RJR Case Study

5/21/2018 RJR Case Study

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McGraw-Hill Ryerson 2003 McGrawHi ll Ryerson Limited

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

17 32


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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

17 33


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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.

17 36


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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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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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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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%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 + 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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Total value of RJR = Total unlevered value +Total value of interest tax shields

= $24.557 (Step1) + 5.421 (Step 4)

= $29.978 billion

RJR Case Study

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