18-0

Valuation and Capital Budgeting for the Levered firm(Chapter 18)

18-1

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

18-2

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

18-3

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:

18-4

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

18-5

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.

18-6

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

18-7

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

18-8

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

Note: This assumes we know the value created by the project. A more straightforward assumption is to assume that the ratio is 600/400, based on the amount provided by each source to fund the project. With these values, RS=11.80%.

18-9

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

Note that the chapter examples work out nicely with the perpetuity assumption, in that each approach provides the same value. With a finite life project, the values will deviate based on assumptions made, for example, the repayment of the $600.

18-10

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( CBSW ACC TRBS

BR

BS

SR −

++

+=

18-11

WACC Method

%58.7

)40.1(%)8()60.0(%)77.11()40.0(

=−××+×=

W ACC

W ACC

R

R

S

B=50.1 BS =∴ 5.1

60.05.2

5.1

5.1

5.1==

+=

+ SS

S

BS

B40.060.01 =−=

+ BS

S

Note, when calculating B/S, we are using the target ratio, not the market value which is different from FTE approach

18-12

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

18-13

A Comparison of the APV, FTE, andWACC 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.

18-14

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

18-15

Summary: APV, FTE, and WACC

Which 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

18-16

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.

A scale-enhancing project does not diversify the company's risk in any way. However, it may be beneficial, as the project is likely within the company's core competence.

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.

18-17

Beta and Leverage

Recall that an asset beta would be of the form:

2Market

Asset •

),(•

MarketUCFCov=

18-18

Beta and Leverage: No Corporate Taxes In a world without corporate taxes, and with

corporate debt ( ), it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:

EquityAsset •Asset

Equity• ×=

• In a world without corporate taxes, and with corporate debt, it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:

EquityDebtAsset •Asset

Equity•

Asset

Debt• ×+×=

0debtβ =

18-19

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 •)1(Equity

Debt1•

−×+= CT

• Since must be more than 1 for a

levered firm, it follows that βEquity > βUnlevered firm

−×+ )1(

Equity

Debt1 CT

18-20

Beta and Leverage: With Corporate Taxes If the beta of the debt is non-zero, then:

LC S

BT ×−−+= )••)(1(•• Debtfirm Unleveredfirm UnleveredEquity

18-21

Summary

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

LCFFTE

investment

Initial

)1(1

−+

=∑∞

=tt

W ACC

tW ACC R

UCFNPV

18-22

Summary

4 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.

18-23

Suggested Problems

5, 9, 13