The relevant value to be discounted using a binomial model and backward induction methodology for a putable bond is the value that will be received if the put option is exercised or the computed value, whichever is greater.
In this case, the relevant value at node 1U is the exercise price ($100.000) since it is greater than the computed value of $99.127. At node 1L, the computed value of $103.583 must be used.
Therefore, the value of the putable bond is:
V
0 = (½)[(100.00 + 8) / (1 + 0.043912)] + [(103.583 + 8) / (1 + 0.043912)] = $105.17314
