4. Present Value Composition of Two Bonds I You just purchased two newly-issued

Question

4. Present Value Composition of Two Bonds I You just purchased two newly-issued bonds, Bond A and Bond B. Both have Face Values, and Par Values, of $1,000. Both Bonds have Coupon Interest Rates of 5 percent (5%). Bond A has a five (5) year maturity and Bond B has a thirty (30) year maturity. Minutes after you purchased these bonds, the U.S. Federal Reserve Bank dramatically increase interest rates, and the market rate for both of these bonds in now 8 percent (8%). What is the value (i.e., Present Value) of these bonds now? What percentage, to the nearest on-tenth of a percent, of the Present Value of these bonds is now composed of the Present Value of the Interest Payments? What percentage is now composed of the Present Value of the Principal Repayment? Present Values Percent of Present Value due to Interest Payments Percent of Present Value due to Principal Repayment

Explanation / Answer

Present Value of bond Bond A:

Present Value = 50*(1-(1+8%)^(-5))/8%+1000/(1+5%)^5

=$983.16

Present Value of bond Bond A:

Present Value = 50*(1-(1+8%)^(-30))/8%+1000/(1+5%)^30

=$794.27

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Present Value of interest payment of Bond A = 50*(1-(1+8%)^(-5))/8%

=$199.64

% of present value = 199.64/983.16*100

=20.31%

Present Value of interest payment of Bond B = 50*(1-(1+8%)^(-30))/8%

=$562.89

% of present value = 562.89/794.27*100

=70.87%

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Present Value of principal repayment of Bond A = 100-20.31%

=79.69%

Present Value of principal repayment of Bond B = 100-70.87

=29.13%

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