17-0
Chapter Seventeen
Capital Budgeting
forFinance
the
Corporate
Ross Westerfield Jaffe
Levered Firm


17
Sixth Edition
Prepared by
Gady Jacoby
University of Manitoba
and
Sebouh Aintablian
American University of
Beirut
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17-1
Prospectus
• Recall that there are three questions in corporate
finance.
• The first regards what long-term investments the
firm should make (the capital budgeting question).
• The second regards the use of debt (the capital
structure question).
• This chapter is the nexus of these questions.
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Chapter Outline
17.1 Adjusted Present Value Approach
17.2 Flows to Equity Approach
17.3 Weighted Average Cost of Capital Method
17.4 A Comparison of the APV, FTE, and WACC
Approaches
17.5 Capital Budgeting for Projects that are Not ScaleEnhancing
17.6 APV Example
17.7 Beta and Leverage
17.8 Summary and Conclusions
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17.1 Adjusted Present Value Approach
APV  NPV  NPVF
• The value of a project to the firm can be thought of as the
value of the project to an unlevered firm (NPV) plus the
present value of the financing side effects (NPVF):
• There are four side effects of financing:
– The Tax Subsidy to Debt
– The Costs of Issuing New Securities
– The Costs of Financial Distress
– Subsidies to Debt Financing
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APV Example
Consider a project of the Pearson Company, the timing and
size of the incremental after-tax cash flows for an allequity firm are:
-$1,000
0
$125
$250
$375
$500
1
2
3
4
The unlevered cost of equity is r0 = 10%:
NPV10%
NPV10%
$125
$250
$375
$500
 $1,000 



2
3
(1.10) (1.10) (1.10) (1.10) 4
 $56.50
The project would be rejected by an all-equity firm: NPV < 0.
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APV Example (continued)
• Now, imagine that the firm finances the project with
$600 of debt at rB = 8%.
• Pearson’s tax rate is 40%, so they have an interest
tax shield worth TCBrB = .40×$600×.08 = $19.20
each year.
 The net present value of the project under leverage is:
APV  NPV  NPVF
4
$19.20
APV  $56.50  
t
(
1
.
08
)
t 1
APV  $56.50  63.59  $7.09
 So, Pearson should accept the project with debt.
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APV Example (continued)
• Note that there are two ways to calculate the NPV
of the loan. Previously, we calculated the PV of the
interest tax shields. Now, let’s calculate the actual
NPV of the loan:
4
$600  .08  (1  .4) $600
NPVloan  $600  

t
4
(1.08)
(1.08)
t 1
NPVloan  $63.59
APV  NPV  NPVF
APV  $56.50  63.59  $7.09
 Which is the same answer as before.
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17.2 Flows to Equity Approach
• Discount the cash flow from the project to the
equity holders of the levered firm at the cost of
levered equity capital, rS.
• There are three steps in the FTE Approach:
– Step One: Calculate the levered cash flows
– Step Two: Calculate rS.
– Step Three: Valuation of the levered cash flows at rS.
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Step One: Levered Cash Flows for Pearson
• Since the firm is using $600 of debt, the equity holders only have to
come up with $400 of the initial $1,000.
• Thus, CF0 = -$400
• Each period, the equity holders must pay interest expense. The after-tax
cost of the interest is B×rB×(1-TC) = $600×.08×(1-.40) = $28.80
CF3 = $375 -28.80
CF2 = $250 -28.80
CF1 = $125-28.80
-$400
0
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CF4 = $500 -28.80 -600
$96.20
$221.20
$346.20
-$128.80
1
2
3
4
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Step Two: Calculate rS for Pearson
B
rS  r0  (1  TC )( r0  rB )
S
• To calculate the debt-to-equity ratio, B/S, start with the debt
to value ratio. Note that the value of the project is
4
$125
$250
$375
$500
19.20
PV 




2
3
4
t
(1.10) (1.10) (1.10) (1.10)
(
1
.
08
)
t 1
PV  $943.50  63.59  $1,007.09
 B = $600 when V = $1,007.09 so S = $407.09.
$600
rS  .10 
(1  .40)(.10  .08)  11.77%
$407.09
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Step Three: Valuation for Pearson
• Discount the cash flows to equity holders at rS = 11.77%
-$400
0
$96.20
1
$221.20
2
$346.20
3
-$128.80
4
$96.20
$221.20
$346.20
$128.80
PV  $400 



2
3
(1.1177) (1.1177) (1.1177) (1.1177) 4
PV  $28.56
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17.3 WACC Method for Pearson
S
B
rW ACC 
rS 
rB (1  TC )
SB
SB
• To find the value of the project, discount the unlevered cash
flows at the weighted average cost of capital.
• Suppose Pearson Inc. target debt to equity ratio is 1.50.
B
1.5S  B
1.50 
S
B
1.5S
1.5
S


 0.60
 1  0.60  0.40
S  B S  1.5S 2.5
SB
rW ACC  (0.40)  (11.77%)  (0.60)  (8%)  (1  .40)
rW ACC  7.58%
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Valuation for Pearson using WACC
• To find the value of the project, discount the
unlevered cash flows at the weighted average cost
of capital
$125
$250
$375
$500
NPV  $1,000 



2
3
(1.0758) (1.0758) (1.0758) (1.0758) 4
NPV6.88%  $6.68
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17.4 A Comparison of the APV, FTE, and
WACC Approaches
• All three approaches attempt the same task:
valuation in the presence of debt financing.
• Guidelines:
– Use WACC or FTE if the firm’s target debt-to-value ratio
applies to the project over the life of the project.
– Use the APV if the project’s level of debt is known over
the life of the project.
• In the real world, the WACC is the most widely used
approach by far.
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Summary: APV, FTE, and WACC
Initial Investment
Cash Flows
Discount Rates
PV of financing effects
APV
WACC FTE
All
UCF
r0
Yes
All
UCF
rWACC
No
Equity Portion
LCF
rS
No
Which approach is best?
•Use APV when the level of debt is constant
•Use WACC and FTE when the debt ratio is constant
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17.5 Capital Budgeting for Projects that
are Not Scale-Enhancing
• A scale-enhancing project is one where the project
is similar to those of the existing firm.
• In the real world, executives would make the
assumption that the business risk of the non-scaleenhancing project would be about equal to the
business risk of firms already in the business.
• No exact formula exists for this. Some executives
might select a discount rate slightly higher on the
assumption that the new project is somewhat riskier
since it is a new entrant.
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17.5 Capital Budgeting for Projects that are
Not Scale-Enhancing: An example
• World-Wide Enterprises (WWE) is planning to enter into a
new line of business (widget industry)
• American Widgets (AW) is a firm in the widget industry.
• WWE has a D/E of 1/3, AW has a D/E of 2/3.
• Borrowing rate for WWE is10 %
Borrowing rate for AW is 8 %
• Given: Market risk premium = 8.5 %, Rf = 8%, Tc= 40%
• What is the appropriate discount rate for WWE to use for its
widget venture?
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17.5 Capital Budgeting for Projects that are
Not Scale-Enhancing: An example
•
A four step procedure to calculate discount rates:
1. Determining AW’s cost of Equity Capital (rs)
2. Determining AW’s Hypothetical All-Equity Cost of
Capital. (r0)
3. Determining rs for WWE’s Widget Venture
4. Determining rWACC for WWE’s Widget Venture.
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STEP 1:Determining AW’s cost of Equity
Capital (rs)
r  R  β ( R  R )
s
F
M
F
r  8%  1.5  8.5 %
s
r  20.75 %
s
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STEP 2 :Determining AW’s Hypothetical AllEquity Cost of Capital. (r0)
B
rS  r0 
(1  TC )( r0  rB )
S
2
0.2075  r  (0.6)(r  0.12)
3
0
0
r  0.1825
0
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STEP 3 :Determining rs for WWE’s Widget
Venture
Assuming that the business risk of WWE and AW
are the same,
B
rS  r0 
(1  TC )( r0  rB )
S
1
r  0.1825  (0.6)(0.1825  0.10)
3
s
r  0.199
s
NOTE : rs (WWE) < rs (AW)
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STEP 4: Determining rWACC for WWE’s Widget
Venture.
rW ACC
r
W ACC
r
W ACC
S
B

rS 
rB (1  TC )
SB
SB
3
1
 0.199  0.10(0.6)
4
4
 0.16425  16.425%
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17.6 APV Example:
•
•
•
•
•
•
•
Worldwide Trousers, Inc. is considering a $5 million expansion
of their existing business.
The initial expense will be depreciated straight-line over five
years to zero salvage value
The pretax salvage value in year 5 will be $500,000.
The project will generate pretax earnings of $1,500,000 per year,
and not change the risk level of the firm.
The firm can obtain a five-year $3,000,000 loan at 12.5% to
partially finance the project.
If the project were financed with all equity, the cost of capital
would be 18%. The corporate tax rate is 34%, and the risk-free
rate is 4%.
The project will require a $100,000 investment in net working
capital.
Calculate the APV.
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17.6 APV Example: Cost
Let’s work our way through the four terms in this equation:
APV  Cost  PVunlevered  PVdepreciation  PV interest
project
tax shield
tax shield
The cost of the project is not $5,000,000.
We must include the round trip in and out of net working
capital and the after-tax salvage value.
NWC is riskless, so
we discount it at rf.
100,000 500,000(1  .34)
Salvage value should
Cost  $5.1m 

5
have the same risk as
(1  rf )
(1  r0 ) 5
the rest of the firm’s
 $4,873.561.25
assets, so we use r0.
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17.6 APV Example: PV unlevered project
Turning our attention to the second term,
APV  $4,873.561.25  PVunlevered  PVdepreciation  PV interest
project
tax shield
tax shield
The PV unlevered project is the present value of the unlevered cash
flows discounted at the unlevered cost of capital, 18%.
5
UCFt
$1.5m  (1  .34)


t
t
(
1

r
)
(
1
.
18
)
t 1
t 1
o
5
PVunlevered
project
PVunlevered  $3,095,899
project
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17.6 APV Example: PV depreciation tax shield
Turning our attention to the third term,
APV  $4,873.561.25  $3,095,899  PVdepreciation  PV interest
tax shield
tax shield
The PV depreciation tax shield is the present value of the tax
savings due to depreciation discounted at the risk free rate,
at rf = 4%
D  TC

t
(
1

r
)
t 1
f
5
PVdepreciation
tax shield
$1m  .34

$1,513,619
t
t 1 (1.04)
5
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17.6 APV Example: PV interest tax shield
Turning our attention to the last term,
APV  $4,873.561.25  $3,095,899  $1,513,619  PV interest
tax shield
The PV interest tax shield is the present value of the tax savings
due to interest expense discounted at the firms debt rate, at
rD = 12.5%
TC  rD  $3m 5 0.34  0.125  $3m
PV interest  

t
t
(
1

r
)
(
1
.
125
)
t 1
t 1
D
tax shield
5
5
127,500
PV interest  
 453,972.46
t
t 1 (1.125)
tax shield
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17.6 APV Example: Adding it all up
Let’s add the four terms in this equation:
APV  $4,873.561.25  3,095,899  1,513,619  453,972.46
APV  $189,930
Since the project has a positive APV, it looks like a go.
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17.7 Beta and Leverage
• Recall that an asset beta would be of the form:
Cov(UCF , Market)
β Asset 
σ 2Market
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17.7 Beta and Leverage: No Corp.Taxes
• In a world without corporate taxes, and with
riskless corporate debt, it can be shown that the
relationship between the beta of the unlevered firm
and the beta of levered equity is:
Equity
β Asset 
 β Equity
Asset
 In a world without corporate taxes, and with risky
corporate debt, it can be shown that the relationship
between the beta of the unlevered firm and the beta of
levered equity is:
Debt
Equity
β Asset 
 β Debt 
 β Equity
Asset
Asset
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17.7 Beta and Leverage: with Corp. Taxes
• In a world with corporate taxes, and riskless debt, it
can be shown that the relationship between the beta
of the unlevered firm and the beta of levered equity
is:


Debt
β Equity  1 
 (1  TC ) β Unlevered firm
 Equity



Debt
 Since 1  Equity  (1  TC )  must be more than 1 for a


levered firm, it follows that β Equity  β Unleveredfirm
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17.7 Beta and Leverage: with Corp. Taxes
• If the beta of the debt is non-zero, then:
β Equity  β Unlevered firm  (1  TC )(β Unlevered firm  β Debt ) 
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17.8 Summary and Conclusions
1. The APV formula can be written as:
Additional

Initial
UCFt
APV  
 effects of 
t
investment
t 1 (1  r0 )
debt
2. The FTE formula can be written as:
Amount 
LCFt  Initial

APV  
 

t
t 1 (1  rS )
 investment borrowed 

3. The WACC formula can be written as

Initial
UCFt


t
investment
t 1 (1  rW ACC )
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17.8 Summary and Conclusions (cont.)
4 Use the WACC or FTE if the firm's target debt to
value ratio applies to the project over its life.
5 The APV method is used if the level of debt is
known over the project’s life.
6 The beta of the equity of the firm is positively
related to the leverage of the firm.
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Appendix 17-A:The APV approach to
Valuing Leveraged Buyouts (LBOs)
• An LBO is the acquisition by a small group of investors of a
public or private company financed primarily with debt.
• In an LBO, the equity investors are expected to pay off
outstanding principal according to a specific timetable.
• The owners know that the firm’s debt-to-equity ratio will fall
and can forecast the dollar amount of debt needed to finance
future operations.
• Under these circumstances, the APV approach is more
practical than the WACC approach because the capital
structure is changing.
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The APV Approach to Valuing LBOs:
The RJR Nabisco Buyout
• In 1988, the CEO of the firm announced a bid of $75 per
share to take the firm private in a management buyout.
• Another bid of $90 per share by Kohlberg Kravis and
Roberts (KKR) was followed.
• At the end, KKR emerged from the bidding process with an
offer of $109 a share, totalling $25 billion.
• We use the APV technique to analyze KKR’s winning
strategy.
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The RJR Nabisco Buyout (cont.)
• KKR planned a significant increase in leverage with
accompanying tax benefits.
• The firm issued almost $24 billion of new debt to complete
the buyout with annual interest costs of $3 billion.
4 Steps for RJR LBO valuation
Step1: Calculating the PV of UCF for 1989-93:
PV
1988
PV
1988
$5.404 $4.311 $2.173 $2.336 $2.536





(1.14) (1.14) (1.14) (1.14) (1.14)
2
3
4
5
 $12.224 billion
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The RJR Nabisco Buyout (cont.)
Step1: Calculating the PV of UCF beyond 1993:
Assume :UCF grow at 3 % after 1993
PV
1993
PV
1988
$2.536(1.03)

 $23.746 billion
0.14  0.03
$23.746 billion

 $12.333 billion
(1.14)
5
TOTAL UNLEVERED VALUE = 12.224 +12.333 = $24.557 b
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The RJR Nabisco Buyout (cont.)
Step3: Calculating the PV of interest tax shields 1989-93:
Given: average cost of debt (pretax) = 13.5 %
$1.151 $1.021 $1.058 $1.120 $1.184
PV 




 $3.877 b
(1.135) (1.135) (1.135) (1.135) (1.135)
1988
2
3
4
5
Step4: Calculating the PV of interest tax shields beyond 1993:
•Assume: debt/assets ratio will be maintained at 25 %.
•The WACC method will be appropriate to find terminal value.
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The RJR Nabisco Buyout (cont.)
1
r  0.14  (1  0.34)(0.14  0.135)  0.141
3
s
r
W ACC
3
1
 (0.141)  0.135(1  0.34)  0.128  12.8%
4
4
PV
1993
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$2.536(1.03)

 $26.654 billion
0.128  0.03
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The RJR Nabisco Buyout (cont.)
• We know that: VL= VU + PVTS
PVTS = VL (1993)-VU(1993)
VL (1993)(from Step4) and Vu (1993)(from Step1)
PVTS = $26.654 –23.746 = $2.908 billion
$2.908 billion
PV 
 $1.544 billion
(1.135)
1988
5
Total value of interest tax shields = 1.544 + 3.877 (from Step3)
= $5.421
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The RJR Nabisco Buyout (cont.)
• Total value of RJR = Total unlevered value +
Total value of interest tax shields
= $24.557 (Step1) + 5.421 (Step 4)
= $29.978 billion
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