Questions-Cost of Capital

Q1) Stock in Dragula Industries has a beta of 1.1. The market risk premium is 7 percent, and T-bills are currently yielding 4.5 percent. The company’s most recent dividend was $1.70 per share, and dividends are expected to grow at a 6 percent annual rate indefinitely. If the stock sells for $39 per share, what is your best estimate of the company’s cost of equity?  We have the information available to calculate the cost of equity using the CAPM and the dividend growth model. Using the CAPM, we find:  RE = 0.045 + 1.1(0.07) = 0.1220, or 12.20% And using the dividend growth model, the cost of equity is  RE = [$1.70(1.06)/$39] + 0.06 = 0.1062, or 10.62% Both estimates of the cost of equity seem reasonable. If we remember the historical return on large capitalization stocks, the estimate from the CAPM model is about the same as the historical average, and the estimate from the dividend growth model is about one percent lower than the historical average, so we cannot definitively say one of the estimates is incorrect. Given this, we will use the average of the two, so:  RE = (0.1220 + 0.1062)/2 = 0.1141, or 11.41%

Q2 Holdup Bank has an issue of preferred stock with a $4.25 stated dividend that just sold for $92 per share. What is the bank’s cost of preferred stock? The cost of preferred stock is the dividend payment divided by the price, so:  RP = $4.25/$92 = 0.0462, or 4.62%

Q3) Mudvayne, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 18 years to maturity that is quoted at 107 percent of face value. The issue makes semiannual payments and has an embedded cost of 6 percent annually. What is the company’s pretax cost of debt? If the tax rate is 35 percent, what is the aftertax cost of debt? The pretax cost of debt is the YTM of the company’s bonds, so:  P0 = $1,070 = $30(PVIFAR%,36) + $1,000(PVIFR%,36)R = 2.694%YTM = 2 × 2.694% = 5.39% And the aftertax cost of debt is: RD = 0.0539(1 – 0.35) = 0.0350, or 3.50%

Q4) Jiminy’s Cricket Farm issued a 30-year, 8 percent semiannual bond 3 years ago. The bond currently sells for 93 percent of its face value. The company’s tax rate is 35 percent. Suppose the book value of the debt issue is $60 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 10 years left to maturity; the book value of this issue is $35 million, and the bonds sell for 57 percent of par. What is the company’s total book value of debt? What is the company’s total market value of debt? What is your best estimate of the aftertax cost of debt? The book value of debt is the total par value of all outstanding debt, so:  BVD = $60,000,000 + 35,000,000 = $95,000,000 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 = 0.93($60,000,000) + 0.57($35,000,000)MVD = $55,800,000 + 19,950,000MVD = $75,750,000 The YTM of the company's coupon bonds is:  P0 = $930 = $40(PVIFAR%,54) + $1,000(PVIFR%,54)R = 4.338%YTM = 2 × 4.338% = 8.68% The aftertax cost of debt is: RD = 0.0868(1 – 0.35) = 0.0564, or 5.64%The YTM of the zero coupon bonds is: PZ = $570 = $1,000(PVIFR%,20)R = 2.850%YTM = 2 × 2.850% = 5.70% So, the aftertax cost of the zero coupon bonds is:  RZ = 0.0570(1 – 0.35) = 0.0371, or 3.71% 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 = 0.0564($55.8/$75.75) + 0.0371($19.95/$75.75) = 0.0513, or 5.13%

Q5) Sixx AM Manufacturing has a target debt−equity ratio of .45. Its cost of equity is 13 percent, and its cost of debt is 6 percent. If the tax rate is 35 percent, what is the company’s WACC? Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find:  WACC = 0.13(1/1.45) + 0.06(0.45/1.45)(1 – 0.35) = 0.1018, or 10.18%