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 $3 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 year 1 and year 2 incomes and then subtract it from the spot price.)

19.67
		$33.46
		$45.15
		$40.50

Answer 1

Present value of inflow
First Year Cash flow
PV= FV e^rt
Where,
FV= Future value
PV = Present Value
t = length of time
r= nominal annual interest rate
=3 / 2.7183^(0.1*1)
=2.7145
Second year's cash flow
=3 / 2.7183^(0.1*2)
=2.4561
Net Investment = $30-2.7145-2.4561
=24.8294
3 year 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
=24.8294 * 2.7183^(0.1*3)
=$33.46