Question

12. The spot price of an investment asset is $40 and the risk-free rate for all maturities is 8% 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?

A) $46.32 B) $41.23 C) $43.55 D) $47.31

Answer 1

Given,
Dividend at the end of 1st and 2nd Year = $2 respectively
Risk Free Rate = r = 8% = 0.08
No of Years = t
Spot Price = P = $40
Now,
e^rt using Excel Formula = e^(0.08*1) = e^0.08 = EXP(0.08) = 1.0832871
e^rt using Excel Formula = e^(0.08*2) = e^0.16 = EXP(0.16) = 1.1735109
e^rt using Excel Formula = e^(0.08*3) = e^0.24 = EXP(0.24) = 1.2712492
Calculation of Present Value of Dividend.
Present Value of Dividend received at the end of first year
= Dividend at the end of first year / e^rt
= $2 / e^(0.08*1)
= $2 / 1.0832871
= $1.84623263768
Present Value of Dividend received at the end of second year
= Dividend at the end of second year / e^rt
= $2 / e^(0.08*2)
= $2 / 1.1735109
= $1.7042875358
3 Year Forward Price
= (Spot Price - Present Value of Dividend)e^rt
= ($40 - $1.84623263768 - $1.7042875358)^e(0.08*3)
= $36.4494798266*1.2712492
= $46.34
≈ $46.32