1. FIN 468: Intermediate Corporate Finance
Topic 8–Cost of Capital
Larry Schrenk, Instructor

2. Topics Excel: Linear Regression Project Review Cost of Capital Equity
Debt
Preferred Shares

3. Excel: Linear Regression

4. Excel Features: Linear Regression
Linear regression finds the line that best fits a series of points. In finance, it is often used to find the beta (b) of a firm’s equity.
In our example, we shall find the beta of MMM using the S&P 500 as a proxy for the market. Since we want to know the sensitivity of the return on MMM to changes in the return on the S&P 500, the return on MMM is the dependent variable (y axis) and the return on the S&P 500 the independent variable (x-axis).

5. Excel Features: Linear Regression
1) You need to have the returns of the assets arranged in columns:

6. Excel Features: Linear Regression
2) Click on Data Analysis under the ‘Tools’ drop-down menu to open the Data Analysis window. Then select ‘Regression’ and click on ‘OK’.

7. Excel Features: Linear Regression
3) The Regression window will appear.

8. Excel Features: Linear Regression
4) In the regression window, input the cells for the y variable (MMM) and the x variable (S&P 500). Click on the ‘Line Fit Plots’ box and click on ‘OK’.

9. Excel Features: Linear Regression
5) A new worksheet will appear with the results and a graph.

10. Excel Features: Linear Regression
6) The blue squares are data points and the pink squares are the corresponding points on the best-fit line.

11. Excel Features: Linear Regression
7) Here is the same graph with a dashed line drawn though the points.

12. Excel Features: Linear Regression
8) The summary statistics provide a wealth of information about the regression. In particular the beta is the coefficient of the x variable.

13. Project Review

14. Project Review I
Provide a brief discussion of the company’s products, markets, and competitors.
Provide a brief discussion of the top management, their qualifications, experience, and how long they have been with the company. Are any of the managers considered a key person that would hurt the firm if they left?
Provide a brief discussion of any risks the firm may face such as competitive pressure, product obsolescence, lawsuits etc.

15. Project Review II
Perform a ratio analysis of at least the last 3 years.
Comparative industry
Trends over time
Explain major changes and deviations from industry
Create a pro-forma 5 year income forecast
Calculate FCF over next five years and a terminal value
Estimate firm’s cost of equity capital using one or more of the following methods:
CAPM
Discounted Cash Flow
Own-Bond-Yield-Plus-Risk-Premium

16. Cost of Capital

17. Cost of Capital
Rate of return that the suppliers of capital – bondholders and stockholders require as compensation for their contributions of capital

18. Leverage and Marginal Cost
As firms take on more debt, financial leverage increases increasing the riskiness of the firm and causing lenders to require a greater return
Additional debt may therefore increase cost of capital
The marginal cost is the cost to raise the additional funds for the potential investment project

19. Firm vs. Project Cost of Capital
Cost of capital for entire company
Important for firm/security valuation
Cost of capital for a specific project
WACC must be adjusted for the riskiness of the project

20. Target Weights Assume current capital structure is correct
Estimate capital structure based on historical trends
Use average of comparable companies capital structure

21. Choosing the Right Discount Rate
The numerator focuses on project cash flows.
The denominator is the discount rate.
The denominator should:
Reflect the opportunity costs of the firm’s investors.
Reflect the project’s risk.
Be derived from market data.

22. Cost of Equity Capital

23. Where Do We Stand?
Earlier chapters on capital budgeting focused on the appropriate size and timing of cash flows.
This chapter discusses the appropriate discount rate when cash flows are risky.

24. Asset Betas and Project Discount Rates
When a firm uses no leverage, its equity beta equals its asset beta.
An unlevered beta simply tells us how risky the equity of a company might be if it used no leverage at all.

25. Finding the Right Discount Rate
When an all-equity firm invests in an asset similar to its existing assets, the cost of equity is the appropriate discount rate to use in NPV calculations.
When a firm with both debt and equity invests in an asset similar to its existing assets, the WACC is the appropriate discount rate to use in NPV calculations.

26. The Cost of Equity Capital
From the firm’s perspective, the expected return is the Cost of Equity Capital:
To estimate a firm’s cost of equity capital, we need to know three things:
Risk Free Rate rrf
Risk Premium
Beta

27. Example
Suppose the stock of Stansfield Enterprises, a publisher of PowerPoint presentations, has a beta of 2.5. The firm is 100 percent equity financed.
Assume a risk-free rate of 5 percent and a market risk premium of 10 percent.
What is the appropriate discount rate for an expansion of this firm?
You may want to note that this example assumes expansion into projects that are similar to the existing nature of the business.

28. Example
Suppose Stansfield Enterprises is evaluating the following independent projects. Each costs $100 and lasts one year.
Project
Project b
Project’s Estimated Cash Flows Next Year
IRR
NPV at 30% A
2.5
$150
50%
$15.38 B
$130
30% $0 C
$110
10%
-$15.38

29. Using the Security Market Line
Good project
30%
2.5 A B C
Project
IRR
Bad project 5%
Firm’s risk (beta)
This, again, assumes independent projects. This is a good point at which to review the relation between IRR and NPV.
An all-equity firm should accept projects whose IRRs exceed the cost of equity capital and reject projects whose IRRs fall short of the cost of capital.

30. Estimation of Beta
Market Portfolio - Portfolio of all assets in the market. In practice, a broad stock market index, such as the S&P Composite, is used to represent or proxy the market.
Beta - Sensitivity of a stock’s return to the return on the market portfolio. 3

31. Estimation of Beta Problems Solutions Betas may vary over time.
The sample size may be inadequate.
Betas are influenced by changing financial leverage and business risk.
Solutions
Problems 1 and 2 can be moderated by more sophisticated statistical techniques.
Problem 3 can be lessened by adjusting for changes in business and financial risk.
Look at average beta estimates of comparable firms in the industry.

32. Stability of Beta
Most analysts argue that betas are generally stable for firms remaining in the same industry.
That’s not to say that a firm’s beta can’t change due to…
Changes in production
Changes in operating leverage
Deregulation
Changes in financial leverage

33. Using an Industry Beta
It is frequently argued that one can better estimate a firm’s beta by involving the whole industry.
If you believe that the operations of the firm are similar to the operations of the rest of the industry, you should use the industry beta.
If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firm’s beta.
Don’t forget about adjustments for financial leverage.

34. Determinants of Beta Business Risk Financial Risk
Cyclicality of Revenues
Operating Leverage
Financial Risk
Financial Leverage

35. Cyclicality of Revenues
Highly cyclical stocks have higher betas.
Empirical evidence suggests that retailers and automotive firms fluctuate with the business cycle.
Transportation firms and utilities are less dependent upon the business cycle.
Note that cyclicality is not the same as variability–stocks with high standard deviations need not have high betas.
Movie studios have revenues that are variable, depending upon whether they produce “hits” or “flops,” but their revenues may not especially dependent upon the business cycle.

36. Operating Leverage
The degree of operating leverage measures how sensitive a firm (or project) is to its fixed costs.
Operating leverage increases as fixed costs rise and variable costs fall.
Operating leverage magnifies the effect of cyclicality on beta.
The degree of operating leverage is given by:

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

38. Financial Leverage and Beta
Operating leverage refers to the sensitivity to the firm’s fixed costs of production.
Financial leverage is the sensitivity to a firm’s fixed costs of financing.
The relationship:
Financial leverage always increases the equity beta relative to the asset beta.

39. Example
Consider Grand Sport, Inc., which is currently all-equity financed 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.
Since the firm will remain in the same industry, its asset beta should remain 0.90.
However, 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

40. The Firm versus the Project
Any project’s cost of capital depends on the use to which the capital is being put–not the source.
Therefore, it depends on the risk of the project and not the risk of the firm.
This relation is consistent with the separation principle discussed in a prior chapter. 16

41. 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. Why?

42. Capital Budgeting & Project Risk
Suppose the Conglomerate Company has a cost of capital, based on the CAPM, of 17%. The risk-free rate is 4%, the market risk premium is 10%, and the firm’s beta is 1.3.
17% = 4% × 10%
This is a breakdown of the company’s investment projects:
1/3 Automotive Retailer b = 2.0
1/3 Computer Hard Drive Manufacturer 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

43. Capital Budgeting & Project Risk
SML
24%
Investments in hard drives or auto retailing should have higher discount rates.
Project IRR
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.

44. Using Peers to Find Cost of Equity
Two approaches
Find all equity peers
Delevering betas

45. Beta of Debt Possibilities Use debt ratio and beta of debt to delever
Use debt ratio and beta of debt to delever
Find bAsset from bEquity

46. Delevering Betas Data bEquity = 1.1 Equity = $2,000,000
Debt = $1,000,000
Assume bEquity = 0.1

47. Cost of Equity Capital Asset Pricing Model (CAPM) Peer Comparison
Dividend discount model approach
Bond yield plus risk premium approach

48. Cost of Debt

49. The Cost of Capital with Debt
The Weighted Average Cost of Capital is given by:
Because interest expense is deductable, we multiply the last term by (1 – tC).

50. Example: International Paper
First, we estimate the cost of equity and the cost of debt.
We estimate an equity beta to estimate the cost of equity.
We can often estimate the cost of debt by observing the return on the firm’s debt.
Second, we determine the WACC by weighting these two costs appropriately.

51. Example: International Paper
The industry average beta is 0.82, the risk free rate is 3%, and the market risk premium is 8.4%.
Thus, the cost of equity capital is:
= 3% ×8.4%
= ______

52. Example: International Paper
The yield on the company’s debt is 8%, and the firm has a 37% marginal tax rate.
The debt to value ratio is 32%
rWACC =
S + B S
× rS + B
× rB ×(1 – TC)
= 0.68 × 9.89% × 8% × (1 – 0.37)
= ______
This is International’s cost of capital. It should be used to discount any project where one believes that the project’s risk is equal to the risk of the firm as a whole and the project has the same leverage as the firm as a whole.

53. Cost of Debt Yield-to-maturity approach Debt-rating approach
Calculate firm’s yield-to-maturity on existing bonds
Debt-rating approach
Find the yield on comparably rated bonds for maturities that closely match existing debt
Calculate weighted average interest rate on long-term debt from notes in 10-K

54. Issues in Estimating Cost of Debt
Fixed vs. floating rate debt
Convertible debt
Nonrated debt
Leasing

55. Cost of Preferred Shares

56. Cost of Preferred Stock
Easiest component to estimate

57. Example
Firm has existing preferred stock outstanding with a price of $50 a share that pays $4 dividend and wishes to issue new preferred stock with a floatation cost of 2.5%. What is the cost to the firm for the new issue?

58. Has 10,000,000 common shares; price = $15/share; re = 15%.
Estimating WACC
An example....
Sherwin Co.
Total value = million
Has 10,000,000 common shares; price = $15/share; re = 15%.
Has 500,000 preferred shares, 8% coupon, price = $25/share, $12.5 million value.
Has $40 million long term debt, fixed rate notes with 8% coupon rate, but 7% YTM. Notes sell at premium and worth $49 million.