How to Value a Bond Using Forward Rates

We have seen that a bond can be valued using spot rates by discounting each cash flow by the spot rate for the maturity. We also saw that forward rates can be derived from spot rates. If so, we can also value a bond using forward rates instead of spot rates.

Let’s take a specific cash flow in a bond to understand this. Say, a bond is going to pay $100 as coupon after 2 years. s₂ is the 2-year spot rate is 6%. The present value of this cash flow will be:

PV of $100 = $100/(1+s₂)²

We also know that

(1+s₂)² = (1+s₁) (1+₁f₁)

Replacing this is the PV calculation:

PV of $100 = $100/(1+s₁) (1+₁f₁)

If s1 is 6% and ₁f₁ is 7%.

Here 1/(1+s₁) (1+₁f₁) is called the forward discount factor.

The resulting valuation using either spot rates or forward rates will be the same.