1. Risk, Cost of Capital, and Capital Budgeting
ICFI
By : Else Fernanda, SE.Ak., M.Sc.

2. 1. The Cost of Equity Capital
2. Estimation of Beta
3. Determinants of Beta
4. Extensions of the Basic Model
5. Estimating Cost of Capital
6. Reducing the Cost of Capital
7. Summary and Conclusions

3. Main idea Economic value of time reflects:
(1) opportunity cost of time,
(2) risky cash flow.
We discuss the appropriate discount rate for risky cash flows.

4. The Cost of Equity Capital
A firm with excess cash can either pay a dividend or make a capital investment.
Stockholders can reinvest the dividend in risky financial assets.
The expected return on a project should be the expected return on a financial asset of comparable risk.

5. Example: The Cost of Equity
Assume a 100%-equity firm. ABC Co. has a beta of 2.5. The risk-free rate is 5% and a market risk premium is 10%. What is the appropriate discount rate for an expansion of this firm? R = 5 % +
2.5 (10%) % 30 = R

6. Example (continued)
Suppose ABC is evaluating the following non-mutually exclusive projects. Each costs $100 and lasts one year.
project
beta
cash flow
IRR
NPV at 30% A
2.5
$150
50%
$15.38 B
$130
30% $0 C
$110
10%
-$15.38

7. Using the SML to Estimate the Risk-Adjusted Discount Rate for Projects
Good project
30%
2.5 A B C
Project
IRR
ABC should accept projects A and B, and reject project C.
Bad project 5%
Firm’s risk (beta)

8. Estimation of Beta The beta is given by: Example: Stock i return
Market return 1
-10%
-40% 2 3
-30% 20 10 4 15

9. Example (continued): E(ri) = 0.07; E(rm) = -0.10 cov (ri, rm) = 0.0363
var (rm) =
beta = cov (rGT, rm) / var (rm)
= / = 0.419
In practice, people use regression to estimate beta (characteristic line).

10. About beta: A firm’s beta change due to changes in
product line, technology, market condition (e.g. airline deregulation), financial leverage.
Betas are generally stable for firms remaining in the same industry.
If you believe that the operations of the firm are similar to the operations of the rest of the industry, you may well use the industry beta.

11. Where does beta come from?
Determinants of Beta
Where does beta come from?
Business risks depend on both on the responsiveness of the firm’s revenue to the
business cycle (cyclicity of revenues), and
operating leverage
Financial Risk
Financial leverage

12. Cyclicality of Revenues
Highly cyclical stocks have high betas.
Retailers and high-tech firms fluctuate with the business cycle.
Utilities and food companies are less dependent upon the business cycle.
Note that cyclicality is not the same as variability.
Movie studios: Revenues depend upon whether they produce “hits” or “flops”, but their revenues are not especially dependent upon the business cycle.
Stocks with high standard deviations need not have high betas.

13. Operating Leverage DOL = EBIT D Sales Sales D EBIT ×
The degree of operating leverage measures how sensitive a firm’s cash flow (or project) is to its fixed costs.
Operating leverage increases as fixed costs rise and variable costs fall.
Operating leverage magnifies the effect of cyclicity on beta.
The degree of operating leverage is given by:
DOL =
EBIT
D Sales
Sales
D EBIT ×

14. Operating Leverage  EBIT $  Volume
Total costs
Total costs $
Fixed costs
 Volume
Fixed costs
Volume
Operating leverage increases as fixed costs rise and variable costs fall.

15. Financial Leverage and Beta
Operating leverage refers to the sensitivity of the firm’s cash flow to the firm’s fixed costs of production.
Financial leverage is the sensitivity of a firm’s cash flow to the firm’s fixed costs of financing.
The relationship between the betas of the firm’s debt, equity, and assets is given by:
Set D =0. e = a (1 + Debt/Equity). Equity  is always greater than the asset  with financial leverage.
bAsset =
Debt + Equity
Debt
× bDebt +
Equity
× bEquity

16. Financial Leverage and Beta: Example
XYZ Co. is currently all-equity and has a beta of 0.90.
The firm has decided to lever up to a capital structure of 1 part debt to 1 part equity.
Suppose its asset beta remains at 0.90.
Assuming a zero beta for its debt, its equity beta would become twice as large:
bAsset = 0.90 =
1 + 1 1
× bEquity
bEquity =
2 × 0.90 = 1.80

17. Extensions of the Basic Model
So far, we have considered:
projects with same risk as the firm,
100% equity firm.
We now consider more general cases.

18. The Firm versus the Project
A project should generate return, comparable to return on asset with similar risk.
If a project’s beta is different from that of the firm, do not use corporate discount rate: the project should be discounted at a rate commensurate with its risk.
The use of a single corporate discount rate for all different divisions in the firm is problematic. (See the next figure.) 16

19. Capital Budgeting & Project Risk
Project IRR
The SML can tell us why:
Incorrectly accepted negative NPV projects
Hurdle rate
bFIRM
Incorrectly rejected positive NPV projects rf
Firm’s risk (beta)
A firm that uses one discount rate for all projects may over time increase the risk of the firm while decreasing its value.

20. Example: Capital Budgeting & Project Risk
Suppose JDL Co. has a cost of capital of 17% based on the CAPM. The risk-free rate is 4%; the market risk premium is 10% and the firm’s beta is 1.3.
This is a breakdown of the company’s investment projects:
1/3 Automotive retailer b = 2.0
1/3 Computer Hard Drive Mfr. b = 1.3
1/3 Electric Utility b = 0.6
Average b of assets = 1.3
When evaluating a new electrical generation investment, which cost of capital should be used? 17

21. Capital Budgeting & Project Risk
SML
Project IRR
24%
Investments in hard drives or auto retailing should have higher discount rates.
17%
10%
Project’s risk (b)
0.6
1.3
2.0
r = 4% + 0.6×(14% – 4% ) = 10% 10% reflects the opportunity cost of capital on an investment in electrical generation, given the unique risk of the project.

22. The Cost of Capital with Debt
The weighted average cost of capital is given by:
Margin expense is tax-deductible. So we multiply the last term by (1 – Tc)
Equity
Debt
rWACC =
× rEquity +
× rDebt ×(1 – TC)
Equity + Debt
Equity + Debt S B
rWACC =
× rS +
× rB ×(1 – TC)
S + B
S + B

23. Example: Finding the WACC
 5 mio shares of common shares at $40, and E = 1.2.
12% Ijarah Sukuk, face value = $200 mio, 5 years-to-maturity selling at 100% of the par.
  E(Rm) – Rf = 6%, Rf = 4%, TC = 34%.
Step 1: find out market value of common and sukuk.
Step 2: find out fraction in total firm value.
Step 3: find out after tax cost of sukuk

24. Example: Finding the WACC
RE = Rf + [E(Rm) – Rf]
= 4% * 6% = 11.2%
Rd = 12%
After-tax: 12% (1 – TC)
= 12% * (66%) = 7.92%

25. Example: Finding the WACC
calculate the weighted average of cost.
Capital structure (1)
fraction of firm value (2)
after-tax return (3)
WACC (4)
Common stock
$40 * 5 m = $200 m
50%
11.2%
Sukuk
$200 m * 100% = $ 200 m
7.92%
firm value
$400 m
 9.56%

26. Reducing the Cost of Capital
What is Liquidity?
Liquidity, Expected Returns and the Cost of Capital
Liquidity and Adverse Selection
What the Corporation Can Do

27. What is Liquidity?
Result: the expected return and the firm’s cost of capital are positively related to risk.
New idea: The more liquid a firm’s shares, the lower expected return and lower cost of capital.
Liquidity: The trading costs of a firm’s shares. The costs include brokerage fees, the bid-ask spread and market impact costs.

28. Liquidity, expected returns and the cost of capital
The cost of trading an illiquid stock reduces the total return that an investor receives.
Investors demand a high expected return when investing in stocks with high trading costs.
This high expected return implies a high cost of capital to the firm.

29. Liquidity and the Cost of Capital
An increase in liquidity, i.e. a reduction in trading costs, lowers a firm’s cost of capital.

30. Liquidity and Adverse Selection
One of factors that determine the liquidity of a stock is adverse selection.
This refers to the notion that informed traders can pick off specialists and other uninformed traders.
The informed traders raise the required return on equity, and thereby increasing the cost of capital.

31. What the Corporation Can Do
The corporation has an incentive to raise liquidity of its shares, since higher liquidity would reduce the cost of capital.
(1) Firm can bring in more uninformed traders.
(a) A stock split would make the shares more attractive to small (uninformed) traders.
More uninformed traders means lower adverse selection costs and lower bid-ask spreads.

32. What the Corporation Can Do
(b) Companies can also facilitate stock purchases through the Internet.
Direct stock purchase plans and dividend reinvestment plans handles on-line allow small investors the opportunity to buy securities cheaply.
(2) The companies can also disclose more information, especially to security analysts, to narrow the gap between informed and uninformed traders. This should reduce spreads.

33. Summary and Conclusions
The expected return on any capital budgeting project should be the expected return on a financial asset of comparable risk. Otherwise the shareholders would prefer the firm to pay a dividend.
The expected return on any asset is dependent upon b.
A project’s required return depends on the project’s b.
A project’s b can be estimated by considering comparable industries or the cyclicality of project revenues and the project’s operating leverage.
If the firm uses debt, the discount rate to use is the rWACC.
In order to calculate rWACC, the cost of equity and the cost of debt applicable to a project must be estimated.