# Valuation and Capital Budgeting for the Levered Firm

**Topics:**Depreciation, Weighted average cost of capital, Cost of capital

**Pages:**26 (5347 words)

**Published:**March 18, 2012

VALUATION AND CAPITAL BUDGETING FOR THE LEVERED FIRM

Answers to Concepts Review and Critical Thinking Questions

1.APV is equal to the NPV of the project (i.e. the value of the project for an unlevered firm) plus the NPV of financing side effects.

2.The WACC is based on a target debt level while the APV is based on the amount of debt.

3.FTE uses levered cash flow and other methods use unlevered cash flow.

4.The WACC method does not explicitly include the interest cash flows, but it does implicitly include the interest cost in the WACC. If he insists that the interest payments are explicitly shown, you should use the FTE method.

5.You can estimate the unlevered beta from a levered beta. The unlevered beta is the beta of the assets of the firm; as such, it is a measure of the business risk. Note that the unlevered beta will always be lower than the levered beta (assuming the betas are positive). The difference is due to the leverage of the company. Thus, the second risk factor measured by a levered beta is the financial risk of the company.

Solutions to Questions and Problems

NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.

Basic

1.a.The maximum price that the company should be willing to pay for the fleet of cars with all-equity funding is the price that makes the NPV of the transaction equal to zero. The NPV equation for the project is:

NPV = –Purchase Price + PV[(1 – tC )(EBTD)] + PV(Depreciation Tax Shield)

If we let P equal the purchase price of the fleet, then the NPV is:

NPV = –P + (1 – .35)($140,000)PVIFA13%,5 + (.35)(P/5)PVIFA13%,5

Setting the NPV equal to zero and solving for the purchase price, we find:

0 = –P + (1 – .35)($140,000)PVIFA13%,5 + (.35)(P/5)PVIFA13%,5

P = $320,068.04 + (P)(0.35/5)PVIFA13%,5

P = $320,068.04 + .2462P

.7538P = $320,068.04

P = $424,609.54

b.The adjusted present value (APV) of a project equals the net present value of the project if it were funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt, so:

APV = NPV(All-Equity) + NPV(Financing Side Effects)

So, the NPV of each part of the APV equation is:

NPV(All-Equity)

NPV = –Purchase Price + PV[(1 – tC )(EBTD)] + PV(Depreciation Tax Shield)

The company paid $395,000 for the fleet of cars. Because this fleet will be fully depreciated over five years using the straight-line method, annual depreciation expense equals:

Depreciation = $395,000/5

Depreciation = $79,000

So, the NPV of an all-equity project is:

NPV = –$395,000 + (1 – 0.35)($140,000)PVIFA13%,5 + (0.35)($79,000)PVIFA13%,5

NPV = $22,319.49

NPV(Financing Side Effects)

The net present value of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt, so:

NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments)

Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt RB. So, the NPV of the financing side effects are:

NPV = $260,000 – (1 – 0.35)(0.08)($260,000)PVIFA8%,5 – [$260,000/(1.08)5]

NPV = $29,066.93

So, the APV of the project is:

APV = NPV(All-Equity) + NPV(Financing Side Effects)

APV = $22,319.49 + 29,066.93

APV = $51,386.42

2.The adjusted present value (APV) of a project equals the net present value of the project if it were funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of...

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