Question

On the issue date you bought a 20 year maturity, 6% semiannual coupon Bond. The bond then sold at YTM of 7%. Now four years later the similar Bond sells at YTM of 5%. If you hold the bond now, what is your realized rate of return for the 4-year holding.

Answer 1

Value of Bond =

Where r is the discounting rate of a compounding period i.e. 7%/2 = 3.5% _ _ (Semi Annual )

And n is the no of Compounding periods 20 year * 2 = 40 periods_ _ (Semi Annual )

Coupon 6%/2 = 3%

Value of 20 year Bond =

= 640.652170215 + 252.57246808

= $ 893.22

Value of 16 year Bond

Where r is the discounting rate of a compounding period i.e. 5%/2 = 2.5% _ _ (Semi Annual )

And n is the no of Compounding periods 16 year * 2 = 32 periods_ _ (Semi Annual )

Coupon 6%/2 = 3%

Value of 16 year Bond =

= 655.475338884 + 453.77055093

= $ 1109.25

Coupon Earned = 30 * (4 years * 2 ) = 240

Capital Gain = 1109.25 - 893.22 = 216.03

% Return = (Total Coupon Earned + Capital) / Purcahse Price

= (240 + 216.03) / 893.22

= 456.03 / 893.22

= 51.05%