Question

You are considering buying a 6 month forward contract on a stock that provides a continuous dividend yield of 5% per year. The risk free interest rate is 3.5%. The current stock price is $45 per share and the delivery price at the inception of the contract is $48 per share.

a) What is the value of your position?

b) What is the forward price?

c) How would you modify the equation if the dividend was stated as a yield rather than a dollar amount? (or a dollar amount rather than a yield)

Answer 1

a. Value of forward contract is calculated using the below formula:

where, S = current stock price = 45

q = dividend yield =5%

t = time to maturity = 0.5 years

X = Delivery price = 48

r = risk free rate =3.5%

F = 45 * exp (-0.05 * 0.5) - ( 48 * exp (-0.035 *0.5)) = -3.28

This is generally price of the Forward contract resulting in zero contract value at the initiation of the contract.

b. forward price is given by:

f = S * (e^rt) = 45.79

c. If dollar amount of the Dividend is given instead of the yield, we modify the equation as shown below:

f = (S - Dividend) * (e^rt)