Question

A stock is expected to pay a dividend of $1 per share in 2 months. An investor purchased a forward contract on the stock at a forward price of $50 some time ago. The contract now has 3 months to its delivery date. The stock is currently trading at $55 and the risk free rate is 4% on a continuously compounded basis. Consider the following statements.
I. The price of a forward contract on the stock with 3 months to the delivery date is $54.55
II. The value of the investor’s forward position is $4.51
Which of the following is correct?

a.

Both statements are incorrect.

b.

Both statements are correct.

c.

Statement I is correct, Statement II is incorrect.

Answer 1

Answer is C

beacause claculating forward price=

Forward price of a stock=

(Spot price-Present value of dividend)*e^rt

r is the rate of return i,e 4%

t is the time in years = 3/12=0.25

=present value of dividend = Divident*e^-rt

t is 2 month so 2/12=0.1667

=1/(e^0.1667*4%)

=using excel finance calculator = using EXP function  i,e in  place of e^ using EXP i.e =1/(EXP(0.1667*4%)= 0.9936

so Spot price-Present value of dividend = 55-0.9936=54.0066

Forward price of a stock=54.0066*e^0.25*4%

= by using EXP function from excel =54.0066*EXP(0.25*4%)

= 54.55 so option 1 is correct

Value of the forward contract today= Present price of the contract-purchase price of the contract

=54.55-50= 4.55$

But the option II is stating 4.51$ which is incorrect

So answer is c