CHAPTER 6: PROBLEMS
Ampex common stock has a beta of 1.4. If the risk-free rate is 8 percent, the expected market
return is 16 percent, and Ampex has $20 million of 8 percent debt, with a yield to maturity of
12 percent and a marginal tax rate of 50 percent, what is the weighted average cost of capital
Calvin Inc. earned $2.00 per share during the past year and has just paid a dividend of $.40
per share. Investors forecast that Calvin will continue to retain 80 percent of its earnings for
the next 4 years and that earnings will grow at 25 percent per year through year 5. The
dividend payout ratio is expected to be raised in year 5 to 50 percent, reducing the dividend
growth rate to 8 percent thereafter. If Calvin’s equity β is .9, the risk-free rate is 8.5 percent,
and the market risk premium is 8 percent, what should its price be today?
With an estimated 25% annual growth rate, Calvin’s forecast earnings for the next
5 years are $2.50, $3.13, $3.91, $4.88, $6.10. With a 20% dividend payout rate for the first 4
years and a 50% payout rate thereafter, this earnings stream yields dividends of $0.50, $0.63,
$0.78, $0.98, $3.05. Note that the last term in the series is just $6.10 * 0.50. In year 6, the
forecast dividend is $6.10 * 1.08 * 0.50 = $3.29. This dividend is projected to grow at the
rate of 8% annually.
It is important in answering this question to consider the fact that the dividend payout rate
changed in year 5 to 50%, from 20%. Hence, just taking the initial 40¢ dividend and
multiplying it by (1.25)
will not give you the correct answer.
To determine Calvin’s price today based on these expectations, we must next estimate
Calvin’s cost of equity capital. Using the CAPM, this figure is
) = 8.5% + 0.9 * 8% = 15.7%
The present value at 15.7% of the first 5 dividend payments is $3.42. The present value as of the
end of year 5 of the dividend flows from year 6 on can be found using the dividend growth
model, Po = DIV
- g). Substituting in the numbers previously calculated, we get
Po = DIV
g) = $3.29/(0.157 - 0.08) = $42.73
The present value of this number of today is $42.73/(1.157)5 = $20.61. Adding the value of the
two cash flows gives a price for Calvin’s stock today of $24.03.
Remember that you must discount the price as of the beginning of year 6 by (1.157)
. The former is correct because you are discounting it back 5 years, not 6 years.
As a financial analyst for National Engineering, you are required to estimate the cost of
capital the firm should use in evaluating its heavy construction projects. The firm’s balance
sheet data and other information are listed below. Assume the corporate tax rate is 35