Question

A non-dividend-paying stock is currently worth $61. A forward contract on the stock expires in 0.7 years. The T-bill rate is 8% (continuously compounded) for all maturities.

What is the forward price?

What is the value of the forward contract to the long?

Answer 1

Given:

T-bill rate ( risk free rate ) = 8%
t = 0.7 years
Current Spot Price = $61

1) Forward Price = Forward price is the price at which a seller delivers an underlying asset, financial derivative, or currency to the buyer of a forward contract at a predetermined date.

Formula ;

F=S * e ^(r×t)

where;

F=the contract’s forward price
S=the underlying asset’s current spot price
e=the mathematical irrational constant approximatedby 2.7183 ( value of e has been taken from the net )
r=the risk-free rate that applies to the life of theforward contract
t=the delivery date in years​

Forward Price ;

F = 61 * e ^{( 0.08 * 0.7 )}
F = 61 * e ^{( 0.056 )}
F = 61 * 1.057
F = $ 64.477

So, Forward Price is $ 64.477

Note: Value of e ^{( 0.056 )} = 1.057 taken from google ( You can use a scientific calculator as well )

2) Value of Forward Contract to the long :

Formula ;

the value of a Forward contract to the long is:

V_T(T) = S_T - F₀(T)

where S_T is the spot price of the underlying at T and F₀(T) is the forward price.

The forward price is the price that a long will pay the short at expiration and expect the short to deliver the asset.

Now,

V_T(T) = 61 - 64.477
= - $ 3.477

The "value of a forward contract" refers to how much of a difference there is between the spot price and forward price. If the spot price is greater than the forward price, the buyer profits and gets the difference as cash from the seller and if the spot price is less than the forward price, the seller has gained, so the buyer owes the seller the difference in the two prices. So in this case, seller has gained by $ 3.477