Download Risk, Cost of Capital, and Capital Budgeting

Session 4
Cost of Capital
FIN 625: Corporate Finance
Learning Objectives
LO 1: Estimate the cost of equity
 LO 2: Explain the impact of beta in the
firm’s cost of equity capital
 LO 3: Estimate the cost of debt
 LO 4: Calculate a firm’s weighted average
cost of capital (RWACC)
 LO 5: Estimate RWACC by comparable firms

Topic Outline
1. The Cost of Equity Capital
2. Estimation of Beta
3. The Cost of Debt Capital
4. The Weighted Average Cost of Capital
(RWACC)
5. Firm Versus Project Cost of Capital
6. Estimate RWACC Using Comparable Firms
1. The Cost of Equity Capital
Firm with
excess cash
Pay cash dividend
Shareholder
invests in
financial
asset
A firm with excess cash can either pay a
dividend or make a capital investment
Invest in project
Shareholder’s
Terminal
Value
Because stockholders can reinvest the dividend in risky financial assets, the
expected return on a capital-budgeting project should be at least as great as the
expected return on a financial asset of comparable risk.
The Cost of Equity Capital




From the firm’s perspective, the expected
return is the Cost of Equity Capital:
R i  RF  βi ( R M  RF )
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? ( R  30% )
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects. Each costs $100
and lasts one year.
Project
Project b
A
IRR
NPV at
30%
2.5
Project’s
Estimated Cash
Flows Next
Year
$150
50%
$15.38
B
2.5
$130
30%
0
C
2.5
$110
10%
-$15.38
IRR
Project
Using the SML
Good
A
project
30%
B
5%
C
SML
Bad project
Firm’s risk (beta)
2.5
An all-equity firm should accept projects whose IRRs are
equal to or higher than the cost of equity capital and reject
projects whose IRRs are lower than the cost of equity.
Estimation of Cost of Equity

To estimate a firm’s cost of equity capital,
we need to know three things:
1. The risk-free rate, RF
2. The market risk premium, R M
3. The company beta,
 RF
Cov ( Ri , RM )  i , M
βi 
 2
Var ( RM )
σM
The Risk-free Rate




The government-issued securities are
generally used as proxies for the riskfree asset.
In practice we should match the maturity
of the securities with the expected life of
the firm/project.
For example, if a project is expected to
last for one year, then the interest rate
on Treasury bills may be a good proxy
for the risk-free rate.
If a firm is expected to last for 30 years,
then using the yield-to-maturity (YTM) of
a 30-year government bond may be
more appropriate.
The Market Risk Premium



We may use either historical average or
the Dividend Discount Model (DDM) to
estimate this number. We focus on the
former in this course.
Market portfolio - portfolio of all assets in
the economy. In practice, a broad stock
market index, such as the S&P 500 Index,
is used to represent the market.
The historical average risk premium of the
market portfolio is also changing over
time.
2. Estimation of Beta

Beta - Sensitivity of a stock’s return to the
return on the market portfolio.
Cov ( Ri , RM ) σ i , M
βi 
 2
Var ( RM )
σM

Determinants of beta:

Business Risk




Cyclicality of Revenues
Operating leverage
Financial Risk (financial leverage or debt)
Business risk is similar for firms in the
same industry. But financial leverage can
vary even for firms within the same
industry.
Cyclicality of Revenues

Highly cyclical stocks have higher betas.



Automotive firms fluctuate with the business cycle.
Utilities are relatively less dependent upon the
business cycle.
Cyclicality is not the same as variability—
stocks with high standard deviations need not
have high betas.

Example: Movie industry
Operating Leverage

Operating leverage refers to a firm’s fixed
costs of production.

Operating leverage measures how sensitive
a firm’s (or a project’s) profit is to its
revenue.
Operating leverage increases as fixed costs
rise and variable costs fall.
Operating leverage magnifies the effect of
the cyclicality of revenues on beta.


Using Industry Beta



Because relying on individual firms often results
in larger estimation error than relying on a
portfolio of firms, and that firms in the same
industry have similar business risk.
But business risk is not the only factor that
influences beta.
We should also adjust for the effect of financial
leverage (Section 5).
3. The Cost of Debt Capital

Estimate the cost of debt

Bank debt: interest rate

Publicly traded bonds:

Calculate the yield to maturity (YTM)

Using CAPM (similar to estimating the cost of
equity)
Example
Apple Republic has a bond issue outstanding with
10 years to maturity. The bond is quoted at
90% of the face value. The issue makes
semiannual coupon payments with an annual
coupon rate of 7%. What is the cost of debt for
Apple Republic?
Example
The cost of debt for Apple Republic is the yield-tomaturity (YTM) of the outstanding issue.
By definition, YTM solves the following equation:
Bond price = PV(coupon payments) + PV(par-value at
maturity)
Par-value=$1,000 Bond price=$900
Coupon payments = __$35__
$900 = PV(_$35_ annuity for _20_ periods discounted
at YTM/2)+PV($1,000 at the end of _20_ periods
discounted at YTM/2).
Using a financial calculator (or EXCEL),YTM/2=4.25%.
So YTM=8.5%.
Before and After-Tax Cost of Debt




Interest payment can reduce the tax
liability of a firm.
The after-tax cost of debt takes this into
consideration.
The after-tax cost of debt = (1Tc)*before-tax cost of debt, where Tc is
the marginal corporate tax rate.
In the above example, assume the tax
rate is 35%, then the after-tax cost of
debt = (1-35%)*8.5% = 5.53%.
4. Weighted Average Cost of Capital (RWACC)

The Weighted Average Cost of Capital is given
by:
rWACC =
Equity
Debt
× rEquity +
× rDebt ×(1 – TC)
Equity + Debt
Equity + Debt
S
B
rWACC =
× rS +
× rB ×(1 – TC)
S+B
S+B
• Because interest expense is tax-deductible, we
multiply the last term by (1 – TC).
Debt-Value Ratio




Important: The debt-to-value ratio B/(S+B) is
market-value based.
In practice, the market value of debt is
generally very close to its book value.
But we should never use the equity on the
balance sheet as its market value. We must
rely on stock price to calculate this amount.
We should also use the target or long-run debt
ratio of the firm, which may be different from
the firm’s current debt ratio.
Optimal Capital Structure and RWACC
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:
rS = RF + bi × ( RM – RF)
= 3% + 0.82×8.4%
= 9.89%
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%.
Therefore,
S
B
rWACC =
× rS +
× rB ×(1 – TC)
S+B
S+B
= 0.68 × 9.89% + 0.32 × 8% × (1 – 0.37)
= 8.34%
Example: Estimate Microsoft’s RWACC

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Go to finance.yahoo.com, find Microsoft.
Equity beta = _1.29__
Go to
https://www.federalreserve.gov/releases/h
15/, find the yield of 30-year Treasury
bonds (Microsoft is expected to last for a
long time), which is _3.10%_.
Suppose we use the historical average
market risk premium of 7%.
Therefore, rS = RF + bi × ( RM – RF) =
12.13%
Example: Estimate Microsoft’s RWACC

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Go to www.sec.gov, search company filings, enter
“MSFT”. From the consolidated balance sheet,
find the total debt is _$142.152 Billion_.
From the “Notes to Consolidated Financial
Statements”, find the (weighted average) interest
rate on the outstanding debt is 3% (assumed,
calculation involves around 40 different issues
with their respective yields).
According to IRS tax rate schedule, the marginal
tax rate on Microsoft’s taxable income is 35%.
The market capitalization of Microsoft (from
finance.yahoo.com) is _$481.84 Billion_.
The debt/value ratio is B/VL= 22.78%. The
equity/value ratio is S/VL = 1- B/VL = 77.22%.
Example: Estimate Microsoft’s RWACC
S
B
rWACC =
× rS +
× rB ×(1 – TC)
S+B
S+B
= 77.22%*12.13% + 22.78%*3%*(1-35%)
= 9.811%
5. Firm Versus Project Cost of Capital



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
company.
This suggests that different divisions
of the same firm may have different
costs of capital.
6. Estimate RWACC Using Comparable Firms



If equity beta is not directly estimable, we
need to use comparable firms to estimate a
firm’s cost of equity.
Recall that a firm’s equity faces both business
risk and financial risk.
The equity beta that depends only on the
business risk is called asset beta (basset or b0).
This is the equity beta by assuming there is no
debt in a firm’s capital structure. Therefore we
also call it the unlevered beta. The
corresponding expected rate of return is R0.
Estimate RWACC Using Comparable Firms



Theoretically speaking, b0 is the same for all
the firms in the same industry.
Therefore, we can use comparable firms to
estimate b0. Knowing b0 also allows us to
estimate the cost of (levered) equity.
The relationship between the betas of the
firm’s debt, equity, and assets is given by:
bAsset =
Debt
Equity
× bDebt +
× bEquity
Debt + Equity
Debt + Equity
• Financial leverage always increases the equity beta relative
to the asset beta.
Estimate RWACC Using Comparable Firms
The above equation is based on viewing asset as
a portfolio consisting of debt and equity. This
comes from the balance sheet identity (marketvalue based):
Total Asset = Total Liability(Debt) + Total Equity
 Portfolio beta is a weighted average of the betas
of the securities within the portfolio (Session 1).
 Some other formulas such as
β𝑆
β𝑎𝑠𝑠𝑒𝑡 =
(what you can find from

1+ 1−𝑇𝐶 𝐵/𝑆
Investopedia) is only an approximate
formula.
Example
Consider Grand Sport, Inc., which is currently allequity 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 at 0.90.
Assuming a zero beta for its debt, its equity beta
would become _2*0.90=1.80_.
Using Comparables to Estimate Equity Beta




1. Find the comparable firms whose (levered)
equity betas (bEquity) are available;
2. “Unlever” to estimate asset beta (bAsset)
based on the above equation;
3. Do this for each comparable firm, so obtain
multiple estimates of bAsset . Then take an
average, bAsset .
4. “Relever” based on bAsset and the debt ratio
of our current project (you may need to use
the target debt ratio or debt capacity).
Example



Conglomerate Products has three operating
divisions: the food, electronics, and chemicals.
Conglomerate's CFO wants to estimate the cost
of capital for each division, to be used as an input
in the capital budgeting process.
Currently, Conglomerate is financed 40% by debt.
The company's debt has a beta of about 0.2. The
current interest rate is 7% and the expected
return on the market is 15%. Assume the debt
capacity of the food, electronics, and chemicals
section is 40%, 30%, and 60%, respectively.
Assume corporate tax rate is 40%.
Example



The following three competitors have been
identified as having investments similar to those
of Conglomerate's three divisions:
Company
Equity beta
B/(B+S)
United Foods
0.8
0.3
General Electronics
1.6
0.2
Associated Chemicals
1.2
0.4
The debt of these comparable firms are riskfree.
Estimate the weighted average cost of capital for
each of Conglomerate’s three divisions.
Example



Rwacc (Food Division) = _10.1%_
Rwacc (Electronics Division) = _16.21%_
Rwacc (Chemical Division) = _10.70%_
Readings

Chapter 12