forward rates - value of bond

CFA Level I Fixed Income
#1

Does anyone know how to solve Practice Question 10 on page 527 of volume 5?

For those of you who don’t have the cirriculum, I’ll explain the question. It gives you a table of annual 6 month forward rates. It then asks you to determine the value of a 3-year bond.

This is what I don’t understand. In the solutions it discounts the cash flows of the bonds using only the period forward rate as the spot rate. For example, it will discount the 4th period (2nd year) coupon using just the 4th period forward rate. [1+(f4)/2]. I thought the discount factor was supposed to be like this: [1+(f1)/2][1+(f2)/2][1+(f3)/2][1+(f4)/2]

Does this make sense?

#2

You are correct on the discount factor.

I don’t have the curriculum, but perhaps you can check this: are they discounting the 4th coupon (and principle, I’d expect) using [1 + (f4)/2], then adding that to the 3rd coupon, discounting that sum using [1 + (f3)/2], adding that to the 2nd coupon, and so on? That would make sense.

If not, I don’t know what else to suggest.

#3

Hei.so, check your discount factors.They are computed exactly like you say they are supposed to be calculated (not just using that period’s forward rate).