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1. Valuation and Capital Budgeting for
the Levered Firm
18-1

2. 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 18-2

3. 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
0 1 2 3 4
The unlevered cost of equity is R0 = 10%:
$125 $250 $375 $500
NPV10% = −$1,000 + + + +
(1.10) (1.10) (1.10) (1.10) 4
2 3
NPV10% = −$56.50
The project would be rejected by an all-equity firm: NPV < 0. 18-3

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×$600×.08 = $19.20
each year.
• The net present value of the project under leverage is:
APV = NPV + NPV debt tax shield
4
$19.20
APV = −$56.50 + ∑
t =1 (1.08) t
APV = −$56.50 + 63.59 = $7.09
• So, Pearson should accept the project with debt. 18-4

5. 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: Value the levered cash flows at RS.
18-5

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×RB×(1 – TC) = $600×.08×(1 – .40) = $28.80
18-6

7. Step One: Levered Cash Flows
CF3 = $375 – 28.80 CF4 = $500 – 28.80 – 600
CF2 = $250 – 28.80
CF1 = $125 – 28.80
–$400 $96.20 $221.20 $346.20 –$128.80
0 1 2 3 4
18-7

8. Step Two: Calculate RS
4
$125 $250 $375 $500 19.20
APV : PV = + 2
+ 3
+ 4
+∑
(1.10) (1.10) (1.10) (1.10) t =1 (1.08) t
P V = $943.50 + $63.59 = $1,007.09
B = $600 when V = $1,007.09 so S = $407.09.
RS = 11.77%
18-8

9. Step Three: Valuation
• Discount the cash flows to equity holders at RS = 11.77%
–$400 $96.20 $221.20 $346.20 –$128.80
0 1 2 3 4
$96.20 $221.20 $346.20 $128.80
FTE : NPV = −$400 + + + −
(1.1177) (1.1177) (1.1177) (1.1177) 4
2 3
NPV = $28.56
18-9

10. 18.3 WACC Method
S B
RWACC = RS + RB (1 − TC )
S+B S+B
• 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
18-10

11. WACC Method
B ∴1.5S = B
1.50 =
S
B 1 .5 S 1 .5 S
= = = 0.60 = 1 − 0.60 = 0.40
S + B S + 1 .5 S 2 .5 S+B
RWACC = (0.40) × (11.77%) + (0.60) × (8%) × (1 − .40)
RWACC = 7.58%
18-11

12. WACC Method
• To find the value of the project, discount the
unlevered cash flows at the weighted average
cost of capital
$125 $250 $375 $500
NPV = −$1,000 + + + +
(1.0758) (1.0758) 2 (1.0758)3 (1.0758) 4
NPV7.58% = $6.68
18-12

13. 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.
18-13

14. Summary: APV, FTE, and WACC
APV 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
18-14

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
18-15

16. 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.
18-16

17. 18.7 Beta and Leverage
• Recall that an asset beta would be of the
form:
Cov (UCF , Market )
β Asset =
σ2
Market
18-17

18. Beta and Leverage: No Corporate Taxes
• In a world without corporate taxes, and with riskless
corporate debt (βDebt = 0), it can be shown that the
relationship between the beta of the unlevered firm
and the beta of levered equity is:
Equity
β Asset = × β Equity
Asset
• 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:
Debt Equity
β Asset = × β Debt + × β Equity
Asset Asset
18-18

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:
 Debt 
β Equity = 1 +
 Equity × (1 − TC ) β Unlevered firm

 
 
• Since 1 + Debt × (1 − TC )  must be more than 1 for a
 Equity 
 
levered firm, it follows that βEquity > βUnlevered firm
18-19

20. Beta and Leverage: With Corporate
Taxes
• If the beta of the debt is non-zero, then:
B
β Equity = β Unlevered firm + (1 − TC )(β Unlevered firm − β Debt ) ×
SL
18-20

21. Summary
1. The APV formula can be written as:
Additional
∞
UCFt Initial
APV = ∑ + effects of −
t =1 (1 + R0 ) t investment
debt
4. The FTE formula can be written as:
∞
LCFt  Initial Amount 
FTE = ∑ −
 investment − borrowed 

t =1 (1 + RS ) 
t

7. The WACC formula can be written as
∞
UCFt Initial
NPVWACC =∑ −
t =1 (1 + RWACC )
t
investment 18-21

22. Summary
2 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.
3 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.
4 The beta of the equity of the firm is positively
related to the leverage of the firm.
18-22