If I have an opportunity of investment that costs
I in year 0 and gives me
CF_1 in year 1, I will accept it only if
NPV = -I + (CF_1)/(1+k)
Now in order to discount the cash flows I have to choose
k, the discount rate.
k will be the interest rate of an investment with the same risk. Of course I don't have to choose a random investment, but the best investment at the same risk, that is, the investment with the highest return but the same risk. This alternative investment is then at the efficient frontier. But how can the investment I started from have a higher return then this alternative investment to begin with, given that this alternative investment is at the efficient frontier?
Stated otherwise, If I engage in the investment I started from, in year 0 I will pay
I, and after waiting one year, I will put
CF_1 in my pockets.
If instead I engage in the best alternative investment, after 1 year I will obtain
I(1+k). Of course the NPV condition is at all equal to the condition
CF_1 > I(1+k). But if the investment which gives me
k is at the efficient frontier, how can this last equation be satisfied at all?