Question

consider a bond with $1000 par value, 10% coupon rate and three years to maturity. assume 12% required rate of return. 1-compute the appropriate price for this bond if coupons are paid annually at 10%. 2-compute the appropriate price for this bond if coupons are paid semiannually at 10%. 3- comment on the difference in results between 1 and 2.?

Answer 1

Price of a bond can be calculated using the

P = C/(1+i) + C/(1+i)^2 + C/(1+i)^3+ ..... + C/(1+i)^n + F/(1+i)^n

where:

C = coupon amount

i = the yield to maturity or required rate of return

F = the bond’s par or face value

n = the number of time periods until the bond’s maturity date

Hence, for a bond with $1000 par value, 10% coupon rate and three years to maturity. 12% required rate of return

Bond price if coupons are paid annually

P = 100/(1+12%) + 100/(1+12%)^2 + 100/(1+12%)^3 + 1000/(1+12%)^3

P = $951.96

Bond Price is coupons are paid semi annually

P = 50/(1+6%) + 50/(1+6%)^2 + 50/(1+6%)^3 + 50/(1+6%)^4 + 50/(1+6%)^5 + 50/(1+6%)^6 + 1000/(1+6%)^6

P = $950.83

Price for the bond with Semi-annual coupons is lesser as effective yield or effective required rate of return on the semi-annual payment would be higher which results in lower price.