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 -7.54%
- Bond Dave's price will change by -14.33%
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 8.32%
- Bond Dave's price will change by 20.29%
Explanation:
Bond Sam
if market interest rates increase by 2%:
11% / 2 = 5.5% semiannual payments
5 years to maturity = 10 payments
present value = future value = 1000
-
PV of face value = 1,000 / (1 + 5.5%)¹⁰ = $585.43
- PV of coupon payments = 45 x 7.53763 (PV annuity factor, 5.5%, 10 periods) = $339.19
new market price = $585.43 + $339.15 = $924.62
if interest increases by 2%, present value (market value) will decrease by $75.38 ⇒ 7.54% decrease
if market interest rates decrease by 2%:
7% / 2 = 3.5% semiannual payments
5 years to maturity = 10 payments
present value = future value = 1000
-
PV of face value = 1,000 / (1 + 3.5%)¹⁰ = $708.92
- PV of coupon payments = 45 x 8.31661 (PV annuity factor, 3.5%, 10 periods) = $374.25
new market price = $708.92 + $374.25 = $1,083.17
if interest decrease by 2%, present value (market value) will increase by $83.17 ⇒ 8.32% increase
Bond Dave
if market interest rates increase by 2%:
11% / 2 = 5.5% semiannual payments
18 years to maturity = 36 payments
present value = future value = 1000
-
PV of face value = 1,000 / (1 + 5.5%)³⁶ = $145.52
- PV of coupon payments = 45 x 18.80474 (PV annuity factor, 5.5%, 36 periods) = $711.21
new market price = $145.52 + $711.21 = $856.73
if interest increases by 2%, present value (market value) will decrease by $143.27 ⇒ 14.33% decrease
if market interest rates decrease by 2%:
7% / 2 = 3.5% semiannual payments
18 years to maturity = 36 payments
present value = future value = 1000
-
PV of face value = 1,000 / (1 + 3.5%)³⁶ = $289.83
- PV of coupon payments = 45 x 20.29049 (PV annuity factor, 3.5%, 36 periods) = $913.07
new market price = $289.83 + $913.07 = $1,202.90
if interest decrease by 2%, present value (market value) will increase by $202.90 ⇒ 20.29% increase
