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?
$

You should set your calculator for at least four decimal places of accuracy.
Place your answer in dollars and cents.

Do not include a dollar sign or comma in your answer.

Answer 1

The price of bonds can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, Required Rate), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Par/Face Value).

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Bond 1:

Here, Rate = 7%, Nper = 3, PMT = 1,000*7% = $70 and FV = 1000

Using these values in the above function/formula for PV, we get,

Price of Bond 1 = PV(7%,3,70,1000) = 1000

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Bond 2:

Here, Rate = 5%, Nper = 3, PMT = 1,000*5% = $50 and FV = 1000

Using these values in the above function/formula for PV, we get,

Price of Bond 2 = PV(5%,3,50,1000) = 1000

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Conclusion:

As the coupon rate and required rate of return are same on both the bonds, the bonds will be issued at the par value of 1000. Therefore, the absolute value of the difference between the price of two bonds will be 0 (1,000 - 1,000).