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Chapter 13
Questions 1 & 2
Question 1
Market
value, Cost of Tax After-tax Weighted
Source of capital rupees, million capital, % rate, %cost, %cost, %
Debt 100 7.50% 30.00% 5.25% 0.88%
Equity 500 10.50% 10.50% 8.75%
Firm Value 600
Weighted average cost of capital
9.63%
Key inputs Market capitalization
Risk-free rate, % 7.00% Share price, rupees 25
Market risk premium, % 5.00% Shares outstanding, millions 20
Beta 0.70 Market capitalization 500
Cost of Debt premium, % 0.50%
Tax rate, % 30.00%
Question 2 Capital structure changes
Market Debt, Equity, Shares
value, Cost of Tax After-tax Weighted rupees, rupees, outstanding, Price,
Source of capital rupees, million capital, %rate, %cost, %cost, % million million millions rupees
Debt 300 8.00% 30.00% 5.60% 2.58% Original 100.0 500.0 20.0 25.0
Equity 350 12.42% 12.42% 6.69% Appreciation 50.0 20.0 2.5
Firm Value 650
Weighted average cost of capital
9.27% Increase 200.0 (200.0) (7.3)
Total 300.0 350.0 12.7 27.5
Key inputs Unlevered beta
Risk-free rate, % 7.00% Original beta 0.70
Market risk premium, % 5.00% Original debt to equity 0.20
Beta 1.08 Unlevered beta 0.58
Cost of Debt premium, % 1.00%
Tax rate, % 30.00% New debt to equity 0.86
New beta 1.08
Cost-of-debt premium 2.1%
for equivalent cost of capital to
Question 1, %
Pretax cost of debt 9.1%
for equivalent cost of capital to
Question 1, %
Chapter 13
Question 3
Since the financial projections for Bangalore Bread are in Indian rupees, the risk-free rate should be the Indian rate, not the German
rate. The beta for EuropeCo also is irrelevant, since the company's composition (and consequently business risk) does not match that of
Bangalore Bread and the financial risk for EuropeCo is similar to that of Bangalore Bread, as they have similar capital structures.
Chapter 13
Question 4
In Chapter 11, ke is estimated using:
Key inputs
Price-to-earnings ratio 15.0
Return on equity, % 13.5%
Long-run growth in cash flow, % 6.7%
Implied cost of equity, % 10.1%
Earnings 1 ROE , becauseCF Earnings 1
Price ROE
ee
g
g
kg
−
= + = −
Chapter 13
Question 5
Returns, %
ConglomCo Market Summary output
Month 1 1.3% 1.0%
Month 2 2.0% 1.2%
Month 3 5.0% 3.4% Multiple R0.89
Month 4 –1.0% 0.3% R-squared 0.79
Month 5 –1.4% –0.6% Adjusted R-squared 0.77
Month 6 2.2% 3.7% Standard error 0.01
Month 7 6.1% 4.8% Observations 12
Month 8 0.3% –2.3%
Month 9 –4.0% –4.5% ANOVA
Month 10 3.8% 3.9% df SS MS F
Month 11 –1.2% –1.3% Regression 1 0.007 0.01 38.75
Month 12 – 1.8% Residual 10 0.002 –
Total 11 0.009
Average 2.96% 2.51%
Volatility 2.14% 1.64% Coefficients Standard error t- stat P- value
Intercept – – 0.49 0.63
Variable 1 0.93 0.15 6.22 –
The beta, "Variable 1" from the regression, is 0.93. This says that ConglomCo's stock returns are a little less sensitive to market movements
than the average firm in the economy.
Regression statistics
Chapter 13
Question 6
Scenario 1: Probability of default = 35% Scenario 2: Probability of default = 40%
Market price, $Solutions, %Market price, $ Solutions, %
Price 80.00 Yield to maturity 31.25% Price 77.00 Yield to maturity 36.36%
Cost of debt 7.19% Cost of debt 7.79%
Promised final cash flow Promised final cash flow
Face, $ 100.00 Face, $ 100.00
Coupon, % 5.00 Coupon, % 5.00
Final cash flow, $ 105.00 Final cash flow, $ 105.00
Expected final cash flow, $Expected final cash flow, $
Bond satisfies obligations 105.00 Bond satisfies obligations 105.00
Bond defaults 50.00 Bond defaults 50.00
Expected value 85.75 Expected value 83.00
Key data, %Key data, %
Coupon 5.0% Coupon 5.0%
Probability of default 35.0% Probability of default 40.0%
Payment in default 50.0% Payment in default 50.0%
If the probability of default increases to 40 percent, both the yield to maturity and the cost of debt are likely to increase.
When the probability of default increases, the market price should go down. If it goes down to $77, then the yield to maturity increases to 36.36 percent.
At this price, and with the higher probability of default, the cost of debt would rise, but only to 7.79 percent.
Chapter 13
Question 7
In the aftermath of the financial crisis of 2008, the U.S. Federal Reserve and several other central banks throughout the world
lowered interest rates to historically low levels and simultaneously bought trillions of dollars of government bonds. Together,
these actions pushed yields on government bonds to near zero. This poses a challenge in estimating the firm's cost of equity,
as these yields are typically used as an estimate of the (nominal) risk-free rate. One can create a synthetic risk-free rate to address this
by adding the expected inflation rate to the long-term historical average real risk-free rate.
Exhibit 13.13 ConglomCo and Market Returns
%
ConglomCo Market
Month 1 1.3% 1.0%
Month 2 2.0% 1.2%
Month 3 5.0% 3.4%
Month 4 –1.0% 0.3%
Month 5 –1.4% –0.6%
Month 6 2.2% 3.7%
Month 7 6.1% 4.8%
Month 8 0.3% –2.3%
Month 9 –4.0% –4.5%
Month 10 3.8% 3.9%
Month 11 –1.2% –1.3%
Month 12 0.0% 1.8%
