1. Risk and the cost of capital9
Risk and the cost of capital
McGraw-Hill/Irwin
Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

2. 9-1 company and project costs of capital
Firm Value
Sum of value of assets

3. Figure 9.1 company cost of capital
A company’s cost of capital can be compared to CAPM required return
Required
return
Project beta
0.5
Company cost of capital
5.5
0.2
SML

4. 9-1 company and project costs of capital
Company Cost of Capital

5. 9-1 company and project costs of capital
Weighted Average Cost of Capital
Traditional measure of capital structure, risk and return

6. 9-2 measuring the cost of equity
Capital Structure (CS)
Mix of debt and equity within a company
Expand CAPM to include CS
r = rf + β(rm − rf)
requity = rf + β(rm − rf)

7. 9-2 measuring the cost of equity
Estimating Beta
SML shows relationship between return and risk
CAPM uses beta as proxy for risk
Other methods can also determine slope of SML and beta
Regression analysis can be used to find beta

8. Figure 9.2a citigroup Return
Weekly Data
beta =
1.83
alpha =
-0.31
R-squared =
0.64
Correlation =
0.80
Annualized std dev of market =
19.52
Annualized std dev of stock =
44.55
Variance of stock =
Std error of beta
0.14

9. Figure 9.2B citigroup Return
Wkly Data
beta =
3.32
alpha =
0.24
R-squared =
0.49
Correlation =
0.70
Annualized std dev of market =
30.11
Annualized std dev of stock =
142.95
Variance of stock =
Std error of beta
0.34

10. Figure 9.2c disney Return Wkly Data 2010-2011 beta = 0.33 alpha = 0.02
beta =
0.33
alpha =
0.02
R-squared =
0.22
Correlation =
0.47
Annualized std dev of market =
19.52
Annualized std dev of stock =
13.68
Variance of stock =
187.13
Std error of beta
0.06

11. Figure 9.2D disney Return Wkly Data 2008-2009 beta = 0.41 alpha = 0.17
beta =
0.41
alpha =
0.17
R-squared =
0.19
Correlation =
0.44
Annualized std dev of market =
30.11
Annualized std dev of stock =
28.08
Variance of stock =
788.62
Std error of beta
0.08

12. Figure 9.2e campbell’s Return
Wkly Data
beta =
0.33
alpha =
0.02
R-squared =
0.22
Correlation =
0.47
Annualized std dev of market =
13.68
Annualized std dev of stock =
19.52
Variance of stock =
381.22
Std error of beta
0.06

13. Figure 9.2f campbell’s Return, %
Wkly Data
beta =
0.41
alpha =
0.17
R-squared =
0.19
Correlation =
0.44
Annualized std dev of market =
28.08
Annualized std dev of stock =
30.11
Variance of stock =
906.55
Std error of beta
0.08

14. Table 9.1 estimates of betas
Standard Error
Canadian Pacific
1.27
.10
CSX
1.41
.08
Kansas City Southern
1.68
.12
Genesee & Wyoming
1.25
Norfolk Southern
1.42
.09
Rail America
1.15
.14
Union Pacific
1.21
.07
Industry portfolio
1.34
.06

15. 9-2 measuring the cost of equity
Beta Stability
% IN SAME % WITHIN ONE
RISK CLASS CLASS
CLASS YEARS LATER YEARS LATER
10 (High betas)
1 (Low betas)
Source: Sharpe and Cooper (1972)

16. 9-2 measuring the cost of equity
Company cost of capital (COC) is based on the average beta of the assets
The average beta of the assets is based on the % of funds in each asset
Assets = debt + equity

17. 9-2 measuring the cost of equity
Expected Returns and Betas Prior to Refinancing
Expected return (%)
Bdebt
Bassets
Bequity
Rdebt = 8
Rassets = 12.2
Requity = 15

18. 9-2 measuring the cost of equity
Company cost of capital (COC) is based on average beta of assets
Average beta of assets is based on the % of funds in each asset
Example
1/3 new ventures β = 2.0
1/3 expand existing business β = 1.3
1/3 plant efficiency β = 0.6
AVG β of assets = 1.3

19. 9-2 measuring the cost of equity
Company Cost of Capital

20. 9-3 analyzing project risk

21. 9-3 analyzing project risk
Allowing for Possible Bad Outcomes
Example
Project Z will produce one cash flow, forecasted at $1 million at year 1. It is regarded as average risk, suitable for discounting at 10% company COC:

22. 9-3 analyzing project risk
Allowing for Possible Bad Outcomes
Example, continued
Company’s engineers are behind schedule developing technology for project. There is a small chance that it will not work. Most likely outcome still $1 million, but some chance that project Z will generate zero cash flow next year:

23. 9-3 analyzing project risk
Allowing for Possible Bad Outcomes
Example, continued
If technological uncertainty introduces a 10% chance of zero cash flow, unbiased forecast could drop to $900,000:

24. Table 9.2 cash flow forecasts

25. 9-4 certainty equivalents—another way to adjust for risk
Risk, Discounted Cash Flow (DCF), and Certainty Equivalents (CEQ)

26. Figure 9.3 two ways to calculate present value

27. 9-4 certainty equivalents—another way to adjust for risk
Example
Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and beta?

28. 9-4 certainty equivalents—another way to adjust for risk
Example, continued
Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and beta?

29. 9-4 certainty equivalents—another way to adjust for risk
Example, continued
Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and .75 beta?
Assume cash flows change, but are risk-free. What is new PV?

30. 9-4 certainty equivalents—another way to adjust for risk
Example, continued
94.6 is risk-free, is certainty equivalent of 100

31. 9-4 certainty equivalents—another way to adjust for risk
Example, continued
Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and .75 beta?

32. 9-4 certainty equivalents—another way to adjust for risk
Example, continued
Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and .75 beta?
Assume cash flows change, but are risk-free. What is new PV?
Difference between 100 and certainty equivalent (94.6) is 5.4%
This % can be considered annual premium on risky cash flow

33. 9-4 certainty equivalents—another way to adjust for risk
Example, continued
Project A expects CF = $100 mil for each of three years. What is PV of project given 6% risk-free rate, 8% market premium, and .75 beta?
Assume cash flows change, but are risk-free. What is new PV?