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FIN 468: Intermediate Corporate Finance. Topic 8–Cost of Capital Larry Schrenk, Instructor. Topics. Excel: Linear Regression Project Review Cost of Capital Equity Debt Preferred Shares. Excel: Linear Regression. Excel Features: Linear Regression. - PowerPoint PPT Presentation
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FIN 468: Intermediate Corporate Finance
Topic 8–Cost of Capital
Larry Schrenk, Instructor
Topics
Excel: Linear Regression Project Review Cost of Capital
Equity Debt Preferred Shares
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’ drop-down 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.
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.
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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
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Cost of Capital
Rate of return that the suppliers of capital – bondholders and stockholders require as compensation for their contributions of capital
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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
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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
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Target Weights
Assume current capital structure is correct Estimate capital structure based on historical
trends Use average of comparable companies
capital structure
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Choosing the Right Discount Rate
NN
rCF
rCF
rCF
rCF
CFNPV)(
...)()()(
1111 3
32
210
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.
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.
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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. 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.
2. 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.
The Cost of Equity Capital
From the firm’s perspective, the expected return is the Cost of Equity Capital: ( )i rf i M rfE r r β E r r
• To estimate a firm’s cost of equity capital, we need to know three things:
1. Risk Free Rate rrf
M rfE r r2. Risk Premium
iβ3. Beta
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?
E = 5% + 2.5 × 10%ir __ ___E _ir
( )i rf i M rfE r r β E r r
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 2.5 $130 30% $0
C 2.5 $110 10% -$15.38
Using the Security Market Line
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.
Pro
ject
IRR
Firm’s risk (beta)
SML
5%
Good project
Bad project
30%
2.5
A
B
C
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.
Estimation of Beta• 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.
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
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.
Determinants of Beta Business Risk
Cyclicality of Revenues Operating Leverage
Financial Risk Financial Leverage
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.
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:
EBIT SalesDOL
EBIT Sales
Operating Leverage
Sales
$
Fixed costs
Total costs
EBIT
Sales
Operating leverage increases as fixed costs rise and variable costs fall.
Fixed costs
Total costs
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.
b b b asset debt equity
Debt EquityDebt Equity Debt Equity
ExampleConsider 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
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.
Capital Budgeting & Project Risk
A firm that uses one discount rate for all projects may over time increase the risk of the firm while decreasing its value. Why?
Pro
ject
IRR
Firm’s risk (beta)
SML
rf
bFIRM
Incorrectly rejected positive NPV projects
Incorrectly accepted negative NPV projects
Hurdle rate
)( FMFIRMF RRβR
The SML can tell us why:
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 = 2.01/3 Computer Hard Drive Manufacturer b = 1.31/3 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?
Capital Budgeting & Project Risk
Capital Budgeting & Project RiskP
roje
ct IR
R
Project’s risk (b)
17%
1.3 2.00.6r = 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.
10%
24% Investments in hard drives or auto retailing should have higher discount rates.
SML
Using Peers to Find Cost of Equity Two approaches
Find all equity peers
Delevering betas
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Beta of Debt
Possibilities 0 0.1-0.3
Use debt ratio and beta of debt to delever Find bAsset from bEquity
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Delevering Betas
Data bEquity = 1.1 Equity = $2,000,000 Debt = $1,000,000 Assume bEquity = 0.1
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1 20.1 1.1 0.0333 0.7333 7.6663 3assetb
b b b asset debt equity
Debt EquityDebt Equity Debt Equity
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Cost of Equity
Capital Asset Pricing Model (CAPM) Peer Comparison Dividend discount model approach Bond yield plus risk premium
approach
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).
1WACC debt c equityDebt Equityr r r
Debt Equity Debt Equityt
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.
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% + 0.82×8.4%
= ______
( )i rf i M rfE r r β E r r
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%
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.
= 0.68 × 9.89% + 0.32 × 8% × (1 – 0.37) = ______
rWACC = S + BS × rS + S + B
B × rB ×(1 – TC)
Cost of Debt
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
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Issues in Estimating Cost of Debt
Fixed vs. floating rate debt Convertible debt Nonrated debt Leasing
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Cost of Preferred Stock
Easiest component to estimate
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p
pp
p
pp P
Dr
rD
P
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?
57
%21.875.4800.4
025.0100.5000.4
pr
Estimating WACC
pde rPDE
PrPDE
DrPDE
EWACC
%73.12%85.2115.12%7
5.21149%15
5.211150
WACC
An example....Sherwin Co.Total value = 211.5 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.
