A 3 year, 8% coupon, $1000
bond, selling for $949.22
Period Cash flow Present Value
9% 11% 10%
1 40 $38.28 $37.91 $38.10
2 40 $36.63 $35.94 $36.28
3 40 $35.05 $34.06 $34.55
4 40 $33.54 $32.29 $32.91
5 40 $32.10 $30.61 $31.34
6 1040 $798.61
$754.26 $776.06
Total $974.21 $925.07
$949.24
The bond is selling at a discount; hence the yield exceeds the coupon rate. At a
discount rate equal to the coupon rate of 8%, the price would be 1000. Hence
try a discount rate of 9%. At 9%, the
PV is 974.21, which is too high. Try a
higher discount rate of 11%, with a PV of $925.07, which is too low. Trying 10%, which is between 9% and 11%, the PV is exactly equal to the price. Hence the bond yield = 10%.
Computing YTM by Trial and Error