Question

The Faulk Corp. has a bond with a coupon rate of 7 percent outstanding. The Gonas Company has a bond with a coupon rate of 13 percent outstanding. Both bonds have 20 years to maturity, make semiannual payments, and have a YTM of 10 percent. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. A negative answer should be indicated by a minus sign. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Percentage change in price of Faulk Corp. bond % Percentage change in price of Gonas Co. bond % What if rates suddenly fall by 2 percent instead? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Percentage change in price of Faulk Corp. bond % Percentage change in price of Gonas Co. bond %

Answer 1

Faulk Corp. bond:

Assuming fave value to be $1,000.

Coupon = (0.07 * 1,000) / 2 = 35

Number of periods = 20 * 2 = 40

Rate = 10% / 2 = 5%

Current bond price of Faulk corp = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Current bond price of Faulk corp= 35 * [1 - 1 / (1 + 0.05)⁴⁰] / 0.05 + 1,000 / (1 + 0.05)⁴⁰

Current bond price of Faulk corp = 35 * 17.159086 + 142.045682

Current bond price of Faulk corp = $742.61367

If interest rate rises by 2%:

Assuming fave value to be $1,000.

Coupon = (0.07 * 1,000) / 2 = 35

Number of periods = 20 * 2 = 40

Rate = (10% + 2%) / 2 = 6%

New bond price of Faulk corp = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

New bond price of Faulk corp= 35 * [1 - 1 / (1 + 0.06)⁴⁰] / 0.06 + 1,000 / (1 + 0.06)⁴⁰

New bond price of Faulk corp = 35 * 15.046297 + 97.222188

New bond price of Faulk corp = $623.84258

Percentage change in price of Faulk Corp. when interest rate increases by 2% = [(New price - current price) / current price) * 100]

Percentage change in price of Faulk Corp. when interest rate increases by 2% = [(623.84258 - 742.61367) / 742.61367 * 100]

Percentage change in price of Faulk Corp. when interest rate increases by 2% = -15.99%

Gonas company:

Assuming fave value to be $1,000.

Coupon = (0.13 * 1,000) / 2 = 65

Number of periods = 20 * 2 = 40

Rate = 10% / 2 = 5%

Current bond price of Gonas company = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Current bond price of Gonas company= 65 * [1 - 1 / (1 + 0.05)⁴⁰] / 0.05 + 1,000 / (1 + 0.05)⁴⁰

Current bond price of Gonas company = 65 * 17.159086 + 142.045682

Current bond price of Gonas company = $1,257.386272

If interest rate rises by 2%:

Assuming fave value to be $1,000.

Coupon = (0.13 * 1,000) / 2 = 65

Number of periods = 20 * 2 = 40

Rate = (10% + 2%) / 2 = 6%

New bond price of Gonas company = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

New bond price of Gonas company= 65 * [1 - 1 / (1 + 0.06)⁴⁰] / 0.06 + 1,000 / (1 + 0.06)⁴⁰

New bond price of Gonas company = 65 * 15.046297 + 97.222188

New bond price of Gonas company = $1,075.231493

Percentage change in price of Gonas company when interest rate increases by 2% = [(New price - current price) / current price) * 100]

Percentage change in price of Gonas company when interest rate increases by 2% = [(1,075.231493 - 1,257.386272) / 1,257.386272* 100]

Percentage change in price of Gonas company when interest rate increases by 2% = -14.49%

When interest rate decreases by 2%:

Coupon = (0.07 * 1,000) / 2 = 35

Number of periods = 20 * 2 = 40

Rate = (10% - 2%) / 2 = 4%

New bond price of Faulk corp = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

New bond price of Faulk corp= 35 * [1 - 1 / (1 + 0.04)⁴⁰] / 0.04 + 1,000 / (1 + 0.04)⁴⁰

New bond price of Faulk corp = 35 * 19.792774 + 208.289045

New bond price of Faulk corp = $901.036135

Percentage change in price of Faulk Corp. when interest rate decreases by 2% = [(New price - current price) / current price) * 100]

Percentage change in price of Faulk Corp. when interest rate decreases by 2% = [(901.036135 - 742.61367) / 742.61367 * 100]

Percentage change in price of Faulk Corp. when interest rate decreases by 2% = 21.33%

Coupon = (0.13 * 1,000) / 2 = 65

Number of periods = 20 * 2 = 40

Rate = (10% - 2%) / 2 = 4%

New bond price of Gonas company = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

New bond price of Gonas company= 65 * [1 - 1 / (1 + 0.04)⁴⁰] / 0.04 + 1,000 / (1 + 0.04)⁴⁰

New bond price of Gonas company = 65 * 19.792774 + 208.289045

New bond price of Gonas company = $1,494.819355

Percentage change in price of Gonas company when interest rate decreases by 2% = [(New price - current price) / current price) * 100]

Percentage change in price of Gonas company when interest rate decreases by 2% = [(1,494.819355 - 1,257.386272) / 1,257.386272* 100]

Percentage change in price of Gonas company when interest rate decreases by 2% = 18.88%