You are trying to price two bonds that have the same maturity and par value but
ID: 2757100 • Letter: Y
Question
You are trying to price two bonds that have the same maturity and par value but different coupon rates and different required rates of return. Both bonds mature in 3 years and have par values of $1000. One bond has a coupon rate of 7% and a required rate of return of 7%. The other bond has a coupon rate of 5% and a required rate of return of 5%. What is the absolute value of the difference between the price of these two bonds?
$
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Explanation / Answer
Solution.
Calculation of the absolute value of the difference between the price of these two bonds.
Formula = C x [ 1 - (1+r)^-t / r] + F / (1 + r )^t
Bond 1
= 70 x [ 1 - (1 + .07)^3] + 1000 / (1 + .07)^3
= 70 x [1 - [ 1/ (1 + .07)^3] + 1000 / (1 + .07)3
= 70 x {(1- 0.8162) / 0.07} + 1000 / 1.2250
= 70 x 2.6257 + 816.3265
= 183.799 + 816.3265
= 1000.1255
Bond 2
= 50 x [ 1 - (1 + .05)^3] + 1000 / (1 + .05)^3
= 50 x [1 - [ 1 / (1 + .05)^3] + 1000 / (1 + .05)3
= 50 x {(1- 0.8638) / 0.05} + 1000 / 1.1576
= 50 x 2.724 + 863.8562
= 136.2 + 863.8562
= 1000.0562
Difference between the price of these two bonds =
Bond 1 = 1000.1255
Bond 2 = 1000.0562
Difference = 0.0693
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