ESTIMATING THE WACC - 13 pt lecture note F454 SPRING 2013

# Rf r bluebeard equity β m r rf r 4 15 8 16 25b

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RF r + Bluebeard equity β [ M r - RF r ] = 4% + 1.5 [8%] = 16% (25b) Firebird E r = RF r + Firebird equity β [ M r - RF r ] = 4% + 1.125 [8%] = 13% (25c) Gazelle E r = RF r + Gazelle equity β [ M r - RF r ] = 4% + 1.25 [8%] = 14% (25d) STEP 2: D ETERMINE P ROJECT D EBENTURE S F INANCING P ROPORTIONS , Deb D r AND Deb E r . Project Debenture will be financed with additional Blarney Corporation debt and equity; there will be no complex financing ( Deb 0 CFin = 0). Therefore, analogous to (13), we have: Deb E r = Deb r + ( Deb r - Deb D r )[ Deb 0 D / Deb 0 E ] (26) Let Deb 0 V be the value of Project Debenture (the present value of Project Debenture’s expected future FCF using the WACC in equation (28) below as the discount rate), and let Deb 0 E and Deb 0 D be the market values of the portions of Project Debenture’s cash flows going to Blarney Beer’s equity and the added Blarney Beer debt, respectively. Thus, Deb 0 V = Deb 0 E + Deb 0 D . Suppose that management has set at its target the market value financing proportions at [ Deb 0 E / Deb 0 V ] = .75 and [ Deb 0 D / Deb 0 V ] = .25, which implies that [ Deb 0 D / Deb 0 E ] = (1/3) . Next we must estimate Deb D r . For Project Debenture, Deb D r is the incremental interest that Blarney Beer will have to pay per dollar of additional borrowing to 22

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Estimating the WACC, page 23 of 25 finance Project Debenture. Suppose that Blarney Beer would have to pay 10% on its added borrowing if Project Debenture were adopted (that is, taking into account what Project Debenture would do to Blarney Beer’s risk). Thus, assume that, for Project Debenture, Deb D r = 10%. Substituting Deb r = 12.15%, [ Deb 0 D / Deb 0 E ] = (1/3), and Deb D r = 10% into equation (26) , we have: Deb E r = 12.15% + (12.15% - 10%)[1/3] = 12.87% (27) STEP 3: C OMPUTE P ROJECT D EBENTURE S WACC . From Steps 1 and 2 we have for Project Debenture: [ Deb 0 E / Deb 0 V ] = .75, [ Deb 0 D / Deb 0 V ] = .25, Deb D r = 10% and Deb E r = 12.87%. Assume that T = 34%. Substituting into cost of capital equation (1), we have: after tax,Deb WACC r - = Deb Deb Deb Deb 0 0 E D Deb Deb 0 0 E D r r V V + (1 - T) = (.75)(12.87%) + (.25)(10%)(.66) = 11.3% (28) The after tax,Deb WACC r - = 11.3% would be used to discount Project Debenture’s expected future FCF to compute the value of Project Debenture. Project Debenture’s NPV would equal that amount minus the \$40 million initial cost of Project Debenture Ale. EVALUATING PROJECT DEBENTURE (optional reading) Rate after tax,Deb WACC r - has been estimated to be 11.3 percent. The evaluation of Project Debenture now requires the computation of the Project Debenture’s NPV (Step 4); and the determination of the method of financing Project Debenture’s initial outlay so that the target market value proportions assumed in the cost of 23
Estimating the WACC, page 24 of 25 capital estimation will be achieved (Step 5). Paralleling the Project Zed analysis, define the following terms. Deb 0 V = present value of the future free cash flow from Project Debenture Deb 0 I = initial outlay for Project Debenture Deb,Debt 0 I = portion of Deb 0 I that is provided by new borrowing Deb,Equity 0 I = portion of Deb 0 I that is provided by equity financing We know that: Deb 0 I = Deb,Debt 0 I + Deb,Equity 0 I (29) Deb 0 NPV = Deb 0 V - Deb 0 I (30) S TEP 4. D ETERMINING THE NPV OF P ROJECT D EBENTURE .

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