Chapter 18

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

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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.

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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:

2M arket

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

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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?