The effective yield of the bond

by | Mar 3, 2023 | finance

 

A fixed 6% quarterly-pay coupon bond with 5.5 years to maturity is trading at 98.6 per 100 par. What is the effective yield of the bond?

Sample Solution

The effective yield of a fixed 6% quarterly-pay coupon bond with 5.5 years to maturity is calculated by first finding the present value of all future payments (coupons + principal) at the bond’s current market price. The formula for this calculation is: PV = C/(1+r)^i + P/(1+r)^n, where C = coupon rate, r = required return or yield, i = time period (quarterly in this case), P= par value and n=maturity date.

Sample Solution

The effective yield of a fixed 6% quarterly-pay coupon bond with 5.5 years to maturity is calculated by first finding the present value of all future payments (coupons + principal) at the bond’s current market price. The formula for this calculation is: PV = C/(1+r)^i + P/(1+r)^n, where C = coupon rate, r = required return or yield, i = time period (quarterly in this case), P= par value and n=maturity date.

Given our data, we can calculate the present value of this bond as follows: PV = 0.06/(1+r)^4 + 100/(1+r)^22
Solving for r (the required return or yield):
98.6/220=0.045454545 x (1+r ) ^ 22
Rearranging terms to solve for r:
(l/220)= 2 .46740875 x 10 -3
(220 / 98 .6 )^( 1 / 22 ) giving us an effective yearly yield of 6 .18 %

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