Textbook Solutions - 11th edition.docx

8 the book value of debt is the total par value of

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The aftertax rate is more relevant because that is the actual cost to the company. 8. The book value of debt is the total par value of all outstanding debt, so: BV D = $85,000,000 + 35,000,000 BV D = $120,000,000 To find the market value of debt, we find the price of the bonds and multiply by the number of bonds. Alternatively, we can multiply the price quote of the bond times the par value of the bonds. Doing so, we find: MV D = .93($85,000,000) + .59($35,000,000) MV D = $79,050,000 + 20,650,000 MV D = $99,700,000 The YTM of the zero coupon bonds is: P Z = $590 = $1,000(PVIF R %,24 ) R = 2.223% YTM = 2 × 2.223% = 4.45% So, the aftertax cost of the zero coupon bonds is: R Z = .0445(1 – .35) R Z = .0289, or 2.89%
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The aftertax cost of debt for the company is the weighted average of the aftertax cost of debt for all outstanding bond issues. We need to use the market value weights of the bonds. The total aftertax cost of debt for the company is: R D = .0495($79.05 / $99.70) + .0289($20.65 / $99.70) R D = .0452, or 4.52% 9. a. Using the equation to calculate the WACC, we find: WACC = .70(.11) + .05(.05) + .25(.07)(1 – .35) WACC = .0909, or 9.09% b. Since interest is tax deductible and dividends are not, we must look at the aftertax cost of debt, which is: R D  =  .07(1 – .35) R D   = .0455, or 4.55% Hence, on an aftertax basis, debt is cheaper than the preferred stock. 10. Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find: WACC = .12(1 / 1.35) + .06(.35 / 1.35)(1 – .35) WACC = .0990, or 9.90% 11. Here we have the WACC and need to find the debt-equity ratio of the company. Setting up the WACC equation, we find: WACC = .0850 = .11( E/V ) + .061( D/V )(1 – .35) Rearranging the equation, we find: .0850( V/E ) = .11 + .061(.65)( D/E ) Now we must realize that the V/E is just the equity multiplier, which is equal to: V/E = 1 + D/E .0850( D/E + 1) = .11 + .03965( D/E ) Now we can solve for D/E as: .04535( D/E ) = .025 D/E = .5513 12. a. The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company’s debt, so: BV E = 8,000,000($7) = $56,000,000 BV D = $85,000,000 + 50,000,000 = $135,000,000
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CHAPTER 14 -  188 So, the total value of the company is: V = $56,000,000 + 135,000,000 = $191,000,000 And the book value weights of equity and debt are: E/V = $56,000,000 / $191,000,000 = .2932 D/V = 1 – E/V = .7068 b. The market value of equity is the share price times the number of shares, so: MV E = 8,000,000($73) = $584,000,000 Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is: MV D = .97($85,000,000) + 1.08($50,000,000) = $136,450,000 This makes the total market value of the company: V = $584,000,000 + 136,450,000 = $720,450,000 And the market value weights of equity and debt are: E/V = $584,000,000 / $720,450,000 = .8106 D/V = 1 – E/V = .1894 c. The market value weights are more relevant. 13. First, we will find the cost of equity for the company. The information provided allows us to solve for the cost of equity using the dividend growth model, so: R E = [$3.90(1.06) / $73] + .06 R E = .1166, or 11.66% Next, we need to find the YTM on both bond issues. Doing so, we find: P 1 = $970 = $35(PVIFA R%,42 ) + $1,000(PVIF R %,42 ) R = 3.641% YTM = 3.641% × 2 = 7.28% P 2 = $1,080 = $40(PVIFA R%,12 ) + $1,000(PVIF R%,12 ) R = 3.187% YTM = 3.187% × 2 = 6.37%
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To find the weighted average aftertax cost of debt, we need the weight of each bond as a percentage of the total debt. We find: x D1 = .97($85,000,000) / $136,450,000 x D1 = .6043 x D2 = 1.08($50,000,000) / $136,450,000 x D2 = .3957 Now we can multiply the weighted average cost of debt times one minus the tax rate to find the weighted average aftertax cost of debt. This gives us: R D = (1 – .35)[(.6043)(.0728) + (.3957)(.0637)] R D = .0450, or 4.50%
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