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Investment decisions, Present Value and Net Present Value
This paragraph is going to teach you how you should make up your mind when having the choice between several investment opportunities (only the financial aspect will be considered, everything else being supposed to be equal).
We define the Present Value at t=0 (PV_0) of a stream of future cash flows F = F_0, F_1, …, F_n (respectively earned at t=0, 1, …, n) to be the sum of these cash flows when they are discounted at rate r. In this way, PV_0 = F_0 + F_1 / (1+r) + … + F_n / (1+r)^n.
What does the rate r correspond to ? Well, r denotes the rate at which you would have been able to invest your money during the period under consideration: for instance, F_1 is received at t=1. How much money should you have at t=0 so that it is worth the same as receiving F_1 at t=1 ? The answer is F_1 / (1+r), because if you have a chance to invest this amount at rate r, then at t=1 you will indeed receive (1+r) x F_1 / (1+r) = F_1.
Similarly, we define the Net Present Value at t=0 (NPV_0) of an investment to be the different between the present value at t=0 of the expected cash flows generated diminished by the present value at t=0 of the negative cash flows incurred by the firm in order to invest in the project.
NPV_0 (Project) = PV_0 (Revenue from the project) – PV_0 (Money invested in the project).
When deciding between several investment opportunities, you must always pick the one yielding the highest NPV (unless there are other non-financial priorities at stake).
Example: compensation packages of managers (vested stock options)
In order to prevent managers from conducting short-term investment policies, the company often grants them vested stock options, that is to say options to purchase stocks of the company at a fixed price in the future, but only after a certain period of time (for instance, we are at time t=0 and John is granted 1,000 stock options with exercise price 100 and a vesting period of 5 years means that John will be able to purchase 1,000 shares of his company at a price of 100 anytime after t=5 years). This practice encourages long-term profitability instead of short-term results which may prove detrimental to the long-term prosperity of the firm.