Question

Cost of Debt KatyDid Clothes has a $150 million (face value) 30-year bond issue selling for 104 percent of par that carries a coupon rate of 11 percent, paid semiannually. What would be Katydid’s before-tax component cost of debt?

Answer 1

Answer:

the annual pre-tax cost of debt is 10.56%

Explanation:

the beore-tax component cost of debt will be the actual market rate of the bonds, as they offer an interest rate of 11% but are selling at 104 points not at par thus, there is a difference between the rates.

We solve for the rate which makes the coupon and maturity 104

with excel or a financial calculator

PV of the coupon payment

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 5.500 (100 x 11%/2)

time 60 (30 years x 2 payment per year)

rate 0.052787474

$5.5 \times \frac{1-(1+0.0527874736258532)^{-60} }{0.0527874736258532} = PV$

PV $99.4338

PV of the maturity

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   100.00

time   60.00

rate  0.052787474

$\frac{100}{(1 + 0.0527874736258532)^{60} } = PV$  

PV   4.57

Adding both we should get 104 which is the amount the bonds is selling:

PV coupon $99.4338 + PV maturity  $4.5662 = $104.0000

The rate is generated using goal seek or wiht a financial calculator.

This rate is a semiannual rate, so we multiply by 2 to get the annual cost of debt:

0.052787474 x 2 = 0.105574947

The cost of debt for the firm is 10.56%