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 an income of $2 at the end of the first year and at the end of the second year. What is the three-year forward price? (Hint: First find the PV of $2 income at year 1 and year 2 using 10% rate and subtract it from spot price.)

		$19.67
		$35.84
		$45.15
		$40.50

Answer 1

PV of Dividend income of $2 at the end of first year
PV= FV e^rt
Where,
FV= Future value
PV = Present Value
t = length of time
r= nominal annual interest rate
=2 / 2.7183^(0.1*1)
=1.81
PV of Dividend income of $2 at the end of second year
PV= FV e^rt
Where,
FV= Future value
PV = Present Value
t = length of time
r= nominal annual interest rate
=2 / 2.7183^(0.1*2)
=1.64
PV of Total Income = $1.81+1.64
=$3.45
Net Spot price = $30-3.45
=$26.55
3 years forward price
P(t)= P0 e^rt
Where,
P(t) = value at time
P0= present value
t = length of time
r= nominal annual interest rate
=26.55 * 2.7183^(0.1*3)
=35.84