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Chapter 18 Valuation and Capital Budgeting for the Levered Firm Notes

18.1 Adjusted Present Value (APV) Approach

•adjusted present value (APV) method is best described by the following formula: APV = NPV + NPVF

•adjusted present value (APV) base case NPV of a project’s operating cash flows plus present value of any financing benefits

•there are 4 major side effects:

1) The tax subsidy to debt. For perpetual debt, the value of the tax subsidy is TCB. (TC is the corporate tax rate, and B is the

value of the debt.) The material on valuation under corporate taxes is actually an application of the APV approach.

2) The costs of financial distress. The possibility of financial distress, and bankruptcy is particular, arises with debt financing.

Financial distress imposes costs, thereby lowering value.

3) The costs of issuing new securities. Investment bankers participate in the public issuance of corporate debt. These bankers

must be compensated for their time and effort, a cost that lowers the value of the project.

4) Subsidies to debt financing. The interest rate on debt issued by the provinces and the federal government is substantially

below the yield on debt issued by risky private corporations. Frequently, corporations are able to obtain loan guarantees

from government, lowering their borrowing costs to a government rate. This subsidy adds value.

•while each of these 4 side effects is important, the tax deduction to debt almost certainly has the highest dollar value in practice

18.2 Flow to Equity (FTE) Approach

•the flow to equity (FTE) approach is an alternative capital budgeting approach

•the formula simply calls for discounting the cash flow from the project to the equity holders of the levered firm at rS

•for a perpetuity, this becomes cash flow from project to equity holders of the levered firm / rS

•levered cash flow can be calculated directly from unlevered cash flow (UCF)

•the key here is that the difference between the cash flow that equity holders receive in an unlevered firm and the cash flow that

equity holders receive in a levered firm is the after-tax interest payment

•this can be written as UCF – LCF = (1 – TC) rBB where LCF is the cash flow to the levered equity holders

•to calculate the discount rate, rS: rS = r0 + (B / S) (1 – TC) (r0 – rB)

•the present value of the project’s LCF is LCF / rS

•the NPV of the project is simply the difference between the present value of the project’s LCF and the investment not borrowed

18.3 Weighted Average Cost of Capital (WACC) Method

•weighted average cost of capital (WACC) the average cost of capital on the firm’s existing projects and activities; the

weighted average cost of capital for the firm is calculated by weighting the cost of each source of funds by its proportion of the

total market value of the firm; it is calculated on a before- and after-tax basis

•the WACC approach begins with the insight that projects of levered firms are simultaneously financed with both debt and equity

•the cost of capital is a weighted average of the cost of debt and the cost of equity

•the formula for determining the weighted average cost of capital, rWACC, is

rWACC = [S / (S + B)] rS + [B / (S + B)] rB (1 – TC)

•the weight for equity, S / (S + B), and the weight for debt, B / (S + B), are target ratios

•target ratios are generally expressed in terms of market values, not book values

•the formula calls for discounting the unlevered cash flow of the project (UCF) at the weighted average cost of capital, rWACC

•the net present value of the project can be written algebraically as ∑ UCFt / (1 + rWACC)t – Initial investment

•if the project is a perpetuity, the net present value is UCF / rWACC – Initial investment

18.4 A Comparison of the APV, FTE, and WACC Approaches

A Suggested Guideline

•the net present value of a project is exactly the same under each of the three methods

•in theory, this should always be the case; however, one method usually provides an easier computation than another, and, in

many cases, one or more of the methods is virtually impossible computationally

•use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life

•use APV if the project’s level of debt is known over the life of the project

The Three Methods of Capital Budgeting with Leverage

•APV method ∑ UCFt / (1 + r0)t + Additional effects of debt – Initial investment

UCFt = the project’s cash flow at date t to the equity holders of an unlevered firm

r0 = cost of capital for project in an unlevered firm

•FTE method ∑ LCFt / (1 + rS)t – (Initial investment – Amount borrowed)

LCFt = the project’s cash flow at date t to the equity holders of a levered firm

rS = cost of equity capital with leverage