# Ch. 6 Estimating the Project Cost of Capital - Capital Budgeting and Investment Analysis

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```					            Ch. 6
Estimating the Project Cost of
Capital
Capital Budgeting and Investment
Analysis
By Alan Shapiro
Introduction
• The cost of capital for a project is the
shareholders of the firm for undertaking that
project
• Unless the investment generates sufficient
funds to repay suppliers of capital, the firm’s
value will suffer
Introduction cont.
• This rate must take account of both the time
value of money, measured by risk-free rate of
return and the riskiness of the project’s cash
flows
• A project whose risk characteristics differ
from the corporate or divisional norm will
have its own unique cost of capital
Risk and the cost of capital for a
project
• Each project has its own required return,
reflecting three basic elements
– the real or inflation adjusted risk-free interest rate
– An inflation premium approx. equal to the
amount of expected inflation
• The minimum or required return is the
project’s cost of capital and sometimes
referred to as a hurdle rate
Risk and the cost of capital for a
project cont.
• The cost of capital for a project depends on
the riskiness of the assets being financed not
on the identity of the firm undertaking the
project
Capital Asset Pricing Model (CAPM)
• The only risk that will be rewarded with a risk
premium will be the asset’s systematic or
unavoidable risk as measured by the asset’s
“Beta” coefficient
• CAPM is still the most widely used risk-based
cost of capital model
• The CAPM asserts that the risk premium for
any asset equals the asset’s beta multiplied by
CAPM cont.
• Cost of capital for project i = risk free interest

• Long term treasury bond rate = 5.5%
• Estimated beta of project = 1.15
• Diff. between return on market and risk free T
-bond rate=7%
• Calculate the required rate of return? = 13.6%
• Historical equity risk premium does not measure the
forward looking equity risk premium, that is, the risk
premium that equity investors expect to realize on
stocks bought today
• Dimson et al. (2002) survey historical risk premium
for 16 countries over the period 19000-2001 and find
that MRP falls within the range 3.5% to 5.3%
• Aswath Damodaran
• Pablo Fernandiz
Estimating the Project Beta
• Find a portfolio of firms that share similar risk
characteristics and use the firm’s beta to
proxy for the project beta
• Example: if a steel company decides to enter
the petroleum refining business, it will
estimate the average beta of a portfolio of
firms already in the industry and substitute
this value for Beta
• Financial risks will differ if they use different
amounts of debt financing
Financial structure and appropriate
discount rates
• Debt vs. Equity
• Unlevering is converting a levered equity beta
to its unlevered or all equity value

• D = market value of debt
• E = market value of equity
• K*=Rf+βa(Rm-Rf) is the all equity rate
Estimating Carborundum’s cost of capital (Pg. 151)
• Kennecott Copper is considering acquiring
Carborundum company
• Carbo’s equity beta is 1.16
• T-bond rate is 7.6%
• Market risk premium = 7.5%
• MV of Carbo’s equity= \$27 million and MV debt =
\$86.2 million
• If they decide to go ahead with the acquisition, they
will issue additional debt of \$100 mill followed by
immediately payment of \$140 mill div to Kennecott
Carborundum’s cost of capital (Pg. 151) cont.

• Calculate Carbo’s pre acquisition cost of
equity as 16.3%
• Unlevering Carbo’s equity beta
• Carbo’s unlevered or asset Beta = 1.00
• Carbo’s D/E would rise from 0.32 to 1.42
• Equity Beta = 1.71
• Cost of equity capital = 20.4%
The cost of capital for the firm
• A project to be acceptable to the firm’s
shareholders, it must generate a stream of
returns sufficient to compensate the suppliers
of capital in proportion to the amount and
cost of capital supplied by each. This minimum
return is the cost of capital to the firm
• Weighted average cost of capital (WACC) is
used to discount for project’s cash flows
ignoring financing charges such as interest and
dividend payments
The cost of equity capital
• It is the minimum rate of return necessary to
induce investors to buy or hold the firm’s
stock
• It is the rate used by shareholders to capitalize
their portion of corporate CFs
• Alternative: Dividend growth model
•   Estimated cost of equity capital=Dividend yield + Expected dividend growth rate
Example: Estimating HP cost of equity (Pg. 187)

• Risk free = 4.29%
• MRP = 5%
• Beta = 1.35
• Stock price= \$20.25
• D1 = \$0.36
• Div expected to grow from \$0.32 in 2003 to
\$0.50 in 2008, CAGR=9.34%
• Both CAPM and Dividend growth model
The cost of debt capital
• Yield to maturity (YTM)
• The interest rate on debt equals the nominal
risk-free rate plus risk premiums sufficient to
compensate debt holders for the possibility of
default; The higher the probability of default
is, the greater the risk premium will be
• Because interest is tax deductible, the true
cost of debt to the firm is the after tax interest
rate
Cost of Debt cont.
• The cost of debt capital equals Kd(1-T) where
Kd is the interest rate on new debt sold at par
and T is the firm’s marginal Tax rate
• For profitable firms like Coca-Cola and Merck,
the after-tax cost of debt is two-thirds of its
before tax cost
The cost of preferred stock
• Preferred stock is a hybrid of debt and equity
• Like debt, preferred stock carry fixed
commitment by the firm to make periodic
payments
• In case of Bankruptcy, they get their money
before shareholders but after debt holders
Calculating WACC
• The component costs of capital vary with the
firm’s capital structure
• As the fraction of debt in the capital structure
goes up, the returns to the different sources
of capital become riskier. This increase in risk
cause the cost of each capital component to
rise, offsetting the benefit of cheaper debt
WACC %
Proportion   Before Tax cost After Tax Cost   Weighted cost
Equity          0.60         20              20               12
Debt            0.35         14              8.4              2.94
Preferred stock 0.05         16              16               0.8
WACC =           15.74%

Debt should be substituted for equity until the
point at which the advantage of debt are just
offset by the effect of increasing risk

The less equity we put in, the higher the interest
rate charged
Marginal Weights
• The weights when calculating WACC must be
marginal weights that reflect the Target
capital structure
• Target capital structure is the proportions of
debt and equity the firm plans to use in the
future
• The market values of debt and equity, not the
book values should be used
Estimating Galaxy’s WACC (Pg.156)
•   Galaxy maintain capital structure of 70% debt, 10% preferred, and 20%
common stock
•   Debt
– \$0 to 7,000,000                       10%
– 7,000,001 to 10,500,000               11%
– Over 10,500,000                       14%
•   Preferred
– 0 to 250,000                          18%
– 250,001 to 375,000                    24%
– Over 375,000                          28%
•   Common stock
– O to 2,000,000                        28%
– 2,000,001 to 5,000,000                32%
– Over 5,000,000                        40%
Galaxy WACC Solution (pg.157)
Range %                   Debt %   Preferred %   Common %
0 - 2,500,000             10       18            28
2,500,001 - 3,750,000     10       24            28
3,750,001 – 10,000,000    10       28            28
10,000,001 – 15,000,000   11       28            32
15,000,001 – 25,000,000   14       28            32
25,000,001 and up         14       28            40

The first \$2,500,000 raised consists of
\$1,750,000 debt , \$250,000 in preferred
stock, and \$500,000 in common stocks with
costs of 10%, 18% and 28%
Galaxy WACC Solution (pg.157)
Range (\$)                 WACC
0 - 2,500,000             0.144
2,500,001 - 3,750,000     0.150
3,750,001 – 10,000,000    0.154
10,000,001 – 15,000,000   0.169
15,000,001 – 25,000,000   0.190
25,000,001 and up         0.206
Flotation costs
• Flotation costs include all legal, accounting,
printing, marketing, and other expenses
associated with the new security issue
• Internal funds are usually considered to be
less expensive than external funds
Misusing the WACC
• The required return or cost of capital for a
project depends on the assets being financed,
not on the identity of the company that
undertakes the project
• WACC can be used only to value assets the
firm already owns or new assets of similar risk
The cost of capital for a Division
• Divisional cost of capital may be valid in some
cases in which the use of a companywide cost
of capital would be inappropriate
• Three Stage Process:
– Identifying corporate proxies whose business
closely parallels the division’s operations
– The cost of capital must be estimated for each of
the proxy firms
– Averaging the resulting estimates of the individual
asset betas
• APV = NPV of project if all equity Financed +
NPV of financing side effects caused by
project acceptance
Arranging low cost financing (pg.163)
• 10 year, \$12.5 million loan at 8% interest
• Market interest rate is 15% and marginal tax
rate is 40%
• Annual after tax interest PMT
=0.6*0.08*\$12.5 million = \$600,000

• NPV = \$6,398,930
APV cont.
• Borrowing money at 8% while the market rate
is 15% is a good deal
• This analysis captures both tax benefits and
the interest subsidies
• Interest subsidy = difference between interest
PMT of loan at market rate and the interest
PMT at the current rate
• Interest subsidy =\$1,875,000-\$1,000,000
APV cont.
• Annual tax benefit associated with the loan is
0.4*0.08*\$12,500,000 = \$400,000 which is the
annual tax write off associated with the
interest payment

• Adding the two figures yield a total benefit of
\$6,398,930, the same as the NPV calculated
previously
Levered Equity method (LE)
• This approach discounts the levered cash
flows- that is, the project’s cash flows net of
debt payments- at the levered cost of equity
capital, Ke
• This cost of equity capital with leverage is
estimated using the levered equity beta and is
the same one that appears in the WACC
LE cont.
• The CFs discounted with the LE method are
the unlevered CFs used in the WACC and APV
methods less the after-tax debt charges
associated with the project’s financing
Giant manufacturing (pg. 165)
• Invest \$30 million in new solar power source
• Annual FCF of \$4,880,000 in perpetuity
• K*=16%

• Suppose that the project can support a
permanent addition to debt equal to \$6.5
million. If interest rate on debt is 10% and Tax
is 30%
APV method
• In this case the only financing side effect is the
tax savings provided by the tax deductibility of
interest payments
• 0.30 * 0.1 * \$6,500,000 = \$195,000

• 30 Million + 2.5 Million = 32.5 Million
• Using market values, the debt ratio for this
project is 6.5/32.5 or 20%
WACC method
LE method
• We need to combine the levered cost of
equity which we have already calculated to be
17.05% with cash flows to equity
• Annual after tax interest expense
=0.7*0.1*\$6.5 million = \$455,000
• Subtracting this from\$4.888 million in FCF
yield free cash flow to equity of \$4,433,000
• Giant’s initial equity investment \$23.5 million
(\$30 million-\$6.5 million)
LE method cont.

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 views: 29 posted: 9/24/2013 language: pages: 38