Question

Jones Cricket Institute issued a 30 year, 8 percent semi-annual bond 3 year ago. The bond currently sells for 93 percent of its face value. The Company’s tax rate is 35%. a. What is the pre-taxed cost of debt? b. What is the after tax cost of debt? c. Which is more relevant, the pre-tax or the after- tax cost of debt? Why? In question 4 above, suppose the book value of the debt issues is $60 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 10 years to mature. The book value of this issue is $35 million and the bond sell for 57 percent of par. a. What is the company’s total book value of debt? b. The total market value? c. What is your best estimate of the after-tax cost of debt now?

Answer 1

1. the pre-taxed cost of debt is its yield to maturity (YTM)

Assume that Face value or par value of debt is M= $1000

Therefore price P0 = 93% of $1000 = $930

Coupon semiannual C = 1,000*8%*0.5 = $40

Time n = (30 -3) *2 = 54

And i is YTM=?

Formula for calculation of YTM of bond is

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Therefore we have,

$ 930 = $40 * [1 – 1 / (1+i) ^54] /i + 1000 / (1+i) ^54

Now we have to use trial and error method to find out the value of i

If i= 4.34% semiannual

Therefore annual YTM = 4.34% *2 = 8.68%

Therefore pre-tax cost is 8.68%

2. The after tax cost of debt = 8.68% *(1 – T)

Where T is the tax rate =35%

Therefore

After tax cost of debt = 8.68% *(1 – 0.35) = 5.64%

c) After- tax cost of debt is more relevant as it is used in weighted average cost of capital (WACC) calculation of the company. WACC is used as discount rate in Net present value calculations.

(a)The book value of debt is the total par value of all outstanding debt

Total Book value = $60,000,000 + $ 35,000,000 = $95,000,000

(b)The market value of debt = $60,000,000 * 93% + $ 35,000,000 *57% = $75,750,000

(c) The pretax cost of debt is the YTM of the company’s bonds, so:

Now calculate The YTM of the zero coupon bond

Price of zero coupon bond Pz = 57% * $1,000 = $570

We have n = 10

Bond price Pz= M / (1+i) ^n

Therefore we have,

$570 = 1000 / (1+i) ^10

Or i = 5.78%

Pre-tax cost of debt for zero coupon bonds is 5.78%

The tax rate =35%

And the after tax cost of the zero coupon bonds = 5.78% * (1 – 0.35) = 3.76%

The after tax cost of debt for the company is the weighted average of the after tax cost of debt for all debts. We can use the market value as weights of the bonds.

The total after tax cost of debt for the company

= 5.64 % *($55,800,000/$75,750,000) + 3.76 % *($19,950,000/ $75,750,000)

= 4.15% + 0.99% = 5.14%

The best estimate of the after-tax cost of debt is 5.14%