Interest rate sensitivity An investor purchased the following 5 bonds. Each bond

Question

Interest rate sensitivity

An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 9% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell and each then had a new YTM of 7%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table. Round your answers to the nearest cent or to two decimal places.

   %

PLEASE EXPLAIN FULLY

Price @ 9% Price @ 7% Percentage Change 10-year, 10% annual coupon $   $      % 10-year zero $   $      % 5-year zero $   $      % 30-year zero $   $      % $100 perpetuity $   $  

   %

PLEASE EXPLAIN FULLY

Explanation / Answer

Solution.

zero coupon bond = 1000/(1+i) pwr t

perpuity = coupon / (1+t)

Annual coupon bond = present value of $ 10 coupon received every year for 10 years and present value of bond principal received after 10 years.

Face value of all the bonds is $100 Bonds Price at 9% Price at 7% Change % change 10 year 10% annual coupon 113.42 121.07 7.65 6.74 10 - year zero 46.32 50.84 4.52 9.76 5 - year zero 68.06 71.30 3.24 4.76 30 - year zero 9.94 13.14 3.20 32.19 $100 perpuity 125.00 142.86 17.86 14.29

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