My homework question is question 4, but it is based off of question 3 Calculatin

Question

My homework question is question 4, but it is based off of question 3 Calculating Cost of Debt Shanken Corp. issued a 30-year, 5.9 percent semiannual bond 6 years ago. The bond currently sells for 108 percent of its face value. The company's tax rate is 35 percent. a. What is the pretax cost of debt? b. What is the aftertax cost of debt? c. Which is more relevant, the pretax or the aftertax cost of debt? Why? Calculating Cost of Debt For the firm in the previous problem, suppose the book value of the debt issue is $35 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 12 years left to maturity; the book value of this issue is $80 million and the bonds sell for 61 percent of par. What is the company's total book value of debt? The total market value? What is your best estimate of the aftertax cost of debt now? 3. 4.

Explanation / Answer

3. Face value of the bond = $100

Selling Price of the bond is 108% of the Face value which is $108 ($100*108%)

Time to Maturity will be 24 years since the bond was issued 6 years ago. Again since the bonds are paying semi-annual payments then time to maturity in semi-annual periods will be (24*2 = 48 semi-annual periods)

Coupon Payments (full year) = $100*5.9% = 5.9

Coupons (half Yearly) = $2.95

So, Price of the coupon = Coupon Interest * pvifa (ytm%, n years) + Face Value of the bond * pvif (ytm%, n years)

108 = 2.95* pvifa (ytm%, 48) + 100* pvif (ytm%, 48)

Interpolating the results we get,

Let us suppose that ytm% = 3%

108 = 2.95*25.27 + 100*0.242

108 = 98.75

Again ytm% = 2.5%

108 =2.95* 27.78 + 100*0.306

108 = 112.55

Or, (3-2.5) %/ (3-r)% = 98.75 -112.55/ (98.75-108)

Or, 0.5%/ (3-r)% = -13.8/-9.25

Or, 0.5*9.25/13.8 = 3-r

Or, 3-r = 0.335

Or, r = 2.665%

So, effective interest rate yearly would be = {(1.02665)^2 -1}*100 = 5.40%

Again Tax rate is 35%

So, After Tax cost of Debt = 5.4%* (1-0.35) = 3.51%

4) Book Value of the Debt of this Issue is $35 million

Again companies issues, new zero coupon bond;

So we need to calculate the yield to maturity of the bond

Let us suppose that the par value of bond is $100

Time to Maturity is 12 years

Selling Price of the bond is 61% of the bond so the Market Price of the bond is $61 ($100*61%)

So, Price of the bond = Coupon Interest* pvifa (ytm%, n years) + Face Value * pvif (ytm%, n years)

Or, 61 = 0*pvifa (ytm%, 12 yrs) + 100* pvif (ytm%, 12 yrs) (since zero coupon bonds so interest will be 0)

Or, 61 = 100/ (1+r) ^12

Or, (1+r) ^12 = 1.6394

Or, r = 4.20%

After Tax cost of Debt = Pre Tax Cost of Debt* (1- Tax rate)

Or, After Tax Cost of Debt = 4.2*(1-0.35) = 2.73%

Total Book value of Debt = Initial Book Value of Debt + Book Value of Debt from the Second Issue

Or, Total Book Value of Debt = $35 million + $80 million = $115 million

Total Market Value of Debt = Initial Market Value of Debt + Market Value of Debt from the Second Issue

Initial Market Value of Debt = Book Value * 108% (since bonds were selling at 108% of Par)

Or, Initial Market Value of Debt = $35*108% = $37.8 million

Market Value of Debt from the Second Issue = $80*61% (since bonds were selling at 61% of Par)

Or, Market Value of Debt from the Second Issue = $48.80 million

So total Market value of debt = $37.8 million + $48.8 million = $86.6 million

So the overall estimation of the cost of Debt would be = After Tax cost of debt of the Initial Issue * Weight of the Initial Issue + After Tax cost of Debt of the second Issue * Weight of the Second Issue

Or, Overall estimation of the cost of Debt = 3.51%* 37.8/ 86.6 + 2.73* 48.8/86.6

Overall estimation of the cost of Debt = 1.532% + 1.538% = 3.07%

So the overall estimation of the after cost of debt of the firm is 3.07%

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