ESTIMATING THE WACC - 13 pt lecture note F454 SPRING 2013

# When the firm issues new debt to finance project zed

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When the firm issues new debt to finance Project Zed, it receives an amount from the lender that is equal to the present value of what the firm will pay to the lender in interest and principal in the future. Borrowing is, at least approximately, a zero net present value activity for the borrower and for the lender (in a competitive market, lenders earn just their cost of capital, implying that lending for the lender is a zero NPV activity). The NPV of Project Zed goes to the firm’s (Todd Corporation’s) shareholders. This means that the market value of the additional debt issued to finance Project Zed, Zed 0 D equals the amount received by the firm to finance the initial outlay; that is: Zed,Debt 0 I = Zed 0 D (20) 19

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Estimating the WACC, page 20 of 25 Since [ Zed 0 D / Zed 0 V ] = .4 (see assumption immediately preceding equation (13)) and Zed 0 V = \$150 million (see (18a-b)), it follows that: Zed 0 D = 0 0 Zed Zed D V Zed 0 V = .4 (\$150 million) = \$60 million (21) Equations (20) and (21) imply that: Zed,Debt 0 I = \$60 million (22) Using (16): Zed,Equity 0 I = Zed 0 I - Zed,Debt 0 I = \$100 million - \$60 million = \$40 million (23) Thus, given that Zed 0 V = \$150 million and Zed 0 I = \$100 million, in order to meet market value target [ Zed 0 D / Zed 0 V ] = .4, the funds to finance Project Zed’s initial cost ( Zed 0 I = \$100 million) must be in the form of Zed,Debt 0 I = \$60 million and Zed,Equity 0 I = \$40 million . 20
Estimating the WACC, page 21 of 25 ANOTHER ILLUSTRATION: Blarney Beer Corporation plans to introduce a new ale, Debenture Ale. This project (Project Debenture) will require an initial outlay of \$40 million, and is judged by management to be significantly riskier than Blarney’s existing product line. STEP 1: E STIMATE P ROJECT D EBENTURE S O PPORTUNITY C OST OF C APITAL Deb r : Project Debenture will be financed with additional Blarney Corporation debt and equity; there will be no complex financing ( Deb 0 CFin = 0). The opportunity cost of capital for Debenture Ale is therefore defined as follows: Deb r = Deb Deb Deb Deb 0 0 E D Deb Deb 0 0 E D r r V V + + Deb 0 Deb 0 CFin V Deb 0 CFin = Deb Deb Deb Deb 0 0 E D Deb Deb 0 0 E D r r V V + (24) Blarney has identified four relatively small publicly traded breweries that have risks similar to Project Debenture. They have the following financial characteristics. Exhibit 4. Debenture Ale Comparables [ 0 E / 0 V ] [ 0 D / 0 V ] [ 0 0 CFin / V ] equity β E r D r CFin r r Spike .4 .5 .1 1.25 14% 8% 16% 11.2% Bluebeard .2 .8 0 1.50 16% 12% n/a 12.8% Firebird .7 .3 0 1.125 13% 10% n/a 12.1% Gazelle .5 .5 0 1.25 14% 11% n/a 12.5% Average* 12.15% * 12.15 = (11.2% + 12.8+ 12.1% + 12.5%)/4. The opportunity cost of capital is computed using equation (9). The estimated opportunity cost of capital for Project Debenture is Deb r = 12.15%. 21

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Estimating the WACC, page 22 of 25 The comparables’ equity rates (the E r ) are computed using the equity β shown in Exhibit 4. Assuming that RF r = 4% and [ M r - RF r ] = 8%, it follows that (using, from Exhibit 4, Spike equity β = 1.25, Bluebeard equity β = 1.50, Firebird equity β = 1.125 and Gazelle equity β = 1.25): Spike E r = RF r + Spike equity β [ M r - RF r ] = 4% + 1.25 [8%] = 14% (25a) Bluebeard E r =
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