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Valuation and Capital Budgeting for the Levered Firm
Chapter 18
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
18-2
Key Concepts and Skills Understand the effects of leverage on the
value created by a project Be able to apply Adjusted Present Value
(APV), the Flows to Equity (FTE) approach, and the WACC method for valuing projects with leverage
18-3
Chapter Outline18.1 Adjusted Present Value Approach
18.2 Flows to Equity Approach
18.3 Weighted Average Cost of Capital Method
18.4 A Comparison of the APV, FTE, and WACC Approaches
18.5 Capital Budgeting When the Discount Rate Must Be Estimated
18.6 APV Example
18.7 Beta and Leverage
18-4
18.1 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
18-5
APV Example
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.
Consider a project of the Pearson Company. The timing and size of the incremental after-tax cash flows for an all-equity firm are:
18-6
APV Example 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 + NPV debt tax shield
4
1 )08.1(
20.19$50.56$
tt
APV
09.7$59.6350.56$ APV So, Pearson should accept the project with debt.
18-7
18.2 Flow 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 (LCFs) Step Two: Calculate RS.
Step Three: Value the levered cash flows at RS.
18-8
Step One: Levered Cash Flows Since the firm is using $600 of debt, the equity holders
only have to provide $400 of the initial $1,000 investment. 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
18-9
Step One: Levered Cash Flows
–$400 $221.20
CF2 = $250 – 28.80
$346.20
CF3 = $375 – 28.80
–$128.80
CF4 = $500 – 28.80 – 600
CF1 = $125 – 28.80
$96.20
0 1 2 3 4
18-10
Step Two: Calculate RS
))(1( 00 BCS RRTS
BRR
4
1432 )08.1(
20.19
)10.1(
500$
)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
P V = $943.50 + $63.59 = $1,007.09
BS
BV
To calculate the debt to equity ratio, , start with
18-11
Step Three: Valuation Discount the cash flows to equity holders at RS = 11.77%
56.28$
)1177.1(
80.128$
)1177.1(
20.346$
)1177.1(
20.221$
)1177.1(
20.96$400$
432
NPV
NPV
0 1 2 3 4
–$400 $96.20 $221.20 $346.20 –$128.80
18-12
18.3 WACC Method
To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital.
Suppose Pearson’s target debt to equity ratio is 1.50
)1( CBSWACC TRBS
BR
BS
SR
18-13
WACC Method
%58.7
)40.1(%)8()60.0(%)77.11()40.0(
WACC
WACC
R
R
S
B50.1 BS 5.1
60.05.2
5.1
5.1
5.1
SS
S
BS
B40.060.01
BS
S
18-14
WACC Method To find the value of the project, discount the
unlevered cash flows at the weighted average cost of capital
432 )0758.1(
500$
)0758.1(
375$
)0758.1(
250$
)0758.1(
125$000,1$ NPV
NPV7.58% = $6.68
18-15
18.4 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, by far, the most widely used.
18-16
Summary: APV, FTE, and WACCAPV WACC FTE
Initial Investment All All Equity Portion
Cash Flows UCF UCF LCF
Discount Rates R0 RWACC RS
PV of financing
effects Yes No No
18-17
Summary: APV, FTE, and WACCWhich approach is best? Use APV when the level of debt is constant Use WACC and FTE when the debt ratio is
constant WACC is by far the most common FTE is a reasonable choice for a highly levered
firm
18-18
18.5 Capital Budgeting When the Discount Rate Must Be Estimated 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 the assumption that the new project is somewhat riskier since it is a new entrant.
18-19
18.7 Beta and Leverage Recall that an asset beta would be of the
form:
2Market
Asset σ
),(β
MarketUCFCov
18-20
Beta and Leverage: No Corporate Taxes In a world without corporate taxes, and with riskless corporate
debt (Debt = 0), it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:
EquityAsset βAsset
Equityβ
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:
EquityDebtAsset βAsset
Equityβ
Asset
Debtβ
18-21
Beta and Leverage: With Corporate 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:
firm UnleveredEquity β)1(Equity
Debt1β
CT
Since must be more than 1 for a
levered firm, it follows that Equity > Unlevered firm
)1(
Equity
Debt1 CT
18-22
If the beta of the debt is non-zero, then:
LC S
BT )ββ)(1(ββ Debtfirm Unleveredfirm UnleveredEquity
Beta and Leverage: With Corporate Taxes
18-23
Summary1. 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
of effects
Additional
)1(1 0
tt
t
R
UCFAPV
borrowed
Amount
investment
Initial
)1(1tt
S
t
R
LCFFTE
investment
Initial
)1(1
tt
WACC
tWACC R
UCFNPV
18-24
Summary4 Use the WACC or FTE if the firm's target debt to
value ratio applies to the project over its life. WACC is the most commonly used by far. FTE has appeal for a firm deeply in debt.
5 The APV method is used if the level of debt is known over the project’s life. The APV method is frequently used for special
situations like interest subsidies, LBOs, and leases.
6 The beta of the equity of the firm is positively related to the leverage of the firm.
18-25
Quick Quiz Explain how leverage impacts the value
created by a potential project. Identify when it is appropriate to use the APV
method? The FTE approach? The WACC approach?