Question

Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has six years to maturity, whereas Bond Dave has 19 years to maturity.
a) If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
b) If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave?

• Bond Sam's price will change by -9.12%
• Bond Dave's price will change by -18.05%

b. If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave?

• Bond Sam's price will change by 10.26%
• Bond Dave's price will change by 24.35%

Explanation:

Bond Sam

9% / 2 = 4.5% semiannual payments

6 years to maturity = 12 payments

present value = future value = 1000

• PV of face value = 1,000 / (1 + 4.5%)¹² = $589.66
• PV of coupon payments = 35 x 9.11858 (PV annuity factor, 4.5%, 12 periods) = $319.15

new market price = $589.66 + $319.15 = $908.81

if interest increases by 2%, present value (market value) will decrease by $91.19 ⇒ 9.12% decrease

if market interest rates decrease by 2%:

5% / 2 = 2.5% semiannual payments

6 years to maturity = 12 payments

present value = future value = 1000

• PV of face value = 1,000 / (1 + 2.5%)¹² = $743.56
• PV of coupon payments = 35 x 10.25776 (PV annuity factor, 2.5%, 12 periods) = $359.02

new market price = $743.56 + $359.02 = $1,102.58

if interest decrease by 2%, present value (market value) will increase by $102.58 ⇒ 10.26% increase

Bond Dave

9% / 2 = 4.5% semiannual payments

19 years to maturity = 38 payments

present value = future value = 1000

• PV of face value = 1,000 / (1 + 4.5%)³⁸ = $187.75
• PV of coupon payments = 35 x 18.04999 (PV annuity factor, 4.5%, 38 periods) = $631.75

new market price = $187.75 + $631.75 = $819.50

if interest increases by 2%, present value (market value) will decrease by $180.50 ⇒ 18.05% decrease

if market interest rates decrease by 2%:

5% / 2 = 2.5% semiannual payments

6 years to maturity = 12 payments

present value = future value = 1000

• PV of face value = 1,000 / (1 + 2.5%)³⁸ = $391.28
• PV of coupon payments = 35 x 24.3486 (PV annuity factor, 2.5%, 38 periods) = $852.20

new market price = $391.28 + $852.20 = $1,243.48

if interest decrease by 2%, present value (market value) will increase by $243.48 ⇒ 24.35% increase