Dinklage Corp. has 6 million shares of common stock outstanding. The current sha
ID: 2718061 • Letter: D
Question
Dinklage Corp. has 6 million shares of common stock outstanding. The current share price is $72, and the book value per share is $7. The company also has two bond issues outstanding. The first bond issue has a face value of $70 million, a coupon rate of 7 percent, and sells for 97 percent of par. The second issue has a face value of $50 million, a coupon rate of 8 percent, and sells for 106 percent of par. The first issue matures in 22 years, the second in 6 years. Suppose the most recent dividend was $4.40 and the dividend growth rate is 6 percent. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 35 percent. What is the company’s WACC?
Explanation / Answer
Calculation of cost of debt for First Bond
Face Value =$ 70 Million
Coupon Rate =7% semi-annual payment
Semi-annual coupon amount = $70,000,000 * 7% * 0.5 = $ 2,450,000
Time to maturity = 22 years or 22*2 = 44 semi-annual periods
Current Price = 97% of par value = $ 70,000,000 * 0.97 = $ 67,900,000
Let r be pre-tax semi-annual cost of debt, then current price of the bond issue can be calculated as
$ 67,900,000 = $ 2,450,000 * [(1-(1/(1+r)^44))/r] + $ 70,000,000/(1+r)^44
$ 67,900,000 - $ 2,450,000 * [(1-(1/(1+r)^44))/r] - $ 70,000,000/(1+r)^44 = 0
If r = 4% (annual rate of 8%), then LHS will be
= $ 67,900,000 - $ 2,450,000 * [(1-(1/(1+0.04)^44))/0.04] - $ 70,000,000/(1+0.04)^44
= $ 67,900,000 - $ 2,450,000 * [(1-(1/5.6165151)/0.04] - $ 70,000,000/5.6165151
= $ 67,900,000 - $ 2,450,000 * [(1-0.1780463)/0.04] - $ 70,000,000 * 0.1780463
= $ 67,900,000 - $ 2,450,000 * [0.8219537/0.04] - $ 70,000,000 * 0.1780463
= $ 67,900,000 - $ 2,450,000 * 20.548841 - $ 70,000,000 * 0.1780463
= $ 67,900,000 - $ 50,344,661.17 - $12,463,244.38
= $ 5,092,094.452
At a semi-annual rate of 3.50% (annual rate of 7%), the present value of the bond is equal to par value of $ 70,000,000. This is because when ytm is equal coupon rate price of bond is equal to par value
At 3.5%, LHS will be
= $ 67,900,000 - $ 2,450,000 * 22.282791 - $ 70,000,000 * 0.2201023
= $ 67,900,000 - $ 54,592,838 - $15,407162
= $ 67,900,000 - $ 70,000,000
= -$2,100,000
Semi-annual YTM = 0.035 + (-2100000 * (0.035-0.04)) / (5092094.452-(-2100000)
Semi-annual YTM = 0.035 + (10500/7192094.452)
Semi-annual YTM = 0.035 + 0.0014599363
Semi-annual YTM = 0.0364599363
Annual YTM = 0.0364599363 * 2 = 0.07291987 or 7.29% (rounded off)
Calculation of cost of debt for Second Bond
Face Value =$ 50 Million
Coupon Rate =8% semi-annual payment
Semi-annual coupon amount = $50,000,000 * 8% * 0.5 = $ 2,000,000
Time to maturity = 6 years or 6*2 = 12 semi-annual periods
Current Price = 106% of par value = $ 50,000,000 * 1.06 = $ 53,000,000
Let r be pre-tax semi-annual cost of debt, then current price of the bond issue can be calculated as
$ 53,000,000 = $ 2,000,000 * [(1-(1/(1+r)^12))/r] + $ 50,000,000/(1+r)^12
$ 53,000,000 - $ 2,000,000 * [(1-(1/(1+r)^12))/r] - $ 50,000,000/(1+r)^12 = 0
If r = 3.25% (annual rate of 6.5%), then LHS will be
= $ 53,000,000 - $ 2,000,000 * [(1-(1/(1+0.0325)^12))/0.0325] - $ 50,000,000/(1+0.0325)^12
= $ 53,000,000 - $ 2,000,000 * [(1-(1/1.4678468)/0.0325] - $ 50,000,000/1.4678468
= $ 53,000,000 - $ 2,000,000 * [(1-0.68127)/0.0325] - $ 50,000,000 * 0.68127
= $ 53,000,000 - $ 2,000,000 * [0.31873/0.0325] - $ 50,000,000 * 0.68127
= $ 53,000,000 - $ 2,000,000 * 9.8070764 - $ 50,000,000 * 0.68127
= $ 53,000,000 - $ 19,614,512.78 - $ 34,063,500.87
= -$677,653.646
Let r = 3.50% (annual yield of 7%), LHS will be
= $ 53,000,000 - $ 2,000,000 * [(1-(1/(1+0.035)^12))/0.035] - $ 50,000,000/(1+0.035)^12
= $ 53,000,000 - $ 2,000,000 * [(1-(1/1.5110687)/0.035] - $ 50,000,000/1.5110687
= $ 53,000,000 - $ 2,000,000 * [(1-0.6617833)/0.035] - $ 50,000,000 * 0.6617833
= $ 53,000,000 - $ 2,000,000 * [0.3382167/0.035] - $ 50,000,000 * 0.6617833
= $ 53,000,000 - $ 2,000,000 * 9.663343 - $ 50,000,000 * 0.6617833
= $ 53,000,000 - $ 19,326,668.67 - $ 33,089,164.91
= $584,166.4164
Semi-annual YTM = 0.0325 + ((-677653.646 * (0.0325-0.035))/(584166.4164-(-677653.646))
Semi-annual YTM = 0.0325 + (1694.134115/1261820.0624)
Semi-annual YTM = 0.0325 + 0.0013426 = 0.0338426 or 3.3842611%
YTM = 3.3842611 * 2 = 6.768522% or 6.77% (rounded off)
Market Value of First Bond = $ 67.9 Million
Market Value of Second Bond = $ 53 Million
Market Value of Total Debt = $ 120.9 Million
Pre-tax weighted cost of Debt = ($67.9 Million/$ 120.9 Million) * 7.29% +($53 Million/$ 120.9 Million) * 6.77%
Pre-tax weighted cost of debt = 0.5616 * 7.29% + 0.4384 * 6.77%
= 4.094064% + 2.967968%
= 7.062032% or 7.06% (rounded off)
Calculation of cost of equity
Current Share Price =$ 72
Most recent dividend = $4.40
Dividend growth rate = 6%
Expected Dividend next year = $ 4.40 * 1.06 = $ 4.664
Current Price = Expected Dividend next year / (required rate of return – growth rate)
Required rate of return – growth rate = Expected Dividend next year /Current Price
Required rate of return = (Expected Dividend next year / Current price) + growth rate
Required rate of return = ($ 4.664 /$ 72) + 0.06
= 0.064778 + 0.06 = 0.124777 or 12.48% (rounded off)
Total outstanding equity shares =6 Million
Current Price = $ 72
Market Value of Equity = 6 Million * $ 72 = $ 432 Million
Total Market Value of Debt = $ 120.9 Million
Weight of Equity = $ 432 Million /($ 432 Million + $ 120.9 Million) = 0.7813
Weight of Debt = $ 120.9 Million /($ 432 Million + $ 120.9 Million) = 0.2187
Tax rate = 35%
Weighted Average Cost of Capital (WACC) = 0.7813 * 12.48% + 0.2187 * 7.06% * (1-0.35)
= 9.750624% + 1.0036143%
= 10.7542383% or 10.75% (rounded off)
Weighted Average Cost of Capital of the firm = 10.75%
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.