Question

Kenny Electric Company's noncallable bonds were issued several years ago and now have 20 years to maturity. These bonds have a 9.25% annual coupon, paid semiannually, sells at a price of $1,075, and has a par value of $1,000. If the firm's tax rate is 40%, what is the component cost of debt for use in the WACC calculation

Answer 1

Answer:

5.08%

Explanation:

This question asks us to calculate the component cost of debt which is used in the WACC calculation if the firm’s tax rate is 40%

To calculate this, we need to know the yield to maturity of the firm. This can be calculated using a formula. In this formula, we will specify that the yield to maturity be represented as the letter Y.

Hence mathematically:

46.25 * [1-(1+Y/2)ˆ-40]/Y/2 + 1000/(1+Y/2)ˆ40 = 1075

Solving this, we get Y = 8.46%

The cost of debt = 8.46% * (1-40%) = 5.08%

Answer 2

Answer:

Cost of debt after taxes 5.08%

Explanation:

We solve for the tax rate using excel goal seek:

PV of the coupon plus present value of the maturity should equal 1,075 which is the market price of the bond:

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

C 46.250

time 40

rate 0.042328446

$46.25 \times \frac{1-(1+0.0423284456569404)^{-40} }{0.0423284456569404} = PV$

PV $884.5345

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

Maturity   1,000.00

time   40.00

rate  0.042328446

$\frac{1000}{(1 + 0.0423284456569404)^{40} } = PV$  

PV   190.47

PV c $884.5345

PV m  $190.4655

Total $1,075.0000

Now, as this is semiannually we multiply by two:

0.0423284456569404 x 2 = 0.084656891

Last we apply the after-tax cost of debt:

0.084656891  ( 1 - 0.4) = 0.050794135

Cost of debt after taxes 5.08%