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ESTIMATING THE WACC - 13 pt lecture note F454 SPRING 2013

We then estimate the r for each of these comparables

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that have the same underlying business risk as does Zed. We then estimate the r for each of these “comparables” and compute their average r and use this average as our estimate of Zed’s r. So, let Project Zed be the production of a consumer electronics product, and that we identify three publicly traded manufacturers (Miko Corporation, United Industries, and Cora, Inc.) of similarly risky consumer electronic products. Miko, United, and Cora have the following characteristics. Exhibit 3. Data on Zed’s Comparables [ 0 E / 0 V ] [ 0 D / 0 V ] [ 0 0 CFin / V ] equity β E r D r CFin r r Miko .4 .5 0.1 1.375 15% 10% 12% 12.2% United 0.6 0.4 0 1.125 13% 9% N/a 11.4% Cora 0.8 0.2 0 1.000 12% 8% N/a 11.2% Average* 11.6% * 11.6% = (12.2% + 11.4% + 11.2%)/3. Using the Miko, United and Cora comparable data, we estimate the opportunity cost of capital for Zed to be Zed r = 11.6%. Again let RF r = 4% and [ M r - RF r ] = 8%. Beta measures Miko equity β = 1.375, United equity β = 1.125, and Cora equity β = 1.0 would be obtained from an external source (e.g., Bloomberg) and then used by the analyst (appraiser) to compute the equity rates for the comparables. The computation of the comparables’ equity rates is shown in (12a), (12b) and (12c) below. 15
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Estimating the WACC, page 16 of 25 Miko E r = RF r + Miko equity β [ M r - RF r ] = 4% + 1.375 [8%] = 15% (12a) United E r = RF r + United equity β [ M r - RF r ] = 4% + 1.125 [8%] = 13% (12b) Cora E r = RF r + Cora equity β [ M r - RF r ] = 4% + 1.0 [8%] = 12% (12c) STEP 2: D ETERMINE Z ED S F INANCING P ROPORTIONS , D r AND E r . Assume that the target impact of Project Zed on the firm’s equity and debt market values (that is, the financing proportions) are 60% equity, 40% debt, and no complex financing ([ Zed 0 E / Zed 0 V ] = .6, [ Zed 0 D / Zed 0 V ] = .4, and [ Zed 0 CFin / Zed 0 V ] = 0). Set Zed 0 CFin = 0 in (11), and then rearrange (11) to obtain the following equation for Zed’s equity cost of capital: Zed E r = Zed r + ( Zed r - Zed D r )[ Zed 0 D / Zed 0 E ] (13) Equation (13) has the same form as equation (8). Letting Zed 0 V be the increase in the value of the firm due to Project Zed, as noted above management has decided that [ Zed 0 E / Zed 0 V ] = .6 and [ Zed 0 D / Zed 0 V ] = .4, which implies [ Zed 0 D / Zed 0 E ] = (2/3) . Now we must estimate Zed D r . For the project, Zed D r is the incremental interest that the firm will have to pay per dollar of additional borrowing to finance Zed. The most practical approach for doing this is to estimate the interest rate that the company would have to pay on its incremental borrowing given that the project is adopted (that is, taking into account what the project will do to the risk of the firm). Suppose that this rate is 8%; thus, let Zed D r = 8%. Substitute Zed r = 11.6%, [ Zed 0 D / Zed 0 E ] = (2/3), and Zed D r = 8% into (13). We find that: Zed E r = Zed r + ( Zed r - Zed D r )[ Zed 0 D / Zed 0 E ] = 11.6% + (11.6% - 8%)[2/3] = 14% (14) So, Zed E r = 14% . Now to compute the after-tax WACC for Project Zed. 16
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Estimating the WACC, page 17 of 25 STEP 3: C OMPUTE Z ED S A FTER -T AX WACC . From Steps 1 and 2 we have for Project Zed: [ Zed 0 E / Zed 0 V ] = .6, [ Zed 0 D / Zed 0 V ] = .4, Zed D r = 8% and Zed E r = 14%. Assume that corporate tax rate T = 30%. Substituting into cost of capital equation (1) , we have: after tax,Zed WACC r - = Zed Zed Zed Zed 0 0 E D Zed Zed 0 0 E D r r V V + (1 - T) = (.6)(14%) + (.4)(8%)(.70) = 10.64% (15) The after tax,Zed WACC r - = 10.64%
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