Week 6 Supplemental Problem Solutions
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12-26.
26. Your company operates a steel plant. On average, revenues from the plant are $30 million per
year. All of the plant’s costs are variable costs, and they are consistently 80% of revenues, including
energy costs associated with powering the plant, which represents one-quarter of the plant’s costs, or
an average of $6 million per year. Suppose the plant has an asset beta of 1.25, the risk-free rate is 4%,
and the market risk premium is 5%. The tax rate is 40%, and there are no other costs.
Estimate the value of the plant today assuming no growth.
Suppose you enter a long-term contract that will supply all of the plant’s energy needs for a fixed cost of $3
million per year (before tax). What is the value of the plant if you take this contract?
How would taking the contract in part (b) change the plant’s cost of capital? Explain.
a.
FCF = (30 – 0.8(30))(1 – 0.40) = 3.6 million
Ru = 4% + 1.25
5% = 10.25%
V= 3.6 / 0.1025 = 35.12 million
b.
FCF without energy = (30 – 18)(1 – 0.40) = 7.2
Cost of capital = 10.25%
Energy cost after tax = 3(1 – .40) = 1.8
Cost of capital = 4%
V = 7.2/.1025 – 1.8/.04 = 70.24 – 45 = 25.24 million
c.
FCF = 7.2 – 1.8 = 5.4
5.4/25.24 = 21.4%
Risk is increased because now energy costs are fixed. Thus a higher cost of capital is appropriate.
13-2.
2. Excel Project and Excel Solution Assume that the CAPM is a good description of stock price
returns. The market expected return is 7% with 10% volatility, and the risk-free rate is 3%. News
arrives that does not change any of these numbers but it does change the expected return of the
following stocks:
At current market prices, which stocks represent buying opportunities?
On which stocks should you put a sell order in?
According to the CAPM, we should hold the market portfolio. But once new news arrives and we update our
expectations, we may find profitable trading opportunities if we can trade before prices fully adjust to the
news. Assuming we initially hold the market portfolio, we can improve gain by investing more in stocks
with positive alphas and less in stocks with negative alphas. a.
Green Leaf, HanBel
b.
Rebecca Automobile and possibly NatSam (although its alpha is close enough to zero that we might
regard it as insignificant).
13-12.
12. Consider the price paths of the following two stocks over six time periods:
Neither stock pays dividends. Assume you are an investor with the disposition effect and you bought at time 1
and right now it is time 3. Assume throughout this question that you do no trading (other than what
is specified) in these stocks.
Which stock(s) would you be inclined to sell? Which would you be inclined to hold on to?
How would your answer change if right now is time 6?
What if you bought at time 3 instead of 1 and today is time 6?
What if you bought at time 3 instead of 1 and today is time 5?
a.
Sell 1, hold 2.
b.
Sell both.
c.
Sell both.
d.
Sell 2, hold 1.
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