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Cost of Capital Session 7
Cost of CapitalSession 7
Cost of CapitalCost of Capital - The return the
firm’s investors could expect to earn if they invested in securities with comparable degrees of risk
Capital Structure - The firm’s mix of long term financing and equity financing
Cost of Capital The cost of capital represents the
overall cost of financing to the firm The cost of capital is normally the
relevant discount rate to use in analyzing an investment
The overall cost of capital is a weighted average of the various sources:– WACC = Weighted Average Cost of
Capital– WACC = After-tax cost x weights
Cost of Debt The cost of debt to the firm is the effective yield to
maturity (or interest rate) paid to its bondholders
Since interest is tax deductible to the firm, the actual cost of debt is less than the yield to maturity:– After-tax cost of debt = yield x (1 - tax rate)
The cost of debt should also be adjusted for flotation costs (associated with issuing new bonds)
with stock with debtEBIT 400,000 400,000- interest expense 0 (50,000)EBT 400,000 350,000- taxes (34%) (136,000) (119,000)EAT 264,000 231,000
Example: Tax effects of financing with debt
Now, suppose the firm pays $50,000 in dividends to the shareholders
with stock with debtEBIT 400,000 400,000- interest expense 0 (50,000)EBT 400,000 350,000- taxes (34%) (136,000) (119,000)EAT 264,000 231,000- dividends (50,000) 0Retained earnings 214,000 231,000
Example: Tax effects of financing with debt
After-tax cost Before-tax cost Taxof Debt of Debt
Savings
33,000 = 50,000 - 17,000OR33,000 = 50,000 ( 1 - .34)
Or, if we want to look at percentage costs:
-=
Cost of Debt
After-tax Before-tax Marginal % cost of % cost of x tax
Debt Debt rate
Kd = kd (1 - T)
.066 = .10 (1 - .34)
-= 1
Cost of Debt
Prescott Corporation issues a $1,000par, 20 year bond paying the market rate of 10%. Coupons are annual. The bond will sell for par since it pays the market rate, but flotation costs amount to $50 per bond.
What is the pre-tax and after-tax cost of debt for Prescott Corporation?
EXAMPLE: Cost of Debt
Pre-tax cost of debt:950 = 100(PVIFA 20, Kd) + 1000(PVIF 20, Kd)using a financial calculator:Kd = 10.61%
After-tax cost of debt:Kd = Kd (1 - T)Kd = .1061 (1 - .34)Kd = .07 = 7%
EXAMPLE: Cost of Debt
Cost of New Preferred Stock
Preferred stock:–has a fixed dividend (similar to debt)–has no maturity date–dividends are not tax deductible and
are expected to be perpetual or infinite
Cost of preferred stock = dividend price -
flotation cost
Cost of Preferred stock: Example
Baker Corporation has preferred stock that sells for $100 per share and pays an annual dividend of $10.50. If the flotation costs are $4 per share, what is the cost of new preferred stock?
10.94% .1094 4 - $100
$10.50 KP ===
Cost of Equity: Retained Earnings
Why is there a cost for retained earnings? Earnings can be reinvested or paid out as
dividends Investors could buy other securities, and
earn a return. Thus, there is an opportunity cost if
earnings are retained
Cost of Equity: Retained Earnings
Common stock equity is available through retained earnings (R/E) or by issuing new common stock:–Common equity = R/E + New
common stock
Cost of Equity: New Common Stock
The cost of new common stock is higher than the cost of retained earnings because of flotation costs–selling and distribution costs (such as sales commissions) for the new securities
Cost of EquityThere are a number of methods used
to determine the cost of equity We will focus on two
Dividend growth ModelCAPM
The Dividend Growth Model Approach
Estimating the cost of equity: the dividend growth model approachAccording to the constant growth (Gordon) model,
D1P0 =----------RE - g
Rearranging D1RE = ------- + g
P0
Example: Estimating the Dividend Growth Rate
PercentageYear Dividend Dollar Change Change
1990 $4.00 - -1991 4.40 $0.40 10.00%1992 4.75 0.35 7.951993 5.25 0.50 10.531994 5.65 0.40 7.62
Average Growth Rate(10.00 + 7.95 + 10.53 + 7.62)/4 = 9.025%
Dividend Growth Model
This model has drawbacks:
Some firms concentrate on growth and do not pay dividends at all, or only irregularly
Growth rates may also be hard to estimate Also this model doesn’t adjust for market risk
Therefore many financial managers prefer the capital asset pricing model (CAPM) - or security market line (SML) - approach for estimating the cost of equity
Capital Asset Pricing Model (CAPM)
)( fmf RRβRkj −+=
Cost ofcapital Risk-free
return
Average rate of returnon common stocks
(WIG)
Co-varianceof returns against
the portfolio(departure from the average)
B < 1, security is safer than WIG averageB > 1, security is riskier than WIG average
The Security Market Line (SML)Required rate
of returnPercent
0.5 1.0 1.5 2.0
SML = Rf + β (Km – Rf)
Beta (risk)
Market risk premium
20.0
18.0
16.0
14.0
12.0
10.0
8.0
5.5Rf
Finding the Required Return on Common Stock using the Capital
Asset Pricing ModelThe Capital Asset Pricing Model (CAPM) can be used to estimate the required return on individual stocks. The formula:
( )RKRK fmjfj −+= β
wherejK = Required return on stock j
fR = Risk-free rate of return (usually current rate on Treasury Bill).jβ = Beta coefficient for stock j represents risk of the stock
mK = Return in market as measured by some proxy portfolio (index)
Suppose that Baker has the following values:fR = 5.5%jβ = 1.0
mK = 12%
.
Finding the Required Return on Common Stock using the Capital
Asset Pricing ModelThen, using the CAPM we would get a required return of
( ) 12%5.5-121.05.5Kj =+=
.
CAPM/SML approach
Advantage: Evaluates risk, applicable to firms that don’t pay dividends
Disadvantage: Need to estimate–Beta– the risk premium (usually based on
past data, not future projections)–use an appropriate risk free rate of
interest
Estimation of Beta: Measuring Market Risk
Market Portfolio - Portfolio of all assets in the economy
In practice a broad stock market index, such as the WIG, is used to represent the market
Beta - sensitivity of a stock’s return to the return on the market portfolio
Estimation of Beta Theoretically, the calculation of beta is
straightforward: 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 (above) 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.
2)(),(
M
iM
M
Mi
σσ
RVarRRCovβ ==
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–Changes in product line–Changes in technology–Deregulation–Changes in financial leverage
What is the appropriate risk-free rate?
Use the yield on a long-term bond if you are analyzing cash flows from a long-term investment
For short-term investments, it is entirely appropriate to use the yield on short-term government securities
Use the nominal risk-free rate if you discount nominal cash flows and real risk-free rate if you discount real cash flows
Survey evidence: What do you use for the risk-free rate?
Corporations Financial Advisors90-day T-bill (4%) 90-day T-bill (10%)
3-7 year Treasuries (7%) 5-10 year Treasuries (10%)
10-year Treasuries (33%) 10-30 year Treasuries (30%)
20-year Treasuries (4%) 30-year Treasuries (40%)
10-30 year Treasuries (33%) N/A (10%)
10-years or 90-day; depends (4%)
N/A (15%)Source: Bruner et. al. (1998)
Weighted Average Cost of Capital (WACC)
WACC weights the cost of equity and the cost of debt by the percentage of each used in a firm’s capital structure
WACC=(E/ V) x RE + (D/ V) x RD x (1-TC)– (E/V)= Equity % of total value– (D/V)=Debt % of total value– (1-Tc)=After-tax % or reciprocal of corp tax
rate Tc. The after-tax rate must be considered because interest on corporate debt is deductible
WACC IllustrationABC Corp has 1.4 million shares common valued at $20 per share =$28 million. Debt has face value of $5 million and trades at 93% of face ($4.65 million) in the market. Total market value of both equity + debt thus =$32.65 million. Equity % = .8576 and Debt % = .1424
Risk free rate is 4%, risk premium=7% and ABC’s β=.74
Return on equity per SML : RE = 4% + (7% x .74)=9.18%
Tax rate is 40%
Current yield on market debt is 11%
WACC Illustration
WACC = (E/V) x RE + (D/V) x RD x (1-Tc)
= .8576 x .0918 + (.1424 x .11 x .60)
= .088126 or 8.81%
Final notes on WACC
WACC should be based on market rates and valuation, not on book values of debt or equity
Book values may not reflect the current marketplace
WACC will reflect what a firm needs to earn on a new investment. But the new investment should also reflect a risk level similar to the firm’s Beta used to calculate the firm’s RE. – In the case of ABC Co., the relatively low
WACC of 8.81% reflects ABC’s β=.74. A riskier investment should reflect a higher interest rate.
Final notes on WACC
The WACC is not constantIt changes in accordance with the
risk of the company and with the floatation costs of new capital
Marginal cost of capital and investment projects
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
Percent
10 15 19 5039Amount of capital ($ millions)
11.23%
70 85 95
Marginal cost of capital
Kmc
A
BC
D EF
GH
10.77%
10.41%
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