CHAPTER 10
Determining the Cost of Capital
Topics in Chapter
- Cost of Capital Components
 Debt
 Preferred
 Common Equity
- WACC
- Flotation costs
What types of long-term capital do firms use?
 Long-term debt
 Preferred stock
 Common equity
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What is the Cost of Capital?
 The required rate of return on funds from investors
 Also called “hurdle” rate because this is the minimum acceptable
rate of return
Note: AP, accruals, and deferred taxes are not sources of funding that
come from investors  not included in the calculation of the cost of
capital.
Therefore, we adjust for AP, accruals & deferred taxes when calculating
the cash flows of a project, but not when calculating the cost of
capital.
Also note:
Other notes:
 A given firm may have more than one provider of capital, each
with its own required return
 In addition to determining the weights in the calculation of the
WACC, we must determine the individual costs of capital
 To do this, we simply solve the valuation equations for the
required rates of return
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The Cost of Debt
 Recall that the formula for valuing bonds is:
1  1
N

1  rd 

VB  Pmt 
rd



FV

  1  r N
d


 Note that rd is not appropriate cost of debt to use in calculating the
WACC, instead we should use the after-tax cost of debt.
Ex: A 15-year, 12% semiannual bond sells for $1,153.72. What’s rd?
Since interest is tax deductible, the after tax (AT) cost of debt is:
rd AT = rd BT(1 - T)
Use nominal rate.
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The Cost of Preferred Equity
 As with debt, calculate the cost of preferred equity by solving the
valuation equation for rp:
rps = D / Vps
 Note: Preferred dividends are not tax-deductible, so there is no tax
adjustment for the cost of preferred equity
Is preferred stock more or less risky to investors than debt?
 More risky; company not required to pay preferred dividend.
However, firms have an incentive to pay preferred dividend.
Otherwise, (1) cannot pay common dividend, (2) difficult to raise
additional funds.
Why is yield on preferred lower than rd?
 Corporations own most preferred stock, because 70% of preferred
dividends are nontaxable to corporations.
 Therefore, preferred often has a lower B-T yield than the B-T yield
on debt.
 The A-T yield to investors and A-T cost to the issuer are higher on
preferred than on debt, which is consistent with the higher risk of
preferred.
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The Cost of Common Equity
What are the two ways that companies can raise common equity?
 Directly, by issuing new shares of common stock.
 Indirectly, by reinvesting earnings that are not paid out as
dividends (i.e., retaining earnings).
Why is there a cost for reinvested earnings?
 Earnings can be reinvested or paid out as dividends.
 Investors could buy other securities, earn a return.
 Thus, there is an opportunity cost if earnings are reinvested.
Opportunity cost: The return stockholders could earn on
alternative investments of equal risk.
 They could buy similar stocks and earn rs, or company could
repurchase its own stock and earn rs. So, rs, is the cost of
reinvested earnings and it is the cost of equity.
Three ways to determine the cost of equity, rs:
1. CAPM: rs = rrf + (rm - rrf)β
rs = rrf + (RPM)β
2. Discounted Cash Flow (DCF) approach: rs = D1/P0 + g
rs = D0(1+g) + g
P0
3. Own-Bond-Yield-Plus-Risk-Premium Approach
rs = bond yield + bond risk premium
rs = rd + bond RP
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Method 1:
Ex: CAPM Cost of Equity: rRF = 7%, RPM = 6%, b = 1.2.
Issues in Using CAPM
 Most analysts use the rate on a long-term (10 to 20 years)
government bond as an estimate of rRF.
 Most analysts use a rate of 5% to 6.5% for the market risk
premium (RPM)
 Estimates of beta vary, and estimates are “noisy” (they have a wide
confidence interval).
Method 2:
DCF Cost of Equity, rs: D0 = $4.19; P0 = $50; g = 5%.
Estimating the Growth Rate
 Use the historical growth rate if you believe the future will be like
the past.
 Obtain analysts’ estimates: Value Line, Zacks, Yahoo!Finance.
 Use the earnings retention model, illustrated on next page.
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Earnings Retention Model
 Suppose the company has been earning 15% on equity (ROE =
15%) and retaining 35% (dividend payout = 65%), and this situation
is expected to continue.
What’s the expected future g?
 Growth from earnings retention model:
g = (Retention rate)(ROE)
g = (1 - payout rate)(ROE)
g = (1 – 0.65)(15%) = 5.25%.
Method 3:
The Own-Bond-Yield-Plus-Risk-Premium Method: rd = 10%, RP = 4%.
rs
= rd + RP
What’s a reasonable final estimate of rs?
Method
Estimate
CAPM
14.2%
DCF
13.8%
rd + RP
14.0%
Average
14.0%
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Estimating Weights for the WACC
 The weights are the percentages of the firm that will be financed by
each component.
 If possible, always use the target weights for the percentages of the
firm that will be financed with the various types of capital.
Book-value Weights
 Get from firm’s balance sheet, since it lists the total amount of
long-term debt, preferred equity, and common equity
 Determine the proportion that each source of capital is of the total
capital weights
Market-value Weights
 The market recalculates the values of each type of capital on a
continuous basis.
 Calculate the total market (price times quantity) of each type of
capital
Note: market-values is always preferred over book-value
 book-values represent the historical amount of securities sold,
whereas market values represent the current amount of securities
outstanding
Also note: If you don’t know the market value of debt, then it is usually
reasonable to use the book values of debt, especially if the debt is shortterm.
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Ex: Suppose the stock price is $50, there are 3 million shares of stock,
the firm has $25 million of preferred stock, and $75 million of debt.
Vce =
Vps =
Vd =
Total value =
wce =
wps =
wd =
If rd=10% and the tax rate is 40%, rps is 9% and rs is 14%, what’s the
WACC?
WACC = wdrd(1 - T) + wpsrps + wcers
What factors influence a company’s WACC?
 Market conditions, especially interest rates and tax rates.
 The firm’s capital structure and dividend policy.
 The firm’s investment policy. Firms with riskier projects generally
have a higher WACC.
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Is the firm’s WACC correct for each of its divisions?
 NO! The composite WACC reflects the risk of an average project
undertaken by the firm.
 Different divisions may have different risks. The division’s
WACC should be adjusted to reflect the division’s risk and capital
structure.
Flotation Costs
 When a company sells securities to the public, it must use the
services of an investment banker
 Services provided by the investment banker:
-Setting the price of the issue, and
-Selling the issue to the public
 The cost of these services are referred to as “flotation costs,” and
they must be accounted for in the WACC
 Generally, we do this by reducing the proceeds from the issue by
the amount of the flotation costs, and recalculating the cost of
capital
The Cost of Debt with Flotation Costs
Simply subtract the flotation costs (F) from the price of the bonds, and
calculate the cost of debt as usual:
VB
1 

 F   Pmt 


1
1  rd N
rd

FV

  1  r N
d


 Note that we still must adjust this calculation for taxes
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The Cost of Preferred with Flotation Costs
 Simply subtract the flotation costs (F) from the price of preferred,
and calculate the cost of preferred as usual:
rP 
D
VP  F 
The Cost of Common Equity with Flotation Costs
 Simply subtract the flotation costs (F) from the price of common,
and calculate the cost of common as usual:
rS 
D0 1  g 
D1
g
g
VS  F 
VS  F 
A Note on Flotation Costs
 The amount of flotation costs are generally quite low for debt and
preferred stock (often 1% or less of the face value)
 For common stock, flotation costs can be as high as 25% for small
issues, for larger issues they will be much lower
 Note that flotation costs will always be given, but they may be
given as a dollar amount, or as a percentage of the selling price
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The Cost of Retained Earnings
 The firm may choose to finance new projects using only internally
generated funds (retained earnings)
 These funds are not free because they belong to the common
shareholders (i.e., there is an opportunity cost)
 Therefore, the cost of retained earnings is exactly the same as the
cost of new common equity, except that there are no flotation
costs:
k RE 
D 0 1  g 
D1
g 
g
VCS
VCS
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