World-Wide Enterprises (WWE) is planning to enter into a new line of business (widget industry) ... the appropriate discount rate for WWE to use for its widget ...
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Capital Budgeting for the Levered Firm
Corporate Finance Ross Westerfield Jaffe
University of Manitoba
American University of Beirut
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
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%:
The project would be rejected by an all-equity firm: NPV < 0.
CF3 = $375 -28.80
CF2 = $250 -28.80
CF1 = $125-28.80
0 1 2 3 4Step One: Levered Cash Flows for Pearson
-$400 $96.20 $221.20 $346.20 -$128.80
0 1 2 3 4
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
Which approach is best?
are Not Scale-Enhancing
Borrowing rate for AW is 8 %
Assuming that the business risk of WWE and AW
are the same,
NOTE : rs (WWE) < rs (AW) because D/E (WWE) < D/E (AW)
Worldwide Trousers, Inc. is considering a $5 million expansion of their existing business.
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.
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%.
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%
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%
Let’s add the four terms in this equation:
Since the project has a positive APV, it looks like a go.
5 The APV method is used if the level of debt is known over the project’s life.
6 The beta of the equity of the firm is positively related to the leverage of the firm.
4 Steps for RJR LBO valuation
Step1: Calculating the PV of UCF for 1989-93:
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
Step3: Calculating the PV of interest tax shields 1989-93:
Given: average cost of debt (pretax) = 13.5 %
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)
= $24.557 (Step1) + 5.421 (Step 4)
= $29.978 billion