Homework SourseBoth Bond Sam and Bond Dave have 9 percent coupons make semi
Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are prices at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam? Of Bond Dave? If rates were suddenly fall by 2 percent instead, what would the percentage change in the price on Bond Sambe then? Of Bond Dave? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds?
Solution
. Both bonds sell at par, so the initial YTM on both bonds is the coupon rate, 9 percent. If the YTM suddenly rises to 11 percent:
P SAM = $45(PVIFA 5.5% ,6 5.5%,6) + $1,000(PVIF 5.5% ,6) = $950.04
P DAVE = $45(PVIFA 5.5% ,40 ) + $1,000(PVIF 5.5% ,40 ) = $839.54
Percentage change in price = (New price – Original price) / Original price
DPSam% = ($950.04 – 1,000) / $1,000 = – 5.00%
DPDave% = ($839.54 – 1,000) / $1,000 = – 16.05%
