Question

A 20 year, 4% coupon bond has a price of $900 and face value of $1000. If the YTM decreases by 0.50% over the next year, what is the bond's total return over the next year?

Answer 1

First, we need to find the YTM, for that we need to put the following values in the financial calculator:

N = 20;

PV = -900;

PMT = 4%*1000 = 40;

FV = 1000;

Press CPT, then I/Y, which gives us 4.79

So, YTM = 4.79%

YTM after 1 year = 4.79% - 0.50% = 4.29%

Bond's Value after 1 year = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{4%*$1,000} * {(1 - (1 + 0.0429)^-19) / (0.0429)}] + [$1,000 / {1 + 0.0429}^19]

= [$40 * {0.5497 / 0.0429}] + [$1,000 / 2.2206]

= [$40 * 12.8177] + $450.32

= $512.71 + $450.32 = $963.03

Total Return = [P1 - P0 + Coupon] / P0

= [$963.03 - $900 + $40] / $900 = $103.03 / $900 = 0.1145, or 11.45%