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:
<u>Bond Sam</u>
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
<u>Bond Dave</u>
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
