Question

A one-year forward contract is written on a dividend-paying stock. The current stock is $63.375 and it is known that the stock will pay a dividend of $1.50 per share in one month and a dividend of $2 per share in seven months’ time. The price of a one-month Treasury bill is 0.9967, a seven month Treasury bill 0.9741, and a twelve-month Treasury bill 0.9512, assuming a face value of $1. What is the forward price?

Answer 1

The one month interest rate is given by one month treasury bill

1*e^(-r*1/12) =0.9967

=>r=12*ln(1/0.9967)=0.039665=3.97%

Similarly, 7 month interest rate r= 12/7*ln(1/0.9741) =0.044985 =4.50%

and 12 month interest rate r =ln(1/0.9512) =0.050031=5.00%

Now, Forward price of a dividend paying stock is given by

F= (S-I) * e^(r*t)

where, S=spot price,

I=present value of dividends

r=continuously compounded interest rate for period t

t= time till expiry

So, I = 1.50*e^(-0.039665*1/12) + 2.00*e^(-0.044985*7/12)

=1.50*0.9967+2.00*0.9741

=$3.44325

So,

F= (63.375-3.44325)*e^(0.050031*1)

=$63.00647

which is the required forward price