Problem 1
Pick a stock of your choice which you think is likely to be in a high-growth stage and
which has publicly-available financial statements for fiscal year 2016. From financial
statements, obtain Total Revenue, EBIT, Capital Expenditures, Net Working Capital,
Depreciation, and the Debt-to-Equity ratio (use Long-term debt as a measure of total
debt) for fiscal year 2016. Make sure the company has positive debt and positive EBIT.
The income statement numbers should be for the entire year, not just for the fourth
quarter. (Note: possible sources for financial statements include the company’s website,
finance.yahoo.com, or the Securities and Exchange Commission (www.sec.gov).)
Assume that the stock will be in a high growth stage over the next 8 years (2017-2024),
after which it will reach a stable, lower-growth phase in year 9 (year 2025), which will
last into the indefinite future. In addition, assume the following parameters:
The tax rate = 34%.
T-bill rate = 6.5 percent
Market risk premium = 5.5 percent.
High-growth phase:
Expected growth rate in EBIT, Capital Expenditures, Revenues, NWC,
and Depreciation: 7.5%.
Equity Beta during the high growth period: 1.34.
Cost of debt = 8.75%
Debt-to-equity stays constant over the high-growth phase.
Stable growth phase:
Expected growth rate in FCFF = 4.5%
Equity Beta during stable growth phase: 1.12
Cost of debt = 7.5%
Debt-to-equity ratio in the stable growth phase will fall to 60% of what it
was in the high-growth phase
Capital expenditures are offset by depreciation.
Use the FCFF approach to calculate the enterprise value of the firm, the equity value of
the firm, and the intrinsic share value as of the end of 2016.
2
Problem 2
Let M be the month of your birthday.
Define D = M if M > 5; and D = M + 5 if M ≤ 5.
Assume the yield curve for default-free zero coupon bonds is currently as follows:
Maturity (Years) YTM
1 D%
2 D+1%
3 D+2
A. What are the implied one-year forward rates?
B. Assume that the pure expectations hypothesis of the term structure is correct. If
market expectations are accurate, what will the pure yield curve (that is, the yields
to maturity on one and two year zero coupon bonds) be next year?
C. If you purchase a two-year zero coupon bond now, what is the expected total rate
of return over the next year? What if you purchase a three-year zero coupon
bond? Ignore taxes.
Problem 3
Choose a stock that you would like to study that has a current set of liquid put and call
options. You can check whether the stock has listed options at https://finance.yahoo.com.
Select a single option maturity date between 12/15/2017 and 6/15/2018, and gather data
on the ten call options expiring on that date that have strike prices closest to the current
stock price. The data items you’ll want to gather include the following: (1) strike price;
(2) last trade price for each of the ten call options; (3) last trade price for the stock; (4)
maturity, in years, for the ten contracts; and (5) implied volatility as reported by Yahoo
Finance. (Note: if Yahoo Finance reports zero trading volume for an option contract, use
the average of the contract’s bid and ask prices to measure the last trade price.)
A. Write a formula in Excel for the Black-Scholes option value of a call, and then
use either Solver or Goal Seek to calculate the implied volatility for each of the
ten call options. In your calculations, you can assume the following:
Dividend yield is zero
Annualized, continuously-compounded risk-free rate is equal to the 1-year
Treasury rate (see www.treasury.gov for data).
B. Compare the implied volatilities you calculated against the ones reported in
Yahoo Finance. Are they the same? If not, what might explain the discrepancy?
C. Graph the implied volatilities for the 10 options against the moneyness of the
contract (measured as the ratio of stock price to option strike price). Describe the
shape of your graph. Based on the results, what can you say about market demand
for the different options and about the accuracy of your Black-Scholes
calculation?