An investor purchased the following 5 bonds. Each bond had a par value of $1,000

Question

An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 8% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell and each then had a new YTM of 6%. 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.

Price @ 8% Price @ 6% Percentage Change 10-year, 10% annual coupon $   $      % 10-year zero $   $      % 5-year zero $   $      % 30-year zero $   $      % $100 perpetuity $   $      %

Explanation / Answer

The Price can be computed using the following formula: PV= Present Value factor(YTM,n)*Face Value + Annuity Factor(YTM,n)*Coupon Particulars of the Bond Price @ 8% Price @ 6% Percentage change 1 10 year-10% annual coupon 0.4632*1000 + 6.71*10= 731.6 0.5584*1000 + 7.36*10= 632 731.6-632/ 731.6= 13.61% 2 10 year-zero 0.4632*1000 + Annuity factor*0= 463.2 0.5584*1000 + Annuity factor*0= 558.4 463.2-558.4/463.2= 20.55% 3 5 year-zero 0.6805*1000 + Annuity factor*0= 680.5 0.7473*1000 + Annuity factor*0= 747.3 680.5-747.3/680.5= 9.82% 4 30 year-zero 0.0994*1000 + Annuity factor*0= 99.38 0.1741*1000 + Annuity factor*0= 174.11 99.38-174.11/ 99.38= 75.20% 5 $100 perpetuity 100/8%= 1250 100/6%= 1666.67 1250-1666.67/1250= 33.33%

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