An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 12% annual coupon. Bond L matures in 12 years, while Bond S matures in 1 year.
Assume that only one more interest payment is to be made on Bond S at its maturity and that 12 more payments are to be made on Bond L.
In order to calculate coupon rate we would first calculate coupon amount by using the present value of bond formula. | ||||
Price of bond | Interest payment*(1-((1+r)^-n)/r) + Face value*(1/(1+r)^n) | |||
where r represents yield to maturity and n represents number of years. | ||||
a. | ||||
We would first calculate price of bond L under different interest rate | ||||
Calculation of price of bond L if interest rate is 5% | ||||
Coupon amount | $120 | 1000*12% | ||
Price of bond | 120*((1-(1.05^-12))/0.05)+1000*(1/(1.05^12)) | |||
Price of bond | 120*8.8635+1000*0.55684 | |||
Price of bond | $1,620.43 | |||
Calculation of price of bond S if interest rate is 5% | ||||
Price of bond | 1120*(1/(1.05^1)) | |||
Price of bond | 1120*0.95238 | |||
Price of bond | $1,066.67 | |||
Calculation of price of bond L if interest rate is 9% | ||||
Price of bond | 120*((1-(1.09^-12))/0.09)+1000*(1/(1.09^12)) | |||
Price of bond | 120*7.1607+1000*0.35553 | |||
Price of bond | $1,214.82 | |||
Calculation of price of bond S if interest rate is 9% | ||||
Price of bond | 1120*(1/(1.09^1)) | |||
Price of bond | 1120*0.91743 | |||
Price of bond | $1,027.52 | |||
Calculation of price of bond L if interest rate is 14% | ||||
Price of bond | 120*((1-(1.14^-12))/0.14)+1000*(1/(1.14^12)) | |||
Price of bond | 120*5.660292+1000*0.207559 | |||
Price of bond | $886.79 | |||
Calculation of price of bond S if interest rate is 14% | ||||
Price of bond | 1120*(1/(1.14^1)) | |||
Price of bond | 1120*0.877193 | |||
Price of bond | $982.46 | |||
Summary | ||||
5% | 9% | 14% | ||
Bond L | $1,620.43 | $1,214.82 | $886.79 | |
Bond S | $1,066.67 | $1,027.52 | $982.46 | |
b. | ||||
This is because longer term bonds are subject to higher interest rate risk as the increase in interest rate would decrease the value of bond. | ||||
Thus, long term bonds have greater interest rate risk than do short-term bonds (Option II). | ||||
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