Erna Corp. has 8 million shares of common stock outstanding. The current share p

Question

Erna Corp. has 8 million shares of common stock outstanding. The current share price is $73, and the book value per share is $7. Erna Corp. also has two bond issues outstanding. The first bond issue has a face value of $85 million, has a 7 percent coupon, and sells for 97 percent of par. The second issue has a face value of $50 million, has an 8 percent coupon, and sells for 108 percent of par. The first issue matures in 21 years, the second in 6 years. Suppose the most recent dividend was $4.10 and the dividend growth rate is 6 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 35 percent. What is the company’s WACC? (Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

Answer:

Value of stock: $73 * 8m = 584m
Rate of equity...use Gordon growth model and solve for "r": P0 = D1 / (r - g), where D1 = D0(1+g)
D1 = 4.10(1.06) = 4.346...if you round to 4.35...
73 = 4.35 / (r - 0.06)
0.05959 = r - 0.06
r = 0.11959, or 11.959% < "re" for rate equity

Value of first bond: 85m * 0.97 = 82,450,000
Value of second bond: 50m * 1.08 = 54m

Total capital: 584m + 82,450,000 + 54m = 720,450,000
weight of equity: 584,000,000 / 720,450,000 = 0.81060 <"we"
weight of debt: (1 - weight of equity) = 0.18940< "wd"

Rate of debt "rd" ...calc IRR of each and then weight the rates
bond 1: Cash flows are:
CF0: (82,450,000)
CFs 1 - 41: 85m * (0.07/2) = 2.975m <semi-annual coupon
CF 42: coupon + par paid at maturity: 2.975m + 85m = 87,975,000
IRR: 3.64051 * 2 = 7.28102%

bond 2: cash flows are:
CF0: (54m)
CFs 1 - 11: 50m * (0.08/2) = 2m <semi-annual coupon
CF 12: coupon + par paid at maturity: 2m + 50m = 52m
IRR: 3.18729 * 2 = 6.37458%

Total debt: 54m + 82,450,000 = 136,450,000
weight of bond 2: 54m / 136,450,000 = 0.39575
weight of bond 1: (1 - weight of bond2 ) = 0.60425
rate debt "rd" is (w bond1 * rate bond1) + (w bond2 * rate bond2) = (0.60425 * 0.0728102) + (0.39575 * 0.0637458) = 0.044 + 0.02523 = 0.06922 or 6.922% <"rd"
After Tax rate of debt "ATrd): rd * (1 - tx) = 0.06922 * ( 1 - 0.35) = 0.04499

WACC = (we * re) + (wd * ATrd)
= (0.81060 * 0.11959) + (0.18940 * 0.04499)
= 0.09694 + 0.00852
= 0.10546, or 10.546%

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