Question

Consider a forward contract for one share of a stock, with T = 0.5 (6 months).
The current stock price is S0 = 50. We assume that the risk-free interest rate is r = 0.05,
and that the stock pays discrete dividends, there being exactly one dividend payment, of
size 0.75, between times 0 and T, and the payment happens at time t = 1/3 (4 months).
Calculate the price of the forward contract. Show your work. Use two decimal places in your
answer. Use sufficiently many decimals in intermediate calculations to make sure that your
two decimals in the final answer are correct.

Answer 1

Particulars	Amount
Spot Price	$                   50.00
PV of Div	$                     0.74
Revised spot Price	$                   49.26
Risk free Rate	5%
First Div	$                     0.75
First div in months	4
First div in Years	0.3333
Total time in Months	6
Total time in Years	0.5
PV of First Div:
= First Div * e^-rt
= $ 0.75 * e^(-0.05*0.3333)
= $ 0.75 * e^(-0.0167)
= $ 0.75 * 0.9835
= $ 0.74
Revised Spot Price = Spot Price - PV of Div
= $ 50 - $ 0.74
= $ 49.26
Future Price = Revised Spot price * e^rt
= $ 49.26 * e^(0.05*0.5)
= $ 49.26 * e^(0.025)
= $ 49.26 * 1.0253
= $ 50.51