第十七章杠杆企业的估价与资本预算

flows at the weighted average cost of capital.
• Suppose Pearson Inc. target debt to equity ratio is 1.50
1.50 B S
1.5SB
B 1.5S 1.50.60 S 10.600.40
SB S1.5S 2.5
The project would be rejected by an all-equity firm: NPV < 0.
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17-10
17.3 WACC Method for Pearson
S
B
rWA CSC BrSSBrB(1T C)
• To find the value of the project, discount the unlevered cash
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17-3
APV Example
Consider a project of the Pearson Company, the timing and size of the incremental after-tax cash flows for an allequity firm are:
17.6 APV Example
17.7 Beta and Leverage
17.8 Summary and Conclusions
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• 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
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17-6
17.2 Flows to Equity Approach
ห้องสมุดไป่ตู้• Discount the cash flow from the project to the equity holders of the levered firm at the cost of levered equity capital, rS.
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17-5
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:
SB
r WA C (0 .C 4) 0 (1.7 1 % 7 (0 ).6) 0 (8 % (1 ) .4)0
r WA C 7 .5 C % 8
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17-4
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.
-$1,000 $125
$250
$375
$500
0
1
2
3
4
The unlevered cost of equity is r0 = 10%: NP 1% 0 V$1,00(0 $ 11 .12 )0 5 (1 $.2 1)5 0 20(1 $.3 1)7 0 35(1 $.5 1)0 0 4 0 NP 1% 0 V$5.5 60
17-8
Step Two: Calculate rS for Pearson
rSr0B S(1TC)r(0rB)
• To calculate the debt to equity ratio, B/S, start with the debt to value ratio. Note that the value of the project is
rS .1 0 $ 4 $ 6.0 0 (1 7 9 0 .4)0 1 ( .0 .0) 8 1.7 1 % 7
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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
0
1
2
3
4
$9.2 60$22 .21 0$34 .26 0$12 .88 0 PV $40 (1 0.11) 7(1.7 11)27 (1 7.11)37 (1 7 .11)47 PV $2.5 86
17-0
第十七章杠杆企业 的估价与资本预算
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17-1
Chapter Outline
17.1 Adjusted Present Value Approach
17-2
17.1 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):
17-11
Valuation for Pearson using WACC
• To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital
N P $ 1 V ,0 0 ( 1 $ .0 1 07 ) 2 ( 1 5 5 .$ 0 2 8 7 )5 2 5 ( 1 0 .$ 0 3 87 ) 7 3 5 ( 1 5 .$ 0 5 87 )0 4
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 When the Discount Rate Must Be Estimated
CF3 = $375 -28.80 CF2 = $250 -28.80 CF1 = $125-28.80
CF4 = $500 -28.80 -600
-$400
$96.20 $221.20 $346.20 -$128.80
0
1
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3
4
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P V $ 12 $ 2 55 $ 0 37 $ 5 50 4 0 1.2 90 (1 .1)0 (1 .1)2 0(1 .1)3 0(1 .1)4 0t 1(1 .0)t8
P V $ 9.5 4 6 0 3 .5 3 9 $ 1 ,0.0 09 7
• B = $600 when V = $1,007.09 so S = $407.09.
• 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.
NP loV an$600 t 41$60 (1 .0 .0 8 )8 t(1.4)(1 $.6 0)0 8 4 0
NP loV an$6.3 59
APV NPV NPVF
A P $ 5 .5 V 6 6 0 .5 3 $ 9 7 .09
• Which is the same answer as before.
• 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
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17-7
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.
NP6.8V% 8 $6.68
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17-12 17.4 A Comparison of the APV, FTE, and WACC Approaches
• The net present value of the project under leverage is:
APV NPV NPVF
4 $19.20
APV$56.50t1(1.08 )t
A P $ 5 .5 V 6 6 0 .5 3 $ 9 7 .09
• So, Pearson should accept the project with debt.