Erna Corp. has 7 million shares of common stock outstanding. The current share p

Question

Erna Corp. has 7 million shares of common stock outstanding. The current share price is $86, and the book value per share is $5. Erna Corp. also has two bond issues outstanding. The first bond issue has a face value of $70 million, has a coupon rate of 9 percent, and sells for 96 percent of par. The second issue has a face value of $45 million, has a coupon rate of 10 percent, and sells for 104 percent of par. The first issue matures in 24 years, the second in 6 years. Suppose the most recent dividend was $5.80 and the dividend growth rate is 7 percent. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 34 percent. What is the company’s WACC?

Explanation / Answer

The WACC = 12.98%

The Calculations are given below:

SPECIFIC COST OF CAPITAL:

1) Cost of Equity Kd = (D1/P0)+ g = (5.8*1.07/86) + .07 = 0.0722 + 0.07 = 0.1422 = 14.22 %

2) Cost of first bond Kd1. The value of Kd1 can be obtained by solving the following equation, by trial and error:

            67.2 = 70 * PVIF Kd1, 48 + 3.15 (1-0.34) * PVIFA Kd1, 48

Using discount rate of 3% for half year, we have PV = 70* 0.24 + 2.079 * 25.27 = 69.33 $

Using discount rate of 4%, PV = 70*0.15 + 2.079*21.2 = 10.5 + 44.07 = 54.07 $

Interpolating we have Kd1 = 3+ (69.33-67.2)/(69.33-54.07 ) = 3 + 2.13/15.26 = 3 + 0..14= 3.14 %

Annual rate is 3.14 * 2 = 6.28 %

2) Cost of second bond Kd2. The value of Kd2 can be obtained by solving the following equation, by trial and error:

            46.8 = 45 * PVIF Kd2, 12 + 2.25(1-0.34) * PVIFA Kd2, 12

   Using discount rate of 3% for half year, we have PV = 45* 0.701 + 1.485 * 9.954 = 46.32 $

Using discount rate of 4%, PV = 45*0.625 + 1.485*9.385 = 10.5 + 44.07 = 42.06 $

Interpolating we have Kd2 = 3+ (1.32/4.26) = 3 + 0.31 = 3.31 %

The annual rate will be 3.31 * 2 = 6.62 %

THE WEIGHTED AVERAGE COST OF DEBT = (6.28*70 + 6.62*45)/115 = 6.41 %

THE WACC OF THE COMPANY WOULD BE, BASED ON MARKET VALUE WEIGHTS = 12.98 %

as calculated below:

CALCULATION OF WACC Book Book Market Market Specific WCC WACC Value Value Value Value Cost of BV MV Weight Weight Weight Capital Weights Weights Equity 35 0.23 602 0.84 14.22 3.32 11.96 Debt 115 0.77 114 0.16 6.41 4.91 1.02 150 716 8.23 12.98

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