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Unformatted text preview: incorrect. Given this, we would use the average of the two, so: RE = (.1180 + .1058)/2 = .1119 or 11.19% 4. The pretax cost of debt is the YTM of the company’s bonds, so: P0 = $950 = $40(PVIFAR%,24) + $1,000(PVIFR%,24) R = 4.339% YTM = 2 × 4.339% = 8.68% And the aftertax cost of debt is: RD = .0868 (1 – .35) = .0564 or 5.64% 5. a. The pretax cost of debt is the YTM of the company’s bonds, so: P0 = $1,080 = $35(PVIFAR%,46) + $1,000(PVIFR%,46) R = 3.167% YTM = 2 × 3.167% = 6.33% 310 b. The aftertax cost of debt is: RD = .0633(1 – .35) = .0412 or 4.12% c. 6. The aftertax rate is more relevant because that is the actual cost to the company. The book value of debt is the total par value of all outstanding debt, so: BVD = $60,000,000 + 80,000,000 = $140,000,000 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: MVD = 1.08($60,000,000) + .73($80,000,000) = $123,200,000 The YTM of the zero coupon bonds is: PZ = $730 = $1,000(PVIFR%,14) R = 2.273% YTM = 2 × 2.273% = 4.55% So, the aftertax cost of the zero coupon bonds is: RZ = .0455(1 – .35) = .0296 or 2.96% 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: RD = .0412($64.8/$123.2) + .0296($58.4/$123.2) = .0357 or 3.57% 7. Using the equation to calculate the WACC, we find: WACC = .70(.15) + .30(.08)(1 – .35) = .1206 or 12.06% 8. Here we need to use the debtequity ratio to calculate the WACC. Doing so, we find: WACC = .17(1/1.45) + .10(.45/1.45)(1 – .35) = .1374 or 13.74% 9. Here we have the WACC and need to find the debtequity ratio of the company. Setting up the WACC equation, we find: WACC = .0980 = .15(E/V) + .0750(D/V)(1 – .35) Rearranging the equation, we find: .0980(V/E) = .15 + .0750(.65)(D/E) Now we must realize that the V/E is just the equity multiplier, which is equal to: 311 V/E = 1 + D/E .0980(D/E + 1) = .15 + .04875(D/E) Now we can solve for D/E as: .04925(D/E) = .052 D/E = 1.0558 10. 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: BVE = 7,500,000($4) = $30,000,000 BVD = $60,000,000 + 50,000,000 = $110,000,000 So, the total value of the company is: V = $30,000,000 + 110,000,000 = $140,000,000 And the book value weights of equity and debt are: E/V = $30,000,000/$140,000,000 = .2143 D/V = 1 – E/V = .7857 b. The market value of equity is the share price times the number of shares, so: MVE = 7,500,000($49) = $367,500,000 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: MVD = .93($60,000,000) + .965($50,000,000) = $104,050,000 This makes the total market value of the company: V = $367,500,000 + 104,050,000 = $471,550,000 And the market value weights of equity and debt are: E/V = $367,500,000/$471,550,000 = .7793 D/V = 1 – E/V = .2207 The market value weights are more relevant. c. 11. 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 CAPM, so: RE = .052 + 1.2(.07) = .1360 or 13.60% 312 Next, we need to find the YTM on both bond issues. Doing so, we find: P1 = $930 = $35(PVIFAR%,20) + $1,000(PVIFR%,20) R = 4.016% YTM = 4.016% × 2 = 8.03% P2 = $965 = $32.5(PVIFAR%,12) + $1,000(PVIFR%,12) R = 3.496% YTM = 3.496% × 2 = 7.23% 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: wD1 = .93($60,000,000)/$104,050,000 = .536 wD2 = .965($50,000,000)/$104,050,000 = .464 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: RD = (1 – .35)[(.536)(.0803) + (.464)(.0723)] = .0498 or 4.98% Using these costs and the weight of debt we calculated earlier, the WACC is: WACC = .7793(.1360) + .2207(.0498) = .1170 or 11.70% 12. a. Using the equation to calculate WACC, we find: WACC = .112 = (1/1.65)(.15) + (.65/1.65)(1 – .35)RD RD = .0824 or 8.24% b. Using the equation to calculate WACC, we find: WACC = .112 = (1/1.65)RE + (.65/1.65)(.064) RE = .1432 or 14.32% 13. We will begin by finding the market value of each type of financing. We find: MVD = 5,000($1,000)(1.03) = $5,150,000 MVE = 160,000($57) = $9,120,000 And the total market value of the firm is: V = $5,150,000 + 9,120,000 = $14,270,000 Now, we can find the cost of equity using the CAPM. The cost of equity is: RE = .06 + 1.10(.07) = .1370 or 13.70% 313 The cost of debt is the YTM of the bonds, so: P0 = $1,030 = $40(PVIFAR%,40) + $1,000(PVIFR%,40) R = 3.851% YTM = 3.851% × 2 = 7.70% And the aftertax cost of debt is: RD = (1 – .35)(.0770) = .0501 or 5.01% Now we have all of the components to calculate the WACC....
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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