Question

The spot price of an investment asset is $30 and the risk-free rate for all maturities is 10% with continuous compounding. The asset provides a dividend income of $2 at the end of the first year and at the end of the second year. What is the three-year futures price? (Hint: you would first need to find the PV of year 1 and year 2 incomes and then subtract it from  the spot price.)

		$19.67
		$35.84
		$45.15
		$40.50

Answer 1

Particulars	Amount
Spot Price	$                  30.00
PV of Div	$                    3.45
Revised spot Price	$                  26.55
Risk free Rate	10.00%
First Div	$                    2.00
First div in months	12
First div in Years	1.0000
Second Div	$                    2.00
Second div in months	24
Second div in Years	2.0000
Total time in Months	36
Total time in Years	3

PV of First Div:
= First Div * e^-rt
= $ 2 * e^(-0.1*1)
= $ 2 * e^(-0.1)
= $ 2 * 0.9048
= $ 1.81

PV of Second Div:
= Second Div * e^-rt
= $ 2 * e^(-0.1*2)
= $ 2 * e^(-0.2)
= $ 2 * 0.8187
= $ 1.64

Revised Spot Price = Spot Price - PV of Div
= $ 30 - $ 3.45
= $ 26.55

Future Price = Revised Spot price * e^rt
= $ 26.55 * e^(0.1*3)
= $ 26.55 * e^(0.3)
= $ 26.55 * 1.3499
= $ 35.84

Option B is correct.