Jiminy’s Cricket Farm issued a bond with 20 years to maturity and a semiannual c

Question

Jiminy’s Cricket Farm issued a bond with 20 years to maturity and a semiannual coupon rate of 8 percent 3 years ago. The bond currently sells for 96 percent of its face value. The company’s tax rate is 35 percent.

What is the pretax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What is the aftertax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Jiminy’s Cricket Farm issued a bond with 20 years to maturity and a semiannual coupon rate of 8 percent 3 years ago. The bond currently sells for 96 percent of its face value. The company’s tax rate is 35 percent.

a.

What is the pretax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  Pretax cost of debt % b.

What is the aftertax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  Aftertax cost of debt %

Explanation / Answer

Pre-tax cost of debt = 8.46%

After-tax cost of debt = 5.50%

Semi-annual coupon rate = 8%

Let us assume face value P = 100

Semi annual coupon amount A = 100 * 8% * 0.5 = 4

Time to maturity at the time of issue = 20 years

Period elapsed after bond issue = 3 years

Time to maturity n = 20 years – 3 years   = 17 years *2 = 34 semi-annual period

Current Price = 96% of face value   = 100 * 96% = 96

Let r be the semi-annual cost of debt. We can calculate current price of bond from the below equation

Current Price = Semi-annual coupon amount * [(1-(1/(1+r)^n))/r] + Face Value /(1+r)^n

Substituting values from above

96 = 4 * [(1-(1/(1+r)^34))/r] + 100 /(1+r)^34

96 - 4 * [(1-(1/(1+r)^34))/r] - 100 /(1+r)^34 = 0

Let r = 4%, then LHS will be

= 96 - 4 * [(1-(1/(1.04)^34))/0.04] - 100 /(1.04)^34

= 96 – 4 *[(1-(1/3.794316)/0.04] - 100 /3.794316

= 96 – 4 * [(1-0.263552)/0.04] – 100 * 0.263552

= 96 – 4 * (0.736448/0.04) – 100 * 0.263552

= 96 – 4 * 18.4112 – 100 * 0.263552

= 96- 73.64479 – 26.35521

= - 4

Let r = 0.045%, then LHS will be

= 96 - 4 * [(1-(1/(1.045)^34))/0.045] - 100 /(1.045)^34

= 96 – 4 *[(1-(1/4.466362)/0.045] - 100 /4.466362

= 96 – 4 * [(1-0.223896)/0.045] – 100 * 0.223896

= 96 – 4 * (0.776104/0.045) – 100 * 0.223896

= 96 – 4 * 17.24676 – 100 * 0.223896

= 96- 68.98703 – 22.38959

= 4.6234

r can be estimated as follows

r = 0.04 + [(-4 * (0.04-0.045))/(4.6234-(-4)]

r = 0.04 + (0.02/8.6234)

r = 0.04 + 0.00231927

r = 0.04231927 * 2   = 0.08463854 or 8.463854%

Pre-tax cost of debt = 8.46%

Tax rate = 35%

After-tax cost of debt = 8.46% *(1-tax rate) = 8.46% * (1-0.35) = 8.46% * 0.65 = 5.499%

After-tax cost of debt = 5.50% (rounded off)

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