Question

Please explain the reasoning behind the following: why* might an NPV (net present value) of 100$ in years 2-3 to be higher or lower than in years 3-4?

Answer 1

NPV for a time period of n can be calculated using the formula: -C+C1/(1+r)+C2/(1+r)^2+....Cn/(1+r)^n; where C is the initial investment, C1 to Cn are cash inflows and r is the required rate of return.

In the formula, we observe that, the denominator contains (1+r)^n. So, the value of the denominator increases, as n increases. As denominator increases, the value decreases.

In the given scenario, let r be the discount rate. Net Present value of $100 in Year 2-3 will be 100/(1+r)^2+100/(1+r)^3. Net Present value of $100 in Year 3-4 will be 100/(1+r)^3+100/(1+r)^4. The denominators in Year 3-4 is greater than that of the denominators in Year 2-3. So, NPV of $100 in Years 2-3 is higher than in Years 3-4.