Question

A company's 6% coupon rate, semiannual payment, $1000 par value bond that matures in 30 years sells at a price of $515.16. The company's federal-plus-state tax rate is 40%. What is the firm's after-tax component cost of debt for purposes of valculating the WACC?

Answer 1

After-tax cost of debt is 7.2%

Step-by-step explanation:

Given:

Coupon rate = 6% or 0.06 per annum.

Semi- annual coupon rate = 0.06÷2 = 0.03

Par value is 1,000

Coupon payment = 0.03×1000 = $30

Time period = 30×2= 60 semi-annual periods

Bond price = $515.16

Pre-tax cost of debt can be computed using excel function 'RATE'

=RATE(nper,PMT,PV,FV)

nper is 60; PMT is 30; PV is -515.16 (cash outflow); FV is 1000

Rate is 6%

Calculation is shown in attached excel snip.

Yield to maturity = 6×2 = 12%

Federal tax rate is 40% or 0.4

After-tax cost of debt = 0.12 (1-0.4)

= 0.072 or 7.2%

Answer 2

Based on the various components of the bond, the after-tax component cost of debt is 7.2%.

Using Excel, you can find the rate at which the bond is being discounted.

Number of periods will be:

= 30 x 2 payments (semiannual) per year

= 60 periods

Payment:

= Par value x Periodic coupon rate

= 1,000 x 6%/2

= $30

Present value = Selling price of $515.16

Future value = $1,000 par value.

Rate will therefore be:

= 5.99%

= 6%

Annual interest is:

= 6 x 2

= 12%

After tax interest would be:

= Interest x ( 1 - tax)

= 12% x ( 1 - 40%)

= 7.2%

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