FINS5514: Capital Budgeting and
Financing Decisions
Lecture 5: Cost of Capital
Topics Covered Today
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• Different Capital Sources
• Cost of Capital
– The Cost of Capital: Some Preliminaries
– The Cost of Equity
– The Costs of Debt and Preferred Stock
– The Weighted Average Cost of Capital
– Divisional and Project Costs of Capital
– Floatation costs
2
3Different Capital Sources
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• Common shares
• Straight debt
• Hybrids:
– Preference shares
– Convertible debt
4Common Stock & Straight Debt
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• Common shares are characterised by:
– Residual claim on firm’s assets
– Dividends are not tax deductible
– Cannot force liquidation if they receive no return
– Ranking last in liquidation
– Entails voting rights for board of directors
• Straight Debt is characterised by:
– Fixed claim on the firm’s assets
– Tax deductibility of interest payments
– Can force liquidation if firm fails to meet obligations
– Ranking “up the top” in liquidation
– Entails no voting rights for board of directors
5Hybrids – Preference Shares
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• Hybrid securities are a mix of the characteristics of debt
and equity
• Preference shares are characterised by:
– Fixed dividends => increase financial risk
– Floating rate preferred shares - dividends linked to an
underlying security, such as a T-note
– May be redeemable at a fixed date
– Not tax deductible (in Australia)
– Cannot force liquidation if return not received
– But may be cumulative
• Precludes payment of common equity dividends
6Hybrids – Preference Shares
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– Ranking below straight debt but above common equity
in liquidation
– No voting rights for board of directors
• Preference shares may also be convertible into equity
• Preference shares have:
– Tax disadvantage relative to debt
– Flexibility disadvantage relative to equity
• Preferred stock riskier than debt as:
– Rank lower than debt in liquidation
– Less likely to receive payments during “hard times”
7Hybrids – Convertible Debt
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• A debt security with a fixed rate of interest that is
convertible to ordinary shares within or at a
specified time
• Alternatively, it is debt with an inseparable option
entitling the debtholder to convert it into a
specified number of shares at specified conversion
dates
• If the option is not exercised, the debt is repaid at
maturity
• If it is exercised, the debt obligation is extinguished
and replaced with equity
8Why Cost of Capital Is Important
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• We know that the return earned on assets depends on
the risk of those assets
• The return to an investor is the same as the cost to the
company
• Our cost of capital provides us with an indication of how
the market views the risk of our assets
• Knowing our cost of capital can also help us determine
our required return for capital budgeting projects
9Required Return
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• The required return is the same as the appropriate
discount rate and is based on the risk of the cash flows
• We need to know the required return for an investment
before we can compute the NPV and make a decision
about whether or not to take the investment
• We need to earn at least the required return to
compensate our investors for the financing they have
provided
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Cost of Equity
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• The cost of equity is the return required by equity
investors given the risk of the cash flows from the firm
– Business risk
– Financial risk
• There are two major methods for determining the cost
of equity
– Dividend growth model
– SML or CAPM
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The Dividend Growth Model Approach
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• If shares are expected to grow at a constant rate, then the
price can be expressed as:
• where
• D0 is the dividend just paid
• D1 is next projected dividend
• RE is the required return and
• the g is the constant growth rate of dividends
=
× 1 +

−
=


−
• This can be re-written as:

=


+
• This implies that investors will expect to receive the
dividend yield plus some capital gains in return for their
investment
7
13
Dividend Growth Model Example
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• Suppose that your company is expected to pay a
dividend of $1.50 per share next year. There has been a
steady growth in dividends of 5.1% per year and the
market expects that to continue. The current price is
$25. What is the cost of equity?

=
1.50
25
+ .051 = .111 = 11.1%
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Example: Estimating the Dividend Growth Rate
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• Use the historical average
– Year Dividend Percent Change
– 2000 1.23 -
– 2001 1.30
– 2002 1.36
– 2003 1.43
– 2004 1.50
• Use analyst’s forecasts
– Often multiple forecasts are taken and averaged
(1.30 – 1.23) / 1.23 = 5.7%
(1.36 – 1.30) / 1.30 = 4.6%
(1.43 – 1.36) / 1.36 = 5.1%
(1.50 – 1.43) / 1.43 = 4.9%
Average = (5.7 + 4.6 + 5.1 + 4.9) / 4 = 5.1%
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Advantages and Disadvantages of Dividend
Growth Model
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• Advantage – easy to understand and use
• Disadvantages
– Only applicable to companies currently paying dividends
– Not applicable if dividends aren’t growing at a reasonably
constant rate
– Extremely sensitive to the estimated growth rate – an
increase in g of 1% increases the cost of equity by 1%
– Does not explicitly consider risk
• Sharpe won the Nobel prize in Economics in 1990
along with Harry Markowitz and Merton Miller
Sharpe’s contribution
committee:“Developed
according to Nobel
a general theory for the
pricing of financial assets”
12
CAPM: By Sharpe and Lintner
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Cost of equity capital in practice
13
Source: J. R. Graham and C. R. Harvey, “The Theory and Practice of Corporate Finance:
Evidence from the Field,” Journal of Financial Economics 60 (2001): 187–243.
From Survey of CFOs: what method do you use?
Capital asset pricing model (CAPM)
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• Total risk of investing in the firm is the sum of systematic
and unsystematic risk
• Unsystematic risk
– Applies to a single asset or a small group of assets
– For example, a strike by workers at a single firm
• Systematic risk
– Applies to a large number of assets.
– For example, uncertainty about the general economic
system
18
Required rate
of return =
Compensation for the
time value of money +
Compensation
for risk
• Diversification means spreading the risks across many
investments
– Ideally, these investments will have different patterns of
behaviour and different income streams
– This can be used to reduce or eliminate unsystematic risk.
• Systematic risk cannot be removed
• The (fair) expected return of an asset depends only on
that asset’s systematic risk
• CAPM relates systematic risk (β) to returns
– The more risk there is, the higher the expected returns will
be
– Higher expected returns compensate investors for taking
the risk inherent in the investment
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Diversification (continued)
Risk (%)
Diversifiable (Unsystematic) Risk
Market (Systematic) Risk
Number of Investments
Total risk = Unsystematic Risk +
Systematic Risk.
Decreases as more investments are
added
21
The Security Market Line (SML) Approach
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• where
• where Rf is the risk free rate
• RM is the return on the market
– Note that E(RM) – Rf is often called the market risk
premium
• β is the systematic risk of the asset relative to the
average (i.e., the market portfolio)

= +
(( ) − )
• The βi coefficient represents the market risk fraction of the
variance of return of a security
• Expected return E(ri) depends on βI
• To estimate betas:
• Regress stock returns (Rj) against market returns (Rm):
Rj = a + b Rm
where a is the intercept and b is the slope of the regression.
• The slope of the regression corresponds to the beta of the
stock, and measures the riskiness of the stock.
Properties of the β coefficient
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Example – SML
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• Suppose your company has an equity beta of .58 and
the current risk-free rate is 6.1%. If the expected market
risk premium is 8.6%, what is your cost of equity capital?
RE = 6.1 + .58(8.6) = 11.1%
• Since we came up with similar numbers using both the
dividend growth model and the SML approach, we
should feel pretty good about our estimate
24
Advantages and Disadvantages of SML
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• Advantages
– Explicitly adjusts for systematic risk
– Applicable to all companies, as long as we can estimate
beta
• Disadvantages
– Have to estimate the expected market risk premium, which
does vary over time
– Have to estimate beta, which also varies over time
– We are using the past to predict the future, which is not
always reliable
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Example – Cost of Equity
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• Suppose our company has a beta of 1.5. The market
risk premium is expected to be 9% and the current
risk-free rate is 6%. We have used analysts’
estimates to determine that the market believes our
dividends will grow at 6% per year and our last
dividend was $2. Our stock is currently selling for
$15.65. What is our cost of equity?
– Using SML:
– Using DGM:
26
Cost of Debt
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• The cost of debt is the required return on our
company’s debt
• The cost of debt can often be observed as it is the
interest rate that the firm pays on new borrowing.
– It is always used in its after-tax form
• The after-tax cost of debt is the interest on a debt,
less the tax savings generated by that debt.
– Debt results in tax savings because interest payments are
deducted from the company’s income before corporation
tax is levied.
– D ebt reduces the firm’s taxable income.
• Alternatively, the cost of debt can be found
by calculated the yield-to-maturity on the firm’s
existing long-term debt
• This is the return on the investment of buying the
long- term debt of the company at the current
market price
• The cost of debt is NOT the coupon rate
• We may also use estimates of current rates based
on the bond rating we expect when we issue new
debt
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Cost of Debt
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Cost of Preferred Stock
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• Preferred stock generally pays a constant dividend each
period
• Dividends are expected to be paid every period forever
• Preferred stock is a perpetuity:
P0 = D /RP so RP = D / P0
• Your company has preferred stock that has an annual
dividend of $3. If the current price is $25, what is the
cost of preferred stock?
• RP = 3 / 25 = 12%
29
The Weighted Average Cost of Capital
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• We can use the individual costs of capital that we have
computed to get the “average” cost of capital for the
firm.
• This “average” is the required return on our assets,
based on the market’s perception of the risk of those
assets
• The weights are determined by how much of each type
of financing we use
30
Capital Structure Weights
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• Notation
– E = market value of equity = # of outstanding shares times
price per share
– D = market value of debt = # of outstanding bonds times
bond price
– V = market value of the firm = D + E
• Weights
– wE = E/V = percent financed with equity
– wD = D/V = percent financed with debt
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Example: Capital Structure Weights
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• Suppose you have a market value of equity equal to
$500 million and a market value of debt = $475 million.
– What are the capital structure weights?
• V = 500 million + 475 million = 975 million
• wE = E/V = 500 / 975 = .5128 = 51.28%
• wD = D/V = 475 / 975 = .4872 = 48.72%
32
Taxes and the WACC
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• We are concerned with after-tax cash flows, so we need
to consider the effect of taxes on the various costs of
capital
• Interest expense reduces our tax liability
– This reduction in taxes reduces our cost of debt
– After-tax cost of debt = cost of debt – tax savings
= RD-(RD*TC) = RD(1-TC)
• Dividends are not tax deductible, so there is no tax
impact on the cost of equity
WACC = wERE + wDRD(1-TC)
33
Extended Example – WACC – I
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• Equity Information
– 50 million shares
– $80 per share
– Beta = 1.15
– Market risk premium = 9%
– Risk-free rate = 5%
• Debt Information
– $1 billion in outstanding debt
(face value)
– Cost of debt is 7.8%
• Tax rate = 40%
34
Extended Example – WACC – II
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• What is the cost of equity?
– RE = 5 + 1.15(9) = 15.35%
• What is the after-tax cost of debt?
– RD(1-TC) = 7.8(1-.4) = 4.7%
35
Extended Example – WACC – III
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• What are the capital structure weights?
– E = 50 million (80) = 4 billion
– D = (1 billion/1000) (1100) = 1 billion (1.10) = 1.1 billion
– V = 4 + 1.1 = 5.1 billion
– wE = E/V = 4 / 5.1 = .7843
– wD = D/V = 1.1 / 5.1 = .2157
• What is the WACC?
– WACC = .7843(15.35%) + .2157(4.7%) = 13.05%
– Cost of capital and green energy
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Divisional and Project Costs of Capital
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• Using the WACC as our discount rate is only appropriate
for projects that have the same risk as the firm’s current
operations
• If we are looking at a project that does NOT have the
same risk as the firm, then we need to determine the
appropriate discount rate for that project
• Divisions also often require separate
discount rates
37
Using WACC for All Projects – Example
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• Assume:
– Risk free rate of 7%
– Market risk premium of 8%
– Firm beta of 1
– Firm is financed exclusively by common equity
– Project 1 has beta of 0.6, and return of 14%
– Project 2 has beta of 1.4, and return of 16%
• Firm WACC =
38
• Project 1 – individual required return
– 7% + (0.6 * 8%) = 11.8%
– If use individual WACC, accept
– If use firm WACC reject
• Project 2 – individual required return
– 7% + (1.4 * 8%) = 18.2%
– If use individual WACC, reject
– If use firm WACC accept
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• Therefore, using firm WACC may:
– Reject profitable projects with lower than firm risk
– Accept unprofitable projects with greater than firm risk
• Similarly, if two businesses in one large firm, segment
with higher risk will receive greater funds if WACC
unadjusted
40
The Pure Play Approach
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• Find one or more companies that specialize in the
product or service that we are considering
• Compute the beta for each company (assuming that
the capital structures are the same)
• Take an average
• Use that beta along with the CAPM to find the
appropriate return for a project of that risk
• Often difficult to find pure play companies
41
Subjective Approach
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• Consider the project’s risk relative to the firm overall
• If the project has more risk than the firm, use a
discount rate greater than the WACC
• If the project has less risk than the firm, use a
discount rate less than the WACC
• You may still accept projects that you shouldn’t and
reject projects you should accept, but your error
rate should be lower than not considering
differential risk at all
42
Subjective Approach - Example
Risk Level Discount Rate
Very Low Risk WACC – 8%
Low Risk WACC – 3%
Same Risk as Firm WACC
High Risk WACC + 5%
Very High Risk WACC + 10%
• If a firm issues new stocks or bonds, floatation costs
must be paid.
• Sometimes WACC is increased to include floatation
costs
– This is rather inaccurate as the project’s return
should reflect its risk, not the funding source
– These costs are a direct result of accepting the
project so they are relevant cash flows
• Floatation costs increase the total amount of funding
to be raised
Floatation Costs and WACC
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• A firm needs $100 million for investment and
floatation costs are 10%.
– The firm will have 90% of the amount raised to
spend on the investment
– Therefore 90% of the total amount raised must be
equal to $100 million
Amount needed = (1-10%) x Amount raised
$100million =0.90 x Amount raised
Amount raised = $111.11million
Floatation Costs : An example
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• Floatation costs apply to new issues of both debt and equity
• The total floatation cost is a weighted average of the
floatation costs for each element
f A = (E/V) f E + (D/V) f D
• When taking issue costs into account the firm should use
its target capital structure for the weights
– Thetarget capital structure is the firm’s ideal capital
structure as determined by the management.
– Capital structure will be covered later in the semester
Including Floatation Costs
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• Consider a project that will cost $1 million.
• The project will generate after-tax cash flows of
• $250,000 per year for 7 years.
• The WACC is 15%,
• The firm’s target D/E ratio is 0.6
• The flotation cost for equity is 5%, and the flotation cost
for debt is 3%.
• What is the NPV for the project after adjusting for
flotation costs?
Including Floatation Costs: Example
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• A target D/E ratio of 0.6 implies:
• D/V = 0.6/1.6 = 0.375 E/V = 1/1.6 = 0.625
• Therefore, the floatation costs are
• f A = (E/V) f E + (D/V) f D
• fA = (0.625×5%)+ (0.375×3%)= 4.25%
Including Floatation Costs: Example
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• Need to adjust the cost of the investment to account for the
floatation costs
Amount needed = (1-0.0425) xAmount raised
$1million = 0.9575 x Amount raised
Amount raised =$1,044,386.42
• Next the present value of the cash flows
• Cash inflows of the same amount at regular intervals can be
treated as an ordinary annuity
• PVAt = 250000 (1/0.15 – (1/(0.15 x 1.015))
7
= $1,040,105
Including Floatation Costs: Example
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• Finally, the NPV is
NPV = CF + + ...+(1+ r)1
CFn
(1+ r)n
1CF + (
CF2
1 + r)20
NPV = −1,044,386.42+1,040104.93= −4,281.49
• Clearly we should reject this investment as the NPV is
negative
• However, if floatation costs are ignored, the NPV is
positive ($40,105)
Including Floatation Costs: Example
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• Sources of Capital
– equity
– debt
– Hybrids- preference shares, convertible debt
• Cost of Capital
– Cost of equity: DGM, CAPM
– Cost of debt
– Cost of preference shares
– Weighted average cost of capital (WACC)
– Divisional costs of capital
• Floatation costs
Summary
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