Question

You purchase a bond today issued by XYZ Manufacturing with a $1,000 par value and a coupon rate of 6%. The bond matures in 6 years, pays annual coupons, and the yield to maturity is 8% when you purchase the bond. Suppose you sell the bond one year from today and the yield of maturity at that time is 6%.

What was your purchase price for the bond?

At what price did you sell the bond?

What was your total return on the bond (in both dollar and percentage terms)?

Answer 1

Purchase price

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =6

Bond Price =∑ [(6*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^6

k=1

Bond Price = 907.54

Selling price

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =5

Bond Price =∑ [(6*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^5

k=1

Bond Price = 1000

total return = selling price+coupon-purchase price

=1000+60-907.54= 152.46

%age return = total return/purchase price*100 = 152.46/907.54*100=16.799%