Both Bond Sam and Bond Dave have 6 percent coupons, make semiannual payments, an
ID: 2818882 • Letter: B
Question
Both Bond Sam and Bond Dave have 6 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has five years to maturity, whereas Bond Dave has 18 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?
BOND SAM = ____%
BOND DAVE = ___%
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 = ____%
BOND DAVE = ___%
Explanation / Answer
SAM:
Let face value be $1,000
Since bond is priced at par, YTM will be equal to coupon rate of 6%.
Initial bond price will also be $1,000
If interest rates suddenly rise by 2 percent:
Coupon payment = 0.06 * 1000 = 60 / 2 = 30
Number of periods = 5 * 2 = 10
YTM = ( 0.06 + 0.02) / 2 = 0.08 / 2 = 0.04 or 4%
price of bond = Coupon * [ 1 - 1 / ( 1 + r)n] / r + FV / ( 1 + r)n
price of bond = 30 * [ 1 - 1 / ( 1 + 0.04)10] / 0.04 + 1000 / ( 1 + 0.04)10
price of bond = 30 * 8.110896 + 675.5642
price of bond = $918.891
Percentage change in thr price of bond = ( 918.891 - 1000) / 1000 = -0.08111 or -8.111%
BOND SAM = -18.908%
DAVE:
Let face value be $1,000
Since bond is priced at par, YTM will be equal to coupon rate of 6%.
Initial bond price will also be $1,000
If interest rates suddenly rise by 2 percent:
Coupon payment = 0.06 * 1000 = 60 / 2 = 30
Number of periods = 18 * 2 = 36
YTM = ( 0.06 + 0.02) / 2 = 0.08 / 2 = 0.04 or 4%
price of bond = Coupon * [ 1 - 1 / ( 1 + r)n] / r + FV / ( 1 + r)n
price of bond = 30 * [ 1 - 1 / ( 1 + 0.04)36] / 0.04 + 1000 / ( 1 + 0.04)36
price of bond = 30 * 18.908282 + 243.6687
price of bond = $810.92
Percentage change in thr price of bond = ( 810.92 - 1000) / 1000 = -0.18908 or -18.908%
BOND DAVE = -18.908%
SAM:
Let face value be $1,000
Since bond is priced at par, YTM will be equal to coupon rate of 6%.
Initial bond price will also be $1,000
If interest rates suddenly fall by 2 percent:
Coupon payment = 0.06 * 1000 = 60 / 2 = 30
Number of periods = 5 * 2 = 10
YTM = ( 0.06 - 0.02) / 2 = 0.04 / 2 = 0.02 or 2%
price of bond = Coupon * [ 1 - 1 / ( 1 + r)n] / r + FV / ( 1 + r)n
price of bond = 30 * [ 1 - 1 / ( 1 + 0.02)10] / 0.02 + 1000 / ( 1 + 0.02)10
price of bond = 30 * 8.982585 + 820.3483
price of bond = $1,089.826
Percentage change in thr price of bond = ( 1,089.826 - 1000) / 1000 = 0.089826 or 8.9826%
BOND SAM = 8.9826%
DAVE:
Let face value be $1,000
Since bond is priced at par, YTM will be equal to coupon rate of 6%.
Initial bond price will also be $1,000
If interest rates suddenly fall by 2 percent:
Coupon payment = 0.06 * 1000 = 60 / 2 = 30
Number of periods = 18 * 2 = 36
YTM = ( 0.06 - 0.02) / 2 = 0.04 / 2 = 0.02 or 2%
price of bond = Coupon * [ 1 - 1 / ( 1 + r)n] / r + FV / ( 1 + r)n
price of bond = 30 * [ 1 - 1 / ( 1 + 0.02)36] / 0.02 + 1000 / ( 1 + 0.02)36
price of bond = 30 * 25.488842 + 490.22315
price of bond = $1,254.888
Percentage change in thr price of bond = ( 1,254.888 - 1000) / 1000 = 0.25489 or 25.489%
BOND DAVE = 25.489%
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