Erna Corp. has 10 million shares of common stock outstanding. The current share

Question

Erna Corp. has 10 million shares of common stock outstanding. The current share price is $82, 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 $85 million, has a coupon rate of 5 percent, and sells for 97 percent of par. The second issue has a face value of $55 million, has a coupon rate of 6 percent, and sells for 105 percent of par. The first issue matures in 20 years, the second in 9 years. Suppose the most recent dividend was $5.40 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 38 percent. What is the company’s WACC?

Explanation / Answer

Step 1: Calculate After-Tax Cost of Debt (Bonds)

The cost of debt (bonds) can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Coupon Payment, PV = Bond Price and FV = Face Value of Bonds.

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Bond 1

Here, Nper = 20*2 = 40, PMT = 1,000*5%*1/2 = $25, PV = 1,000*97% = $970 and FV = $1,000 [we use 2 since the bond is semi-annual]

Using these values in the above function/formula for Rate, we get,

After-Tax Cost of Debt (Bond 1) = Rate(40,25,-970,1000)*2*(1-38%) = 3.25%

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Bond 2

Here, Nper = 9*2 = 18, PMT = 1,000*6%*1/2 = $30, PV = 1,000*105% = $1,050 and FV = $1,000 [we use 2 since the bond is semi-annual]

Using these values in the above function/formula for Rate, we get,

After-Tax Cost of Debt (Bond 1) = Rate(18,30,-1050,1000)*2*(1-38%) = 3.28%

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Step 2: Calculate Cost of Equity

The cost of equity can be calculated with the use of following formula:

Cost of Equity = Dividend*(1+Growth Rate)/Current Stock + Growth Rate

Using the information provided in the question, we get,

Cost of Equity = 5.40*(1+6%)/82 + 6% = 12.98%

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Step 3: Calculate Weights

The weights are calculated with the use of market value as follows:

Market Value of Bond 1 = Face Value of Bonds*Selling Price Percentage = 85,000,000*97% = $82,450,000

Market Value of Bond 2 = Face Value of Bonds*Selling Price Percentage = 55,000,000*105% = $57,750,000

Market Value of Equity = Number of Common Shares*Current Selling Price = 10,000,000*82 = $820,000,000

Total Market Value of Debt = 82,450,000 + 57,750,000 = $140,200,000

Total Market Value = 140,200,000 + 820,000,000 = $960,200,000

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Weight of Debt = 140,200,000/960,200,000

Weight of Equity = 820,000,000/960,200,000

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Step 4: Calculate WACC

The WACC can be calculated with the use of following formula:

WACC = Weighted Average After-Tax Cost of Debt*Weight of Debt + Cost of Equity*Weight of Equity

Using the values calculated above, we get,

Weighted Average After-Tax Cost of Debt = 3.25%*82,450,000/140,200,000 + 3.28%*57,750,000/140,200,000 = 3.26%

WACC = 3.26%*140,200,000/960,200,000 + 12.98%*820,000,000/960,200,000 = 11.56%

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