Question

GOOG currently trades for $687 per share and pays a dividend of $9 in six months. The riskless rate of interest is 5% per year c.c. What is the fair value of a futures contract on GOOG maturing in 14 months?

Answer 1

Theoretical Futures Price = [Spot Price + PV of Cost of Carry - PV of Dividends]*Future Value Factor = [S + (C*e^-rt) + (D*e^-rt)]*e^rt

Where S = Spot Rate, e = constant (2.71828), r = Risk Free Rate, t = years to expiry

Applying the above formula,

S = 687, r = 0.05, t = 6/12 = ½ and 12/12 = for Dividends and 14/12 = 1.1667 for Futures Contract, C = 0, D = 9

Therefore, Theoretical Futures Price = [687+ 0 + (9*e^-0.05/2) + (9*e^-0.05)]*e^0.05*1.1667

= [687 + 0 + (9*e^-0.025) + (9*e^-0.05)]*e^0.05833

= [687+(9*0.9753)+(9*0.9512)]*1.060067 [Values from table]

= [687+8.7777+8.5608]*1.060067

= 704.3385*1.060067

= $746.65