A 2-year maturity bond with face value of $1,000 makes annual coupon payments of
ID: 2652456 • Letter: A
Question
A 2-year maturity bond with face value of $1,000 makes annual coupon payments of $90 and is selling at face value. What will be the rate of return on the bond if its yield to maturity at the end of the year is (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Please explain the steps
A 2-year maturity bond with face value of $1,000 makes annual coupon payments of $90 and is selling at face value. What will be the rate of return on the bond if its yield to maturity at the end of the year is (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Please explain the steps
Explanation / Answer
a) YTM= 6% Present value of the bond= PV of interest payments + PV of principal(lumpsum) @ maturity Ie. PV of the bond= Coupon payment in $ ( 1-(1+YTM)^-n/YTM ) + Face Value/(1+YTM) where n= no.of years remaining to maturity -here 2-1=1 Substituting ,we have PV of the bond= 90{1-(1+0.06)^-1 /0.06 } + 1000/(1+0.06) ie. 84.9057+943.3962 =1028.3019 Return on the bond=( Market price or PV of the bond - Face value )/Face value *100 ie. (1028.3019 - 1000) /1000 * 100 = 2.83% b) YTM= 9% Present value of the bond= PV of interest payments + PV of principal(lumpsum) @ maturity Ie. PV of the bond= Coupon payment in $ ( 1-(1+YTM)^-n/YTM ) + Face Value/(1+YTM) where n= no.of years remaining to maturity -here 2-1=1 Substituting ,we have PV of the bond= 90{1-(1+0.09)^-1 /0.09 } + 1000/(1+0.09) ie. 82.5688+917.4312= 1000 Return on the bond=( Market price or PV of the bond - Face value )/Face value *100 ie. (1000 - 1000) /1000 * 100 = 0 % c) YTM= 11% Present value of the bond= PV of interest payments + PV of principal(lumpsum) @ maturity Ie. PV of the bond= Coupon payment in $ ( 1-(1+YTM)^-n/YTM ) + Face Value/(1+YTM) where n= no.of years remaining to maturity -here 2-1=1 Substituting ,we have PV of the bond= 90{1-(1+0.11)^-1 /0.11 } + 1000/(1+0.11) ie. 81.0811+900.9009 = 981.982 Return on the bond=( Market price or PV of the bond - Face value )/Face value *100 ie. (981.982 - 1000) /1000 * 100 = - 1.80 % Rate of Return a. 6% 2.83% b. 9.00% 0% c. 11.00% -1.80%
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