# Forward Price

## What is a 'Forward Price'

A forward price is the predetermined delivery price for an underlying commodity, currency or financial asset decided upon by the long (the buyer) and the short (the seller) to be paid at predetermined date in the future. At the inception of a forward contract, the forward price makes the value of the contract at that time, zero.

The Forward Price can be determined by the following formula:

## BREAKING DOWN 'Forward Price'

The forward price of the contract is mainly based on the current spot price of the underlying asset. Although the contract has no intrinsic value at the inception, over time, a contract may gain or lose value. Offsetting positions in a forward contract are equivalent to a zero-sum game. For example, if one investor takes a long position in a pork belly forward agreement and another investor takes a short position in a forward agreement, any gains in the long position equals the losses that the second investor incurs from the short position. By initially setting the value of the contract's value to zero, both parties are on equal ground at the inception of the contract.

## Forward Price Calculation Example

When the underlying asset in the forward contract does not pay any dividends, the forward price can be calculated using the following formula:

F = S x e^(r x t)

Where:

F = the contract's forward price

S = the underlying asset's current spot price

e = the mathematical irrational constant approximated by 2.7183

r = the risk-free rate that applies to the life of the forward contract

t = the delivery date in years

For example, assume a security is currently trading at \$100 per unit. An investor wants to enter into a forward contract that expires in one year. The current annual risk-free interest rate is 6%. Using the above formula, the forward price is calculated as:

F = \$100 x e ^ (0.06 x 1) = \$106.18

If the underlying asset pays dividends over the life of the contract, the formula for the forward price is:

F = (S - D) x e ^ (r x t)

Here, D equals the sum of each dividend's present value, given as:

D = PV(d(1)) + PV(d(2)) + ... + PV(d(x)) = d(1) x e ^ -(r x t(1)) + d(2) x e ^ -(r x t(2)) + ... + d(x) x e ^ -(r x t(x))

Using the example above, assume that the security pays a 50-cent dividend every three months. First, the present value of each dividend is calculated as:

PV(d(1)) = \$0.5 x e ^ -(0.06 x 3/12) = \$0.493

PV(d(2)) = \$0.5 x e ^ -(0.06 x 6/12) = \$0.485

PV(d(3)) = \$0.5 x e ^ -(0.06 x 9/12) = \$0.478

PV(d(4)) = \$0.5 x e ^ -(0.06 x 12/12) = \$0.471

The sum of these is \$1.927. This amount is then plugged into the dividend-adjusted forward price formula:

F = (\$100 - \$1.927) x e ^ (0.06 x 1) = \$104.14