Previously assumed a discount rate currently one firm

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(Previously assumed a discount rate) Currently one firm in the industry: Financing Debt: .40 Equity: .60 Beta: 1.5 iRate: .12 Tc = .40 Mkt Risk premium = .085 Riskless iRate = .08 rB = .10 What is the appropriate discount rate for this venture for firm 2 Could use APV, FTE or WACC thus the appropriate discount rates are r0, rS, and rWACC 1. Determing Firm 1’s cost of equity Capital (rS) ( Use security market line (SML) of Chapter 10 ) Rs = RF + Beta x (RbarM - RF) = .08 + 1.5 x .085 = .2075 NOTE: RbarM = the expected return on the market portfolio RF = the risk-free rate 2. Determing Firm 1’s Hypothetical All-Equity Cost of Capital (r0) (**APV**) rS = r0 + B/S (1 – Tc) (r0 – rB) .2075 = r0 + .4/.6 (.6) (r0 - .12) r0 = .1825 At this pont … assume risk of their venture is about equal to the risk of firms in industry Thus, hypothetical discount rate of Firm 1 if all-equity financed = .1825. NOTE: This would be used if APV approach since APV uses r0 3. Determine rS (*** FTE approach ***) rS = r0 + B/S (1-Tc) x (r0 – rB) = .1825 + 1/3 (.60) x (.1825 - .10) = .199 Firm 1’s cost of equity capital (.199) < Firm 2’s (.2075) NOTE: This occutrs b/c Firm 2 has a higher debt / equity Note both firms are assumed to have the same business risk 4. Determing rWACC (***WACC approach***) rWACC = B/ S+B x rB (1-Tc) + S/ S+B x rS = 1/4 x .10 (.6) + 3/4 x .199 = .16425 NOTE: rS is determined from the beta of the firm’s stock. SEE ch. 12 … beta can easily be estimated for any publicly traded firm APV Example: *Firms generally set a target Debt / Equity ratio (Thus … use WACC and FTE) APV does not work here but is preferred when there are side benefits and side costs to debt In this example: TAX SUSIDY to debt , FLOTATION COSTS and INTEREST SUBSIDY come into play. 10MM (1) project that will last five years This implies straight –line depreciation of 2MM/yr Cash Revenue - Cash Expenses = 3.5MM Tc = .34 Risk-free rate rB = .10 Cost of unlevered Equity r0 = .20 Depreciation tax shield = Depreciation x (Tc) = 2MM x .34 = 680k (2) Rev - Expenses = Rev - Expenses x (1-Tc) = 3.5M x (.66) = 2.31M (3) Cash Flow Projections C0 C1 C2 C3 C4 C5 (1) Initial 10M (2) Dep. Tax Sh. 680k 680k 680k 680k 680k (3) Rev – expenses 2.31M 2.31M 2.31M 2.31M 2.31M To use APV approach: Sum (All-equity value + Additional effects of debt) (A) (B) (A) All Equity Value NPV = Initial Cost + Depreciation Tax Shield + PV(Cash Rev – expenses) = -10MM + 680k x 1 - ( 1 )^5 + 2.310M x 1 - ( 1 ) ^5 .10 1.10 .20 1.20 = -513,951 Depreciation tax shield is discounted at the riskless rate of .10 Revenue and Expenses are discounted at the higher rate of .20 Equity flotation costs would make the NPV more negative.

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