Question

A bond with three years to maturity has a face value of $1000 and a coupon rate of 3%. It is initially bought at a yield to maturity of 7% then sold after one year when market yields have fallen to 3%. What is the rate of return for the first year?

Answer 1

The Bond Price when yield is 7%

Bond Price = C * [( 1 - ( 1 +R)^-N) / R ] + FV / ( 1 +R)^N

Where, C = Coupon payment

R = Yield to Maturity

N = Number of Periods

FV = Face Value

Coupon Payment = Face Value * Coupon rate

= 1000 * 3%

= 30

Bond Price = 30 * [( 1 - ( 1 +7%)^-3] / 7% + 1000 / ( 1 + 7%)^3

= 30 * [( 1 - (1.07)^-3] / 0.07 + 1000 / ( 1.07)^3

= 30 * [( 1 - 0.81629) / 0.07 + (1000 / 1.225043)

= 30 * 2.6244285 + 816.2978768

= 895.0307

Bond Price at the time of purchase that is when yield is 7% is 895.0307.

Now, After One Year, The market rate is 3% Which is equal to the coupon rate, so the bond price after the 1 year is same as of that to the face value because the value of the bond is Discounted cash flows of all the payment that the bond is going to generate over the maturity.

Bond price after 1 year = 1000

Return = (Price after 1 year - price of purchase) / Price of purchase

= (1000 - 895.0307) / 895.0307.

Rate of return = 11.7280%