# Pathwise Valuation

I’m working through the examples in reading 36 of 2017 CFA Level II book and I’ve gotten stuck on example 6. How are the present values obtained in exhibit 28 from the discount rates in exhibit 27? When I use those same discount rates I get a different value.

Ex)

Path 1

=5/1.02 + 5/(1.04646)^2 + 105/(1.08167)^3 = 92.43476

Actual PV = 100.5296

Can anyone tell me what I am doing wrong?

You’re treating the rates as spot rates.

They’re 1-period forward rates.

I understand that the discount rates provided in the example are one-year forwards, but how do I use those to value the bonds? How do I get the prices that are shown in exhibit 28?

Discount the \$105 payment at time 3 back to time 2 using the 1-period forward rate at time 2:

\$105 / 1.08167 = \$97.0721

That gives you the value of that payment at time 2. Add the \$5 coupon at time 2, then discount that entire amount back to time 1 using the 1-period forward rate at time 1:

(\$97.0721 + \$5) / 1.04646 = \$97.5404

That gives you the value of both payments at time 1. Add the \$5 coupon at time 1, then discount that entire amount back to time 0 using the 1-period forward rate at time 0 (which is the 1-period spot rate):

(\$97.5404 + \$5) / 1.02000 = \$100.5298

Voilà!

Thank you! I was totally overthinking it. Seems so obvious now.