Using forward rates to calculate the price of a bond

CFA Level I Fixed Income
#1

Came across this question, I’m not sure why you need to add the forwards each time to get the value. Can someone please explain it? Also, is there a way to do this all in the calculator?

Using the forward rates, the value of a 2 1/2 year $100 par bond w/ 5% coupon is?

Per Yrs. Fwd Rate

1 0.5 1.20%

2 1 1.80%

3 1.5 2.30%

4 2 2.70%

5 2.5 3.00%

#2

I dont think you can do this on the calculator. For this type of question, you have to find the spot rate first, and then use no-arbitrage method to find the PV of the bond. Is the answer $106.831?

#3
  1. Discount $102.50 from time 2.5 to time 2.0: $102.50 / (1 + 3.00%/2) = $100.9852
  2. Add the coupon paid at time 2.0: $100.9852 + $2.50 = $103.4852
  3. Discount $103.4852 from time 2.0 to time 1.5: $103.4852 / (1 + 2.70%/2) = $102.1068
  4. Add the coupon paid at time 1.5: $102.1068 + $2.50 = $104.6068
  5. Discount $104.6068 from time 1.5 to time 1.0: $104.6068 / (1 + 2.30%/2) = $103.4175
  6. Add the coupon paid at time 1.0: $103.4175 + $2.50 = $105.9175
  7. Discount $105.9175 from time 1.0 to time 0.5: $105.9175 / (1 + 1.80%/2) = $104.9727
  8. Add the coupon paid at time 0.5: $104.9727 + $2.50 = $107.4727
  9. Discount $107.4727 from time 0.5 to time 0.0: $107.4727 / (1 + 1.20%/2) = $106.8317

Voilà!

#4

I just did.

#5

Thanks very much for the detailed explanation. Very helpful!

#6

@S2K, savage haha

#7

You guys are too kind.