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Corporate FinanceRoss Westerfield Jaffe
Sixth Edition
17
Chapter Seventeen
Capital Budgeting for the
Levered Firm
Prepared by
Gady Jacoby
University of Manitoba
and
Sebouh Aintablian
American University of
Beirut
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Prospectus
Recall that there are three questions in corporatefinance.
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 Approach17.2 Flows to Equity Approach
17.3 Weighted Average Cost of Capital Method
17.4 A Comparison of the APV, FTE, and WACCApproaches
17.5 Capital Budgeting for Projects that are Not Scale-Enhancing
17.6 APV Example
17.7 Beta and Leverage
17.8 Summary and Conclusions
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17.1 Adjusted Present Value Approach
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
NPVFNPVAPV
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APV Example
Consider a project of the Pearson Company, the timing andsize of the incremental after-tax cash flows for an all-equity firm are:
0 1 2 3 4
-$1,000 $125 $250 $375 $500
50.56$
)10.1(
500$
)10.1(
375$
)10.1(
250$
)10.1(
125$000,1$
%10
432%10
NPV
NPV
The unlevered cost of equity is r0= 10%:
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%.
Pearsons tax rate is 40%, so they have an interesttax shield worth TCBrB= .40$600.08 = $19.20
each year.
NPVFNPVAPV
The net present value of the project under leverage is:
4
1 )08.1(
20.19$
50.56$t
tAPV
09.7$59.6350.56$ APV
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, lets calculate the actual
NPV of the loan:
NPVFNPVAPV
09.7$59.6350.56$ APV
Which is the same answer as before.
59.63$
)08.1(
600$
)08.1(
)4.1(08.600$600$ 4
4
1
loan
ttloan
NPV
NPV
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17.2 Flows to Equity Approach
Discount the cash flow from the project to theequity 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 tocome 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 isBrB(1-TC) = $600.08(1-.40) = $28.80
0 1 2 3 4
-$400 $221.20
CF2= $250 -28.80
$346.20
CF3= $375 -28.80
-$128.80
CF4= $500 -28.80 -600
CF1= $125-28.80
$96.20
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Step Two: Calculate rSfor Pearson
To calculate the debt-to-equity ratio,B/S, start with the debt
to value ratio. Note that the value of the project is
))(1( 00 BCS rrTSBrr
4
1432 )08.1(
20.19
)10.1(
500$
)10.1(
375$
)10.1(
250$
)10.1(
125$
tt
PV
B= $600 when V= $1,007.09 so S= $407.09.
%77.11)08.10)(.40.1(
09.407$
600$10. Sr
09.007,1$59.6350.943$ PV
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Step Three: Valuation for Pearson
Discount the cash flows to equity holders at rS= 11.77%
0 1 2 3 4
-$400 $96.20 $221.20 $346.20 -$128.80
56.28$
)1177.1(
80.128$
)1177.1(
20.346$
)1177.1(
20.221$
)1177.1(
20.96$400$
432
PV
PV
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17.3 WACC Method for Pearson
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.
)1( CBSWACC TrBSBr
BSSr
%58.7
)40.1(%)8()60.0(%)77.11()40.0(
WACC
WACC
r
r
S
B50.1 BS 5.1
60.05.25.1
5.15.1
SSS
BSB 40.060.01
BSS
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Valuation for Pearson using WACC
To find the value of the project, discount theunlevered cash flows at the weighted average cost
of capital
432 )0758.1(
500$
)0758.1(
375$
)0758.1(
250$
)0758.1(
125$
000,1$
NPV
68.6$%88.6 NPV
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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 WACCorFTEif the firms target debt-to-value ratioapplies to the project over the life of the project.
Use theAPVif the projects level of debt is known over
the life of the project.
In the real world, the WACCis the most widely usedapproach by far.
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Summary: APV, FTE, and WACC
APV WACC FTEInitial Investment All All Equity Portion
Cash Flows UCF UCF LCF
Discount Rates r0 rWACC rS
PV of financing effects Yes No No
Which approach is best?
UseAPVwhen the levelof debt is constantUse WACCandFTEwhen the debt ratiois constant
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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-scale-enhancing 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 theassumption that the new project is somewhat riskier
since it is a new entrant.
17.5 Capital Budgeting for Projects that
are Not Scale-Enhancing
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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 anew 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 AWs cost of Equity Capital (rs)
2. Determining AWs Hypothetical All-Equity Cost of
Capital. (r0)
3. Determining rsfor WWEs Widget Venture
4. Determining rWACCfor WWEs Widget Venture.
STEP 1 D t i i AW t f E it
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STEP 1:Determining AWs cost of Equity
Capital (rs)
)(F
MFs
RRRr
%8.51.58% sr
%20.75sr
STEP 2 D t i i AW H th ti l All
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STEP 2 :Determining AWs Hypothetical All-
Equity Cost of Capital. (r0)
))(1( 00 BCS rrTS
Brr
)12.0)(6.0(322075.0
00 rr
1825.00
r
STEP 3 :Determining r for WWEs Widget
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STEP 3 :Determining rsfor WWEs Widget
Venture
))(1( 00 BCS rrTS
Brr
)10.01825.0)(6.0(3
11825.0
s
r
199.0s
r
Assuming that the business risk of WWE and AWare the same,
NOTE : rs (WWE)< rs (AW) because D/E (WWE) < D/E (AW)
STEP 4: Determining r for WWEs Widget
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STEP 4: Determining rWACCfor WWE s Widget
Venture.
)1(CBSWACC
TrBS
Br
BS
Sr
)6.0(10.041199.0
43
WACCr
%425.1616425.0 WACC
r
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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% topartially 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-freerate is 4%.
The project will require a $100,000 investment in net workingcapital.
Calculate the APV.
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17.6 APV Example: Cost
shieldtax
interest
shieldtax
ondepreciati PVPVPVCostAPVproject
unlevered
25.561.873,4$
)1(
)34.1(000,500
)1(
000,1001.5$
5
0
5
rrmCost
f
The cost of the project is not $5,000,000.
We must include the round trip in and out of net working
capital and the after-tax salvage value.
Lets work our way through the four terms in this equation:
NWC is riskless, so
we discount it at rf
.
Salvage value should
have the same risk as
the rest of the firms
assets, so we use r0.
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17.6 APV Example:PV unlevered project
shieldtax
interest
shieldtax
ondepreciati25.561.873,4$ PVPVPVAPVproject
unlevered
ThePV unlevered projectis the present value of the unlevered cash
flows discounted at the unlevered cost of capital, 18%.
Turning our attention to the second term,
899,095,3$
)18.1(
)34.1(5.1$
)1(
5
1
5
1
project
unlevered
tt
tt
o
t
project
unlevered
PV
m
r
UCFPV
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17.6 APV Example:PV depreciation tax shield
shieldtax
interest
shieldtax
ondepreciati899,095,3$25.561.873,4$ PVPVAPV
ThePV depreciation tax shieldis the present value of the tax
savings due to depreciation discounted at the risk free rate,
at rf = 4%
Turning our attention to the third term,
619,513,1$)04.1(
34.1$
)1(
5
1
5
1shieldtax
ondepreciati
tt
tt
f
C
m
r
TD
PV
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17.6 APV Example:PV interest tax shield
shieldtax
interest619,513,1$899,095,3$25.561.873,4$ PVAPV
ThePV interest tax shieldis the present value of the tax savingsdue to interest expense discounted at the firms debt rate, at
rD = 12.5%
Turning our attention to the last term,
46.972,453)125.1(
500,127
)125.1(
3$125.034.0
)1(
3$
5
1shieldtax
interest
5
1
5
1shieldtax
interest
tt
tt
tt
D
DC
PV
m
r
mrT
PV
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17.6 APV Example: Adding it all up
Since the project has a positive APV, it looks like a go.
Lets add the four terms in this equation:
930,189$
46.972,453619,513,1899,095,325.561.873,4$
APV
APV
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17.7 Beta and Leverage
Recall that an asset beta would be of the form:
2
Market
Asset
),(
MarketUCFCov
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17.7 Beta and Leverage: No Corp.Taxes
In a world without corporate taxes, and withrisklesscorporate debt, it can be shown that therelationship between the beta of the unlevered firmand the beta of levered equity is:
EquityAsset AssetEquity
In a world without corporate taxes, and with riskycorporate debt, it can be shown that the relationship
between the beta of the unlevered firm and the beta oflevered equity is:
EquityDebtAsset Asset
Equity
Asset
Debt
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17.7 Beta and Leverage: with Corp. Taxes
In a world with corporate taxes, and riskless debt, itcan be shown that the relationship between the betaof the unlevered firm and the beta of levered equityis:
firmUnleveredEquity )1(EquityDebt1
CT
Since must be more than 1 for a
levered firm, it follows that firmUnleveredEquity
)1(
EquityDebt1 CT
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17.7 Beta and Leverage: with Corp. Taxes
If the beta of the debt is non-zero, then:
L
CS
BT ))(1( DebtfirmUnleveredfirmUnleveredEquity
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17.8 Summary and Conclusions
1. The APV formula can be written as:
2. The FTE formula can be written as:
3. The WACC formula can be written as
investment
Initial
debt
ofeffects
Additional
)1(1 0
tt
t
r
UCFAPV
borrowed
Amount
investment
Initial
)1(1tt
S
t
r
LCFAPV
investment
Initial
)1(1
tt
WACC
t
r
UCF
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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 projects life.
6 The beta of the equity of the firm is positively
related to the leverage of the firm.
17 34 A di 17 A Th APV h
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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 apublic 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 firms debt-to-equity ratio will falland 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 capitalstructure is changing.
17 35 Th APV A h V l i LBO
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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 KKRs winning
strategy.
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The RJR Nabisco Buyout (cont.)
KKR planned a significant increase in leverage withaccompanying tax benefits.
The firm issued almost $24 billion of new debt to complete
the buyout with annual interest costs of $3 billion.
4 Steps for RJR LBO valuationStep1: Calculating the PV of UCF for 1989-93:
54321988 )14.1(
536.2$
)14.1(
336.2$
)14.1(
173.2$
)14.1(
311.4$
)14.1(
404.5$PV
billion224.12$1988PV
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The RJR Nabisco Buyout (cont.)
Step1: Calculating the PV of UCF beyond 1993:Assume :UCF grow at 3 % after 1993
billion$23.74603.014.0
)03.1(536.2$1993 PV
billion333.12$
)14.1(
billion$23.74651988
PV
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 %
b$3.877)135.1(
184.1$
)135.1(
120.1$
)135.1(
058.1$
)135.1(
021.1$
)135.1(
151.1$54321988
PV
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.)
%8.12128.0)34.01(135.04
1)141.0(
4
3
WACCr
141.0)135.014.0)(34.01(3
114.0
sr
billion$26.65403.0128.0
)03.1(536.2$1993
PV
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The RJR Nabisco Buyout (cont.)
We know that: VL= VU + PVTSPVTS = VL (1993)-VU(1993)
VL (1993)(from Step4) and Vu (1993)(from Step1)
PVTS = $26.65423.746 = $2.908 billion
billion544.1$
)135.1(
billion$2.90851988
PV
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