1. Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments,
ID: 2642699 • Letter: 1
Question
1. 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.
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. Round your answers to 2 decimal places. (e.g., 32.16))
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? (Round your answers to 2 decimal places. (e.g., 32.16))
2.
Ponzi Corporation has bonds on the market with 10.5 years to maturity, a YTM of 7.10 percent, and a current price of $1,051. The bonds make semiannual payments.
What must the coupon rate be on these bonds? (Round your answer to 2 decimal places. (e.g., 32.16))
1. 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.
Explanation / Answer
1> Let the FV=1000 Interest factor for 6years=1.045^12 1.70 Interest factor for 19years=1.045^38 5.33 Coupon Value semi-annual=0.035*1000 35 Price of Sam after 6 years=PV of annuity (A=35,N=6,I=4.5%)+PV of 1000=35*(1.70-1)/(1.70*0.045)+1000/(1.045^12) 909.93 Price of Dave after 19 years=PV of annuity (A=35,N=19,I=4.5%)+PV of 1000=35*(5.33-1)/(5.33*0.045)+1000/(1.045^38) 819.60 Percentage Change in Sam=(1000-909.93)/1000 0.0901 or 9.01% Percentage Change in Dave=(1000-819.60)/1000 0.1804 or 18.04% 2> YTM=[C+(M-P)/n]/[0.4M+0.6P] or 0.071=[C+(1051-1000)/21]/(0.4*1051+0.6*1000) or 0.071=(C+2.429)/1020.2 or C=0.071*1020.2-2.429 70.0 or 7%
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