Capital Budgeting for the Levered FirmB.B.ChakrabartiIndian Institute of Management Calcutta

Chapter OutlineAdjusted Present Value ApproachFlows to Equity ApproachWeighted Average Cost of Capital MethodA Comparison of the APV, FTE, and WACC Approaches

Project Data for CalculationsCash revenue: $500,000 per year till infinityCash costs: 72% of salesInitial investment: $475,000Corporate tax rate, tc = 34%Cost of capital for all-equity firm, R0 = 20% Source of funding: Debt $126,229.50 @10% cost (RB) and equity $348,770.50

Adjusted Present Value ApproachAPV = NPV + NPVFThe 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 DebtThe Costs of Issuing New SecuritiesThe Costs of Financial DistressSubsidies to Debt Financing

Calculation of APVUnlevered cash flow, UCF = $500,000*(1-0.72)*(1-0.34) = $92,400NPV of the perpetual project = - Initial investment +PV of UCF (UCF/R0)= - $475,000 + $92,400/0.20= - $13,000APV = NPV + Interest tax shield (tc*B) = - $13,000+0.34*$126,229.50 = $29,918The project is acceptable based on APV.

D/E ratioPV of the project with initial investment = $475,000 + $29,918 = $504,918Amount of debt = $126,229.50 Debt to value ratio = 126,229.50/504,918 = 0.25Debt to equity ratio = 1/3

Cost of Equity and WACCCost of equity, Rs = R0+B/S*(1-tc)*(R0-RB) = 0.20+1/3*0.66*(0.20-0.10) = 0.222

WACC = *0.222+1/4*0.10*0.66 = 0.183

Flow to Equity ApproachDiscount 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 (LCFs)Step Two: Calculate RS.Step Three: Value the levered cash flows at RS.

Calculation of NPV under FTE ApproachLevered cash flow, LCF = {$500,000*(1-0.72)-10%*$126,229.50}*(1-0.34) = $84,068.85

NPV = - Equity investment + PV of LCF (LCF/RS) = - $348,770.50 + $84,068.85/0.222 = $29,918The project is acceptable using FTE approach.

WACC MethodTo find the value of the project, discount the unlevered cash flows at the weighted average cost of capital.NPV = -Initial investment+PV of UCF(UCF/WACC) = - $475,000 + $92,400/0.183 = $29,918The project is acceptable. All methods yield the same result.

A Comparison of the APV, FTE, and WACC ApproachesAll three approaches attempt the same task: valuation in the presence of debt financing.Guidelines:Use WACC or FTE if the firms target debt-to-value ratio applies to the project over the life of the project.Use the APV if the projects level of debt is known over the life of the project.In the real world, the WACC is, by far, the most widely used.

Summary: APV, FTE, and WACCAPVWACCFTEInitial Investment AllAllEquity Portion

Cash FlowsUCFUCFLCF

Discount Rates R0 RWACCRS

PV of financing effectsYesNoNo

Summary: APV, FTE, and WACCWhich approach is best?Use APV when the level of debt is constantUse WACC and FTE when the debt ratio is constantWACC is by far the most commonFTE is a reasonable choice for a highly levered firm

SummaryThe APV formula can be written as:

The FTE formula can be written as:

The WACC formula can be written as

Summary

Use the WACC or FTE if the firm's target debt to value ratio applies to the project over its life.WACC is the most commonly used by far.FTE has appeal for a firm deeply in debt.The APV method is used if the level of debt is known over the projects life.The APV method is frequently used for special situations like interest subsidies, LBOs, and leases.The beta of the equity of the firm is positively related to the leverage of the firm.