We can discount cash flows either by using spot rates or forward rates, because a spot rate is simply a package of short-term forward rates. Assume that the cash flow of period T is $1; then, the present value of the cash flow using the spot rate for period T will be as follows:

         PV of $1 in M periods = 

We know that,

         y_T = [(1 + y₁) (1 + ₁f₁) (1 + ₁f₂) (1 + ₁f₃) ..... (1 + ₁f_T-1)]^{1/ T} - 1

Adding 1 on both sides of the equations,

         (1 + y_T)  = [(1 + y₁) (1 + ₁f₁) (1 + ₁f₂) (1 + ₁f₃) ..... (1 + ₁f_{T - 1})]^{1/ T}

Raising both sides of the equations to the T-th power, we get:

         (1 + y_T)^T = [(1 + y₁) (1 + ₁f₁) (1 + ₁f₂) (1 + ₁f₃) ..... (1 + ₁f_{T - 1})]

The present value of X1 in M periods can be determined by substituting the value calculated in the above step into the present value formula.

         PV of X1 M periods =

The present value of Rs.1 in T period is called the forward discount factor for period T.