Adjusted Present Value Approach • 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
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: -RM1,000 RM125 RM250 RM375 RM500 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.
APV Example (continued) • Now, imagine that the firm finances the project with RM600 of debt at rB = 8%. • Pearson’s tax rate is 40%, so they have an interest tax shield worth TCBrB = 0.40 × RM600 × 0.08 = RM19.20 each year.
The net present value of the project under leverage is: PV of All-Equity project • So, Pearson should accept the project with debt.
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:
PV of After-tax payments PV of loan repayments • Which is the same answer as before.
Flows 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 • Step Two: Calculate rS. • Step Three: Valuation of the levered cash flows at rS.
Step One: Levered Cash Flows for Pearson • Since the firm is using RM600 of debt, the equity holders only have to come up with RM400 of the initial RM1,000. • Thus, CF0 = -RM400 • Each period, the equity holders must pay interest expense. • The after-tax cost of the interest is B×rB×(1-TC) = RM600×.08×(1-.40) = RM28.80
CF4 = RM500 -28.80 -600 CF3 = RM375 -28.80 CF2 = RM250 -28.80 CF1 = RM125-28.80 RM96.20 RM221.20 RM346.20 -RM128.80 0 1 2 3 4 -RM400
Step Two: Calculate rS for Pearson • To calculate the debt to equity ratio, B/S, start with the debt to value ratio. Note that the value of the project is
B = RM600 when V = RM1,007.09 so S = RM407.09.
Step Three: Valuation for Pearson • Discount the cash flows to equity holders at rs = 11.77%
-RM400 RM96.20 RM221.20 RM346.20 -RM128.80 0 1 2 3 4
To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital. • Suppose Pearson Inc. target debt to equity ratio is 1.50
Valuation for Pearson using WACC • To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital
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 the most widely used by far.
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 Which approach is best? • Use APV when the level of debt is constant • Use WACC and FTE when the debt ratio is constant
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.
APV Example: Worldwide Trousers, Inc. is considering a RM5 million expansion of their existing business. • The initial expense will be depreciated straight-line over 5 years to zero salvage value; the pretax salvage value in year 5 will be RM500,000. • The project will generate pretax earnings of RM1,500,000 per year, and not change the risk level of the firm. • The firm can obtain a 5-year RM3,000,000 loan at 12.5% to partially finance the project. • If the project were financed with all equity, the cost of capital would be 18%. The corporate tax rate is 34%, and the risk-free rate is 4%. • The project will require a RM100,000 investment in net working capital. Calculate the APV.
APV Example: Cost Let’s work our way through the four terms in this equation:
Cost of the project • The cost of the project is not RM5,000,000. • 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.
PV unlevered project The PV unlevered project is the present value of the unlevered cash flows discounted at the unlevered cost of capital, 18%.
PV depreciation tax shield 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% Project: RM5 mil Lifespan: 5 years Salvage Value: 0 Capital Allowance: RM1 mil
APV Example: PV interest tax shield 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%
APV Example: Adding it all up Let’s add the four terms in this equation: Since the project has a positive APV, it looks like a go.
Beta and Leverage • Recall that an asset beta would be of the form:
Beta and Leverage: No Corp.Taxes • In a world without corporate taxes, and with riskless corporate debt, it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:
Beta and Leverage: No Corp.Taxes • 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:
Since must be more than 1 for a levered firm, it follows that Beta and Leverage: with Corp. 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:
Beta and Leverage: with Corp. Taxes • If the beta of the debt is non-zero, then:
Summary and Conclusions • The APV formula can be written as: • The FTE formula can be written as: • The WACC formula can be written as
Summary and Conclusions • Use the WACC or FTE if the firm's target debt to value ratio applies to the project over its life. • The APV method is used if the level of debt is known over the project’s life. • The beta of the equity of the firm is positively related to the leverage of the firm.