17-0 mcgraw-hill ryerson © 2003 mcgraw–hill ryerson limited corporate finance ross westerfield ...

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McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited

Corporate Finance Ross Westerfield Jaffe Sixth Edition

17Chapter Seventeen

Capital Budgeting for the Levered Firm

Prepared by

Gady JacobyUniversity of Manitoba

and

Sebouh AintablianAmerican University of Beirut

17-2


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 Scale-Enhancing

17.6 APV Example

17.7 Beta and Leverage

17.8 Summary and Conclusions

17-4


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 and size 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%.

• Pearson’s tax rate is 40%, so they have an interest tax 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$50.56$

tt

APV

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, let’s 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

17-8


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

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 rS for 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 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

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 TrBS

Br

BS

Sr

%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

17-13


Valuation for Pearson using WACC

• 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

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 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

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?•Use APV when the level of debt is constant•Use WACC and FTE when the debt ratio is 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 the assumption 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 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)

)(βF

MFs

RRRr

% 8.51.58% s

r

% 20.75 s

r

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STEP 2 :Determining AW’s Hypothetical All- Equity Cost of Capital. (r0)

))(1( 00 BCS rrTS

Brr

)12.0)(6.0(3

22075.0

00 rr

1825.0 0r

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STEP 3 :Determining rs for WWE’s Widget Venture

))(1( 00 BCS rrTS

Brr

)10.01825.0)(6.0(3

11825.0

sr

199.0 s

r

Assuming that the business risk of WWE and AW are the same,

NOTE : rs (WWE) < rs (AW) because D/E (WWE) < D/E (AW)

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STEP 4: Determining rWACC for WWE’s Widget Venture.

)1( CBSWACC TrBS

Br

BS

Sr

)6.0(10.04

1199.0

4

3 WACC

r

%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% 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

shieldtax

interest

shieldtax

ondepreciati PVPVPVCostAPVproject

unlevered

25.561.873,4$

)1(

)34.1(000,500

)1(

000,1001.5$

50

5

rr

mCostf

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.

Let’s 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 firm’s 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

The PV unlevered project is 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

17-26


17.6 APV Example: PV depreciation tax shield

shieldtax

interest

shieldtax

ondepreciati899,095,3$25.561.873,4$ PVPVAPV

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%

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

TDPV

17-27


17.6 APV Example: PV interest tax shield

shieldtax

interest619,513,1$899,095,3$25.561.873,4$ PVAPV

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%

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

mrTPV

17-28


17.6 APV Example: Adding it all up

Since the project has a positive APV, it looks like a go.

Let’s add the four terms in this equation:

930,189$

46.972,453619,513,1899,095,325.561.873,4$

APV

APV

17-29


17.7 Beta and Leverage

• Recall that an asset beta would be of the form:

2Market

Asset σ

),(β

MarketUCFCov

17-30


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:

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

17-31


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:

firm UnleveredEquity β)1(Equity

Debt1β

CT

Since must be more than 1 for a

levered firm, it follows that firm UnleveredEquity ββ

)1(

Equity

Debt1 CT

17-32


17.7 Beta and Leverage: with Corp. Taxes

• If the beta of the debt is non-zero, then:

LC S

BT )ββ)(1(ββ Debtfirm Unleveredfirm UnleveredEquity

17-33


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

of effects

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

17-34


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.

17-35


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:

54321988 )14.1(

536.2$

)14.1(

336.2$

)14.1(

173.2$

)14.1(

311.4$

)14.1(

404.5$ PV

billion 224.12$1988

PV

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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

billion 333.12$)14.1(

billion $23.74651988

PV

TOTAL UNLEVERED VALUE = 12.224 +12.333 = $24.557 b

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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$54321988PV

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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%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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• 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

billion 544.1$)135.1(

billion $2.90851988

PV

Total value of interest tax shields = 1.544 + 3.877 (from Step3) = $5.421

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• 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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