Topic 8 –Cost of Capital
Larry Schrenk, Instructor
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 Excel: Linear Regression
 Project Review
 Cost of Capital

Equity

Debt

Preferred Shares

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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).

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

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

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

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’.

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

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

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

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.

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

18
 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
 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
 Assume current capital structure is correct
 Estimate capital structure based on historical trends
 Use average of comparable companies capital structure

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The numerator focuses on project cash flows.
NPV

CF
0

CF
1
( 1
 r )

CF
2
( 1
 r )
2

CF
3
( 1
 r )
3

...

( 1
CF
 r
N
)
N
The denominator is the discount rate.
Reflect the opportunity costs of the firm’s investors.
The denominator should:
Reflect the project’s risk.
Be derived from market data.

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 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.

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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.

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Finding the Right Discount Rate
1.
2.
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.


From the firm’s perspective, the expected return is the Cost of Equity Capital:
  i
 r rf
 i
(
 
M
 r rf
)
• To estimate a firm’s cost of equity capital, we need to know three things:
1. Risk Free Rate
2. Risk Premium r rf
 
M
 r rf
3. Beta
β i




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?
  i
 r rf
 i
(
 
M
E
  i
E
= 5% + 2.5 × 10%
  i

__ ___
 r rf
)

B
C
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
2.5
2.5
$130
$110
30%
10%
$0
-$15.38

SML
Good project
A
30% B
C
Bad project
5%
Firm’s risk (beta)
2.5
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.

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.

• Problems
1. Betas may vary over time.
2. The sample size may be inadequate.
3. 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.



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





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.

 Business Risk

Cyclicality of Revenues

Operating Leverage
 Financial Risk

Financial Leverage

 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.





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:
DOL


EBIT Sales
EBIT

Sales

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




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: b asset

Debt
Debt

Equity b debt

Equity
Debt

Equity b equity
• Financial leverage always increases the equity beta relative to the asset beta.

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: b
Asset
= 0.90 =
1
1 + 1
× b
Equity b
Equity
= 2 × 0.90 = 1.80

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.

SML
The SML can tell us why:
Incorrectly accepted negative NPV projects
Hurdle rate
R
F
 β
FIRM
( R
M

R
F
) r f
Incorrectly rejected positive NPV projects
Firm’s risk (beta) b
FIRM
A firm that uses one discount rate for all projects may over time increase the risk of the firm while decreasing its value. Why?

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% + 1.3 × 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?

SML
24%
17%
10%
Investments in hard drives or auto retailing should have higher discount rates.
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.

 Two approaches

Find all equity peers

Delevering betas
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 Possibilities

0

0.1-0.3
 Use debt ratio and beta of debt to delever

Find b
Asset from b
Equity
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 Data
 b
Equity
= 1.1

Equity = $2,000,000


Debt = $1,000,000
Assume b
Equity
= 0.1
b asset

Debt
Debt

Equity b debt

Equity
Debt

Equity b equity b  asset
1
3
0.1

2
3
 
0.7333

7.666
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Cost of Equity
 Capital Asset Pricing Model (CAPM)
 Peer Comparison
 Dividend discount model approach
 Bond yield plus risk premium approach

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 The Weighted Average Cost of Capital is given by: r
WACC

Debt
Debt

Equity r debt

1
 t c
 
Equity
Debt

Equity r equity
• Because interest expense is deductable, we multiply the last term by (1 – t
C
).

 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.

 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:
  i
 r rf
 i
(
 
M
 r rf
)
= 3% + 0.82
× 8.4%
=
______


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% r
WACC
=
S
S + B
× r
S
+
S
B
+ B
× r
B
× (1 – T
C
)
= 0.68 × 9.89% + 0.32 × 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.

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 Yield-to-maturity 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
 Fixed vs. floating rate debt
 Convertible debt
 Nonrated debt
 Leasing

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 Easiest component to estimate
P p

D p r p
 r p

D p
P p

57
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?
r p

50 .
00
4 .
00

1

0 .
025


4 .
00
48 .
75

8 .
21 %

Estimating WACC
WACC

E

E
D

P r e

E

D
D

P r d

E

P
D

P  r p
An example....
Sherwin Co.
Total value =
211.5 million
WACC

Has 10,000,000 common shares; price = $15/share; r e
= 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.
150
211 .
5
15 %

49
211 .
5
7 %

12 .
5
211 .
5
8 %

12 .
73 %