAR?
7. The yield to maturity on a bond from Procter and Gamble today is 3.62%. The YTM on a bond
from Sprint Nextel is 9.60%. Both bonds mature in approximately ten years. The recent yield
on a 10-year U.S. Treasury bond was 2.2%.
a. Compute the risk premium for each bond.
b. Which bond appears to be riskier? Explain why, in one clearly written sentence.
8. During the year 2008, the value of an investment in the S&P 500 index of the U.S. stock
market declined by about 40%. Suppose the rate of return over the next 12 months was a
positive 40%. So it went down by 40% and then up by 40%. What was the geometric average
rate of return per year over the two-year period?
The price of Nike stock on the first trading day in March for the last six years is shown below. Use
this information to answer Questions 9 – 12.
2007
2008
2009
2010
2011
2012
$49.15
$63.79
$44.78
$71.40
$74.61
$108.44
9. What was the arithmetic average return from 2007 to 2012? Please show your answer as a
percent, rounded to two decimal places.
10. What was the geometric average return from 2007 to 2012? Please show your answer as a
percent, rounded to two decimal places.
11. Using Excel or your calculator, compute the standard deviation of the five annual returns.
Show your answer as a percent, rounded to two decimal places. (Hint: Excel will be a lot faster
on this one. Be sure to use the Excel function for the standard deviation of a sample, not a
population.)
Tidbit of information to think about: The annual standard deviation of the total U.S. stock market
(New York Stock Exchange) is about 20%.
12. Show how you can use the equation for a future value to find the stock price in 2012, starting
from the stock price in 2007. For the rate of return, use the geometric average you found in
Question 10. You must show how you solve this with the equation, not the TVM keys. (Hint:
Since the geometric average is, indeed, the average compound percent change per year, your
answer to this question should be equal to the stock price in 2012 – within a penny or two.
Remember to show your work.)
F301 Spring 2012
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