Question

A $48 stock pays a dividend of $1.20 every 6 months, with the first dividend coming 6 months from today. The continuously compounded risk-free rate is 9%. What is the price of a forward contract that expires 1 year from today, immediately after the second dividend?

a. $49.57

b. $51.32

c. $50.07

d. $45.76

e. $49.89

Answer 1

Price of the forward can be calculated as per following formula -

F = (S - D) 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

D = present value of Dividend paid during contract period

Lets calculate D -

D = 1.20 x e^ - (0.09 x 6/12) + 1.20 x e^ - (0.09 x 12/12) = 2.24 (calculated as per value of e = 2.7183)

F = (48 - 2.24) x e ^ ( 0.09 x 1) = $ 50.07

Therefore, forward contract price is $ 50.07 , So, C is correct option