Question

Q3 Forward Prices 24 Points Shares of a certain company's stock can be bought or sold today for So = $100. The forward price for delivery of one share of this stock at time T = 2 is F = $100.80. The stock will make dividend payments at times 5, 1, and . (There is no dividend paid at time 2.) Assume there is an ideal bank with a constant effective rate function R*(t) = R=.05.

Answer 1

Forward price of a dividend paying share is given by

F = (S-I) * (1+R)^T

Where

F is the forward price = $100.8

S is the spot price = $100

I is the present value of dividends = d/(1+R)^(1/2) + d/(1+R)^(2/2)+ d/(1+R)^(3/2)

R = 0.05

T = 2

So, puttiing the values in the equation

100.8 = (100-I) * (1+0.05)^2

=> (100-I) = 91.42857

=> I = 8.571429

=> d/(1+R)^(1/2) + d/(1+R)^(2/2)+ d/(1+R)^(3/2) = 8.571429

=> d * (1/1.05^0.5+1/1.05 +1/1.05^1.5) = 8.571429

=> d* 2.85771 =8.571429

=> d =2.999405 or 3

So the value of dividends is $3 per share