Chapter 15 -- Required Returns and the Cost of Capital

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Chapter 15
Required Returns and the Cost of Capital
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After Studying Chapter 15, you should be able to

1. Explain how a firm creates value and identify the
   key sources of value creation.
2. Define the overall cost of capital of the firm.
   
3. Calculate the costs of the individual components
   of a firms cost of capital - cost of debt, cost
   of preferred stock, and cost of equity.
4. Explain and use alternative models to determine
   the cost of equity, including the dividend
   discount approach, the capital-asset pricing
   model (CAPM) approach, and the before-tax cost of
   debt plus risk premium approach.
5. Calculate the firms weighted average cost of
   capital (WACC) and understand its rationale, use,
   and limitations.
6. Explain how the concept of economic Value added
   (EVA) is related to value creation and the firms
   cost of capital.
7. Understand the capital-asset pricing model's role
   in computing project-specific and group-specific
   required rates of return.

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Required Returns and the Cost of Capital

• Overall Cost of Capital of the Firm
• Project-Specific Required Rates
• Group-Specific Required Rates
• Total Risk Evaluation

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Cost of Capital

• The cost of capital (COC) is the rate of return
  the firm must earn to maintain its market value
  and attract investors
• projects with return gt COC will improve the
  firms value
• projects with return lt COC will harm the firms
  value

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Overall Cost of Capital of the Firm

• Cost of Capital is the required rate of return on
  the various types of financing. The overall cost
  of capital is a weighted average of the
  individual required rates of return (costs).
• By weighting the cost of each source of financing
  by its target proportion in the firms capital
  structure, the firm can obtain a weighted average
  cost that reflects the interrelationship of
  financing decisions. The formula for doing this
  is ka wiki wpkp wsks This is explained
  later.

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Cost of Capital

• COC is estimated
• on an after-tax basis
• at a point in time
• based on expected future values
• holding business and financial risk fixed

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Cost of Capital

• Target capital structure is the optimal mix of
  debt and equity financing for the firm
• most firms seek to maintain a desired mix of debt
  and equity funding
• each new chunk of capital should fit with the
  overall mix

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Cost of Capital

• A firm is currently faced with an investment
  opportunity. Assume the following
• Because it can earn 7 on the investment of funds
  costing only 6, the firm undertakes the
  opportunity.

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Cost of Capital

• Imagine that one week later a new investment
  opportunity is available
• In this instance, the firm rejects the
  opportunity, because the 14 financing cost is
  greater than the 12 expected return.
• Is this action in the best interests of its
  owners?

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Cost of Capital

• Noit accepted a project yielding a 7 return and
  rejected one with a 12 return.
• Is there a better way?
• Yes the firm can use a combined cost, which over
  the long run would provide for better decisions.
• By weighting the cost of each source of financing
  by its target proportion in the firms capital
  structure, the firm can obtain a weighted average
  cost that reflects the interrelationship of
  financing decisions.

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Cost of Capital

• Assuming that a 5050 mix of debt and equity is
  targeted, the weighted average cost in this
  example would be 10 (0.50 x 6 debt) (0.50 x
  14 equity).
• This outcome is clearly more desirable.
• With this cost, the first opportunity would have
  been rejected (7 IRR lt 10 weighted average
  cost), and the second one would have been
  accepted (12 IRR gt 10 weighted average cost).

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Concept of Cost of Capital

• Wren Manufacturing is considering projects 263
  and 264. The basic variables surrounding each
  project using the IRR decision technique and the
  resulting decision actions are summarised in the
  following table.

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Concept of Cost of Capital

• a Evaluate the firms decision-making procedures,
  and explain why the acceptance of project 263 and
  rejection of project 264 may not be in the
  owners best interest.
• b If the firm maintains a capital structure
  containing 40 debt and 60 equity, find its
  weighted average cost using the data in the
  table.
• c Had the firm used the weighted average cost
  calculated in part b, what actions would have
  been taken relative to projects 263 and 264?
• d Compare and contrast the firms actions with
  your findings in part c. Which decision method
  seems more appropriate? Explain why.

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Concept of Cost of Capital

• a. The firm is basing its decision on the cost to
  finance a particular project rather than the
  firms combined cost of capital. This
  decision-making method may lead to erroneous
  accept/reject decisions.
• b. ka wiki wpkp wsks
• ? ka 0.40 (7) 0.60(16)
• ? ka 2.8 9.6
• ? ka 12.4
• ?

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Concept of Cost of Capital

• c. Reject project 263. Accept project 264.
• d. Opposite conclusions were drawn using the two
  decision criteria. The overall cost of capital as
  a criterion provides better decisions because it
  takes into consideration the long run
  interrelationship of financing decisions

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Sources of finance

• The four sources of long-term funds for the
  business firm
• debt,
• preference share capital,
• ordinary share equity capital and
• retained earnings.

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Sources of finance

• This is important!!
• The specific cost of each source of financing is
  the after-tax cost of obtaining the financing
  today, i.e. the marginal cost of raising the next
  dollar of funding
• It is not the historically based cost reflected
  by the existing financing in the firms
  accounting records
• Only the cost of debt needs to be adjusted for
  tax.
• Why do we not adjust the cost of preference
  shares and equity for tax?
• Because dividends are paid from tax-paid profits.
  Therefore, the cost of these is an after-tax cost

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Market Value of Long-Term Financing
Type of Financing Mkt Val Weight Long-Term
Debt 35M 35 Preferred Stock
15M 15 Common Stock Equity 50M
50 100M 100
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Cost of Debt

• Cost of Debt is the required rate of return on
  investment of the lenders of a company.
• Where P0 current market price
• Pt maturity value at time t
• I interest payment in
• After tax cost is
• ki kd (1 T)

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Determination of the Cost of Debt
Assume that Basket Wonders (BW) has 1,000 par
value zero-coupon bonds outstanding. BW bonds are
currently trading at 385.54 with 10 years to
maturity. BW tax bracket is 40.
0 1,000
385.54
(1 kd)10
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Determination of the Cost of Debt
(1 kd)10 1,000 / 385.54 2.5938 (1
kd) (2.5938) (1/10) 1.1 kd 0.1
or 10 ki 10 ( 1 .40 ) ki 6
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Cost of debt

• Du Chen Corporation is selling 10 million of
  20-year, 9 coupon (stated annual interest rate)
  bonds, each with a face value of 1,000.
• Similar-risk bonds earn returns greater than 9
  so the firm must sell the bonds for 980 to
  compensate for the lower coupon interest rate.
• The flotation costs paid to the investment banker
  are 2 of the face value of the bond (2 1000),
  or 20.
• The net proceeds to the firm from the sale of
  each bond are therefore 960 (980 20).

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Cost of debt

• To solve this, we need a financial calculator or
  a spreadsheet. However there is a Yield to
  Maturity (YTM) formula that gives a good
  approximation answer
• kd I (1,000 Nd)/n/(Nd 1000)/2
• Where I the interest payment in
• Nd proceeds from the sale of the bond
• n number of periods until the bond maturity.

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Cost of debt

• The cash flows are
• End of Year Cash flow
• 0 960
• 1-20 -90
• -1,000
• Using the YTM formula, the answer is

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Cost of debt
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Cost of debt

• Assuming a 30 tax rate and before-tax cost of
  9.4,
• ki 0.094 x (1 0.30) 6.6 after-tax
  cost
• The explicit cost of long-term debt is less than
  the explicit cost of other forms of long-term
  financing, because of the tax-deductibility of
  interest.

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Cost of Preferred Stock

• The cost of preference share capital (kp) is the
  ratio of the preference share dividend (Dp) to
  the firms net proceeds (Np) from the sale of
  preference shares
• ? kp Dp / Np
• Example consider an 8.5 pref issue, at par
  2.00 a share with an issue cost of 11 cents per
  share
• ? kp (0.17) / (1.89) 9
• (Np 2.00 0.11 1.89)

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Cost of Preferred Stock

• Comparing the 9 cost of preference capital with
  the 6.6 cost of long-term debt (bonds) shows
  that preference capital is more expensive. The
  difference exists primarily because the cost of
  the debt (interest) is tax-deductible.
• The cost of preference share capital already
  issued is the dividend (Dp) divided by the market
  value (P) of preference share capital
• kp Dp / P
• If the market value of Du Chen Corporations
  preference share capital is 10 million, and
  preference dividend payable is 0.9 million, the
  return on its preference share capital is
• kp 0.90/10.00 9.0

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Cost of Preferred Stock
Cost of Preferred Stock is the required rate of
return on investment of the preferred
shareholders of the company. kP DP / P0
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Determination of the Cost of Preferred Stock
Assume that Basket Wonders (BW) has preferred
stock outstanding with par value of 100,
dividend per share of 6.30, and a current market
value of 70 per share. kP 6.30 / 70 kP
9
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Cost of Equity Approaches

• Dividend Discount Model
• Capital-Asset Pricing Model
• Before-Tax Cost of Debt plus Risk Premium

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Dividend Discount Model
The cost of equity capital, ke, is the discount
rate that equates the present value of all
expected future dividends with the current market
price of the stock.
D1 D2 D
?
P0
. . .

?
(1 ke)1 (1 ke)2 (1 ke)
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Constant Growth Model
The constant dividend growth assumption reduces
the model to ke ( D1 / P0 ) g Assumes that
dividends will grow at the constant rate g
forever.
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Determination of the Cost of Equity Capital
Assume that Basket Wonders (BW) has common stock
outstanding with a current market value of 64.80
per share, current dividend of 3 per share, and
a dividend growth rate of 8 forever. ke ( D1
/ P0 ) g ke (3(1.08) / 64.80) 0.08 ke
0.05 0.08 0.13 or 13
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Determination of the Cost of Equity Capital

• Calculate Du Chen Corporations cost of ordinary
  share equity capital, ke. The market price, P0,
  of its shares is 5. The firm expects to pay a
  dividend, D1, of 40 cents at the end of the
  coming year, 2005. The dividends paid over the
  past 6 years (19992004) were

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Determination of the Cost of Equity Capital

• Calculate the growth rate of dividends
• 1999 div/2004 div 29.7/38.0 0.7816
• PVIFk,5 5
• Or
• 2004 div/1999 div 38.0/29.7 1.2794
• FVIFk,5 5

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Determination of the Cost of Equity Capital

• Substituting D1 0.40, P0 5.00 and g 5
  per cent into the Equation results in the cost of
  ordinary equity
• ke 0.40/5.00 0.05
• 0.08 0.05
• 0.13 or 13

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Growth Phases Model
The growth phases assumption leads to the
following formula (assume 3 growth phases)
D0(1 g1)t Da(1 g2)ta
a
b
P0
?
?????

(1 ke)t (1 ke)t
t1
ta1
?
Db(1 g3)tb
?
(1 ke)t
tb1
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Capital Asset Pricing Model
The cost of equity capital, ke, is equated to
the required rate of return in market
equilibrium. The risk-return relationship is
described by the Security Market Line (SML). ke
Rj Rf (Rm Rf)?j
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Determination of the Cost of Equity (CAPM)
Assume that Basket Wonders (BW) has a company
beta of 1.25. Research by Julie Miller suggests
that the risk-free rate is 4 and the expected
return on the market is 11.4 ke Rf (Rm
Rf)?j 4 (11.4 4)1.25 ke 4
9.25 13.25
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Before-Tax Cost of Debt Plus Risk Premium
The cost of equity capital, ke, is the sum of
the before-tax cost of debt and a risk premium in
expected return for common stock over debt. ke
kd Risk Premium Risk premium is not the
same as CAPM risk premium
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Determination of the Cost of Equity (kd R.P.)
Assume that Basket Wonders (BW) typically adds a
2.75 premium to the before-tax cost of debt.
ke kd Risk Premium 10 2.75 ke
12.75
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Comparison of the Cost of Equity Methods
Constant Growth Model 13.00 Capital Asset
Pricing Model 13.25 Cost of Debt Risk
Premium 12.75
Generally, the three methods will not agree. We
must decide how to weight we will use an
average of these three.
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Weighted average cost of capital

• The WACC (ka) is determined by weighting the cost
  of each specific type of capital by its
  proportion in the firms capital structure
• ? ka (ki x wi) (kp x wp) (ke x ws)
• Note (i) The sum of weights must equal one.
• (ii) It is the after-tax cost of debt that is
  used.

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BWs Weighted Average Cost of Capital (WACC)
n
?
Cost of Capital kx(Wx) WACC 0.35(6)
0.15(9) 0.50(13) WACC 0.021 0.0135
0.065 0.0995 or 9.95
x1
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Weighted average cost of capital

• The costs of the various types of capital for Du
  Chen Corporation are
• Cost of debt, ki 6.6
• Cost of preference capital, kp 9.0
• Cost of new shares, ke 14.0
• The company uses the following weights in
  calculating its WACC

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Weighted average cost of capital
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Weighted average cost of capital

• Source Weight Cost WACC
• Debt 0.40 6.6 2.6
• Pref capital 0.10 9.0 0.9
• Ord equity 0.50 1 3.0 6.5
• Totals 1.00 10.0
• The WACC for Du Chen is 10.
• Assuming an unchanged risk level, the firm should
  accept all projects that earn a return greater
  than or equal to 10

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Limitations of the WACC

• 1. Weighting System
• Marginal Capital Costs
• Capital Raised in Different Proportions than
  WACC

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Limitations of the WACC

• Flotation Costs are the costs associated with
  issuing securities such as underwriting, legal,
  listing, and printing fees.
• a. Adjustment to Initial Outlay
• b. Adjustment to Discount Rate

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Adjustment to Initial Outlay (AIO)
Add Flotation Costs (FC) to the Initial Cash
Outlay (ICO). Impact Reduces the NPV
n
CFt
( ICO FC )
?
NPV
(1 k)t
t1
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Adjustment to Discount Rate (ADR)
Subtract Flotation Costs from the proceeds
(price) of the security and recalculate yield
figures. Impact Increases the cost for any
capital component with flotation costs. Result
Increases the WACC, which decreases the NPV.
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Determining Project-Specific Required Rates of
Return
Use of CAPM in Project Selection

• Initially assume all-equity financing.
• Determine project beta.
• Calculate the expected return.
• Adjust for capital structure of firm.
• Compare cost to IRR of project.

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Determining Project-Specific Required Rate of
Return
1. Calculate the required return for
Project k (all-equity financed). Rk Rf (Rm
Rf)?k 2. Adjust for capital structure of
the firm (financing weights). Weighted Average
Required Return ki of Debt Rk of
Equity
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Project-Specific Required Rate of Return Example
Assume a computer networking project is being
considered with an IRR of 19. Examination of
firms in the networking industry allows us to
estimate an all-equity beta of 1.5. Our firm is
financed with 70 Equity and 30 Debt at
ki6. The expected return on the market is 11.2
and the risk-free rate is 4.
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Do You Accept the Project?
ke Rf (Rm Rf)?j 4 (11.2
4)1.5 ke 4 10.8 14.8 WACC
0.30(6) 0.70(14.8) 1.8 10.36
12.16 IRR 19
gt WACC 12.16
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Determining Group-Specific Required Rates of
Return
Use of CAPM in Project Selection

• Initially assume all-equity financing.
• Determine group beta.
• Calculate the expected return.
• Adjust for capital structure of group.
• Compare cost to IRR of group project.

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Comparing Group-Specific Required Rates of Return
Company Cost of Capital
Expected Rate of Return
Group-Specific Required Returns
Systematic Risk (Beta)
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Project Evaluation Based on Total Risk
RiskAdjusted Discount Rate Approach (RADR) The
required return is increased (decreased) relative
to the firms overall cost of capital for
projects or groups showing greater (smaller) than
average risk.
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RADR and NPV
Adjusting for risk correctly may influence the
ultimate Project decision.
000s
15
10
RADR low risk at 10 (Accept!)
Net Present Value
5
RADR high risk at 15 (Reject!)
0
4
0 3 6 9 12
15
Discount Rate ()
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Adjusting Beta for Financial Leverage
?j ?ju 1 (B/S)(1 TC) ?j Beta of a
levered firm. ?ju Beta of an unlevered
firm (an all-equity financed firm).
B/S Debt-to-Equity ratio in Market Value
terms. TC The corporate tax rate.
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Adjusted Present Value
Adjusted Present Value (APV) is the sum of the
discounted value of a projects operating cash
flows plus the value of any tax-shield benefits
of interest associated with the projects
financing minus any flotation costs.
Unlevered Project Value
Value of Project Financing
APV

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NPV and APV Example
Assume Basket Wonders is considering a new
425,000 automated basket weaving machine that
will save 100,000 per year for the next 6 years.
The required rate on unlevered equity is 11.
BW can borrow 180,000 at 7 with 10,000
after-tax flotation costs. Principal is repaid at
30,000 per year ( interest). The firm is in
the 40 tax bracket.
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Basket Wonders NPV Solution
What is the NPV to an all-equity-financed
firm? NPV 100,000PVIFA11,6 425,000 NPV
423,054 425,000 NPV 1,946
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Basket Wonders APV Solution
What is the APV? First, determine the interest
expense. Int Yr 1 (180,000)(7) 12,600 Int
Yr 2 ( 150,000)(7) 10,500 Int Yr 3 (
120,000)(7) 8,400 Int Yr 4 (
90,000)(7) 6,300 Int Yr 5 (
60,000)(7) 4,200 Int Yr 6 (
30,000)(7) 2,100
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Basket Wonders APV Solution
Second, calculate the tax-shield benefits. TSB Yr
1 (12,600)(40) 5,040 TSB Yr 2 (
10,500)(40) 4,200 TSB Yr 3 ( 8,400)(40)
3,360 TSB Yr 4 ( 6,300)(40)
2,520 TSB Yr 5 ( 4,200)(40) 1,680 TSB Yr
6 ( 2,100)(40) 840
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Basket Wonders APV Solution
Third, find the PV of the tax-shield
benefits. TSB Yr 1 (5,040)(.901) 4,541 TSB
Yr 2 ( 4,200)(.812) 3,410 TSB Yr 3 (
3,360)(.731) 2,456 TSB Yr 4 ( 2,520)(.659)
1,661 TSB Yr 5 ( 1,680)(.593)
996 TSB Yr 6 ( 840)(.535) 449
PV 13,513
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Basket Wonders NPV Solution
What is the APV? APV NPV PV of TS
Flotation Cost APV 1,946 13,513
10,000 APV 1,567