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
Each asset is valued by discounting its forecasted future cash flows at a rate reflecting the risk of that asset.
Value additive property is an important concept that has many applications. A firm’s value is the sum of the value of its various assets.

3. Figure 9.1 company cost of capital
The company cost of capital is not the appropriate discount rate for all its projects. If you consider each project as a mini-firm, the value of that mini-firm depends on its beta.
What happens if the firm uses the same cost of capital to value different projects?
Required
return
Project beta
0.5
Company cost of capital
5.5
0.2
SML
The company cost of capital is not the appropriate discount rate for all its projects. If you consider each project as a mini-firm, the value of that mini-firm depends on its beta. The discount rate depends on the project’s discount rate. The required rate of return depends on the project and not on the company that is undertaking it.

4. 9-1 company and project costs of capital
Company Cost of Capital
This is possibly the most important slide in the chapter. Take time to explain the difference between accounting terminology and finance terminology. While we use the same format for firm value, the meanings are distinctly different. Instead of asset we use value. And in place of debt and equity we use market values, not book values. Note the cost of capital for debt and equity is different. Each variable in the COC equation must be explained in detail or students will not follow the rest of the material.

5. 9-1 company and project costs of capital
Weighted Average Cost of Capital
Traditional measure of capital structure, risk and return
There is much less to cover here, other than to show the WACC formula as the result of the prior exercise.

6. 9-2 measuring the cost of equity
Generally CAPM is used to estimate the cost of equity:
r = rf + β(rm − rf)
requity = rf + β(rm − rf)
Generally the CAPM is used to estimate the cost of equity. But other methods like DCF (Gordon’s model) or APT (arbitrage pricing theory) can also be used for these estimations. These models require different data. Capital structure is the mix of debt and equity that finances the firm.

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
The SML can be used to determine the required rate of return on a project. Regression analysis is used for estimating beta. Generally, monthly returns (60 months) for the firm and the market are used for the estimation.

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
Regression analysis can be used to estimate the beta of a firm. Total return data for the firm is used. A broadly based value-weighted index is used for market return. Generally 5-year (60 months) monthly data is used. Market return is plotted on the x-axis and the company returns on the y-axis. Slope of the fitted line is the beta estimate. A financial calculator can be used to estimate beta. The graph shows the beta estimate for Citigroup. The following five slides repeat the same exercise for three different stocks.

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
Citigroup beta, part two.

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
Disney beta

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
Disney beta, part two.

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
Campbell’s beta.

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
Campbell’s beta, part two.

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
Beta estimates have standard errors. Standard error can be used to construct a range of values for beta within which true beta lies.

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)
The beta values are not stable over time. This frame shows what percentage of firms have same (same risk class) beta after five years.

16. Division’s required return on equity: re = rRF + (rM – rRF)B .
Find the division’s market risk and cost of capital based on the CAPM and the pure play approach, given these inputs:
Target debt ratio = 10%.
rd = 12%.
rRF = 7%.
Tax rate = 40%.
Pure play company beta = 1.7.
Market risk premium = 6%.
Division’s required return on equity:
re = rRF + (rM – rRF)B .
= 7% + (6%)1.7 = 17.2%.
WACCDiv. = wdrd(1 – T) + were
= 0.1(12%)(0.6) + 0.9(17.2%)
= 16.2%.

17. How does the division’s WACC compare with the firm’s overall WACC?
Division WACC = 16.2% versus company WACC = 11.1%.
“Typical” projects within this division would be accepted if their returns are above 16.2%.

18. measuring the cost of equity Extension: Financial Leverage and Beta
The betas used in the CAPM are estimated from returns on stocks. Thus, they are the firm’s stock or equity beta.
Imagine an individual who owns all the firm’s debt and all its equity. In other words, this individual owns the entire firm. What is the beta of her portfolio of the firm’s debt and equity?

19. 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
Bequity = Basset (1+ D/E)
This equation is handy when we can not calculate Be for the Project.
Betas are also calculated for specific assets. Explain how a firm is the weighted sum of its parts.

20. Financial Leverage and Beta
Basset = D/(D+E) x Bd + E/(D+E) x Be
Bd is very low in practice, we can assume Bd = 0
Basset = E/(D+E) x Be
For a levered firm, E/(D+E) < 1, hence
Basset < Be
Let us rewrite it:
Be = Ba x (D+E)/ E
Be = Ba (1 + D/E)

21. How to determine the risk-adjusted cost of capital for a particular division?
Estimate the cost of capital that the division would have if it were a stand-alone firm.
This requires estimating the division’s beta, cost of debt, and capital structure.
One method for Estimating Beta for a Division is the pure play approach.
Find several publicly traded companies exclusively in division’s business.
Use average of their betas as proxy for division’s beta.

22. Ex.: Financial Leverage and Beta
Previously, we calculated a divisional WACC, where Bdivision = 1,7.
Assume that the pure play firms, on the average, have D/V = 40% instead of D/V = 10% as targeted by the firm.
How should we adjust the previous calculation to reflect the difference in financial leverage?
The process is called “unlever – relever”.

23. Unlever - relever Unlever first: Be = Ba (1 + D/E)
WACCdiv = 0,1(12%)(0,6) + 0,9(13,8%)
WACCdiv = 13,14% instead of 16,2%

24. 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?
A numerical example of a risky cash flow is given.
Use CAPM to calculate the risk-adjusted discount rate for risky cash flows. Using a single discount rate may not be appropriate for all situations.

25. 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?
This slide shows the calculation for the PV of the risky cash flows using the risk-adjusted discount rate.

26. 9-4 certainty equivalents—another way to adjust for risk
Example, continued
Now let us calculate the certainty equivalent cash flows.
Certainty equivalent cash flows, when discounted at the risk-free rate, should provide the same PV.
Project B cash flows change, but are risk-free. What is new PV?
Now let us calculate the certainty equivalent cash flows.
Certainty equivalent cash flows, when discounted at the risk-free rate, should provide the same PV. The table provides the example of certainty equivalent cash flows. Note that these are different from risky cash flows. Year 1 CEQ = [100/1.12](1.06) = $94.6; Year 2 CEQ = [100/(1.12^2)](1.06^2) = $89.6; Year 3 CEQ = [100/(1.12^3)](1.06^3) = $84.8.

27. 9-4 certainty equivalents—another way to adjust for risk
Example, continued
94.6 is risk-free, is certainty equivalent of 100
Present value is obtained by discounting risky cash flows using risk-adjusted discount rate. The certainty equivalent cash flows are discounted at the risk-free rate to get the same PV.
Present value is obtained by discounting risky cash flows using risk-adjusted discount rate. The certainty equivalent cash flows are discounted at the risk-free rate to get the same PV.
Here the relationship between risky cash flows and equivalent risk-free cash flows is explored.

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 .75 beta?
The table provides a comparison of risky cash flows and certainty equivalent cash flows.

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?
Difference between 100 and certainty equivalent (94.6) is 5.66%
This % can be considered annual premium on risky cash flow
$94.6 [94.6 = (100/1.12)(1.06)] is the certainty equivalent cash flow of $100 for year 1. This provides another way to look at project cash flows. Similarly, $89.6 and $84.8 are certainty equivalent cash flows for year 2 and year 3 respectively. Since certainty equivalent cash flows are risk-free, these are discounted using the risk-free rate. The present value is the same as before.
1.12/1.06 =
100/ = $94.6
100/(1.0566^2) = $89.6
100/(1.0566^3) = $84.8

30. 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?
If you can calculate the certainty equivalent cash flows for a project directly, then calculating the present value is very easy. All you have to do is to discount them at the risk-free rate. You do not need to estimate the cost of capital. CEQ is conceptually appealing, but very difficult to estimate in practice.