Chapter Seventeen
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17 0 mcgraw hill ryerson

Chapter Seventeen

17

Capital Budgeting for the Levered Firm

Corporate Finance Ross Westerfield  Jaffe

Sixth Edition

Prepared by

Gady Jacoby

University of Manitoba

and

Sebouh Aintablian

American University of Beirut


Prospectus

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.


Chapter outline

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 1 adjusted present value approach

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


Apv example

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:

-$1,000$125 $250 $375 $500

01 2 3 4

The unlevered cost of equity is r0 = 10%:

The project would be rejected by an all-equity firm: NPV < 0.


Apv example continued

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:

  • So, Pearson should accept the project with debt.


Apv example continued1

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:

  • Which is the same answer as before.


17 2 flows to equity approach

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.


Step one levered cash flows for pearson

CF4 = $500 -28.80 -600

CF3 = $375 -28.80

CF2 = $250 -28.80

CF1 = $125-28.80

$96.20

$221.20

$346.20

-$128.80

01 2 3 4

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

-$400


Step two calculate r s for pearson

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

  • B = $600 when V = $1,007.09 so S = $407.09.


Step three valuation for pearson

Step Three: Valuation for Pearson

  • Discount the cash flows to equity holders at rS = 11.77%

-$400 $96.20 $221.20 $346.20 -$128.80

01 2 3 4


17 3 wacc method for pearson

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.


Valuation for pearson using wacc

Valuation for Pearson using WACC

  • To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital


17 4 a comparison of the apv fte and wacc approaches

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.


Summary apv fte and wacc

Summary: APV, FTE, and WACC

APVWACCFTE

Initial Investment AllAllEquity Portion

Cash FlowsUCFUCFLCF

Discount Rates r0 rWACCrS

PV of financing effectsYesNoNo

Which approach is best?

  • Use APV when the level of debt is constant

  • Use WACC and FTE when the debt ratio is constant


17 0 mcgraw hill ryerson

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-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 an example

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?


17 5 capital budgeting for projects that are not scale enhancing an example1

17.5 Capital Budgeting for Projects that are Not Scale-Enhancing: An example

  • A four step procedure to calculate discount rates:

  • Determining AW’s cost of Equity Capital (rs)

  • Determining AW’s Hypothetical All-Equity Cost of Capital. (r0)

  • Determining rs for WWE’s Widget Venture

  • Determining rWACC for WWE’s Widget Venture.


Step 1 determining aw s cost of equity capital r s

STEP 1:Determining AW’s cost of Equity Capital (rs)


Step 2 determining aw s hypothetical all equity cost of capital r 0

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


Step 3 determining r s for wwe s widget venture

STEP 3 :Determining rs for WWE’s Widget Venture

Assuming that the business risk of WWE and AW

are the same,

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


Step 4 determining r wacc for wwe s widget venture

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


17 6 apv example

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.


17 6 apv example cost

17.6 APV Example: Cost

Let’s work our way through the four terms in this equation:

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. Salvage value should have the same risk as the rest of the firm’s assets, so we use r0.


17 6 apv example pv unlevered project

17.6 APV Example: PV unlevered project

Turning our attention to the second term,

The PV unlevered project is the present value of the unlevered cash flows discounted at the unlevered cost of capital, 18%.


17 6 apv example pv depreciation tax shield

17.6 APV Example: PV depreciation tax shield

Turning our attention to the third term,

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%


17 6 apv example pv interest tax shield

17.6 APV Example: PV interest tax shield

Turning our attention to the last term,

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%


17 6 apv example adding it all up

17.6 APV Example: Adding it all up

Let’s add the four terms in this equation:

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


17 7 beta and leverage

17.7 Beta and Leverage

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


17 7 beta and leverage no corp taxes

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:

  • 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:


17 7 beta and leverage with corp taxes

  • Since must be more than 1 for a

    levered firm, it follows that

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:


17 7 beta and leverage with corp taxes1

17.7 Beta and Leverage: with Corp. Taxes

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


17 8 summary and conclusions

17.8 Summary and Conclusions

  • The APV formula can be written as:

  • The FTE formula can be written as:

  • The WACC formula can be written as


17 8 summary and conclusions cont

17.8 Summary and Conclusions (cont.)

  • Use the WACC or FTE if the firm's target debt to value ratio applies to the project over its life.

    5The APV method is used if the level of debt is known over the project’s life.

    6The beta of the equity of the firm is positively related to the leverage of the firm.


Appendix 17 a the apv approach to valuing leveraged buyouts lbos

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.


The apv approach to valuing lbos the rjr nabisco buyout

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.


The rjr nabisco buyout cont

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:


The rjr nabisco buyout cont1

The RJR Nabisco Buyout (cont.)

Step1: Calculating the PV of UCF beyond 1993:

Assume :UCF grow at 3 % after 1993

TOTAL UNLEVERED VALUE = 12.224 +12.333 = $24.557 b


The rjr nabisco buyout cont2

The RJR Nabisco Buyout (cont.)

Step3: Calculating the PV of interest tax shields 1989-93:

Given: average cost of debt (pretax) = 13.5 %

  • 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.


The rjr nabisco buyout cont3

The RJR Nabisco Buyout (cont.)


The rjr nabisco buyout cont4

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

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

= $5.421


The rjr nabisco buyout cont5

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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