Given,
$$ \sum_{t=0}^{N}\left ( \frac{B(t) -C(t)}{(1+Z)^t} \right )=0 $$
Find $Z$.
This equation is from a book called "Science Under Scarcity: Principles and Practice for Agricultural Research Evaluation and Priority Setting" written by Julian M. Alston; George W. Norton; Philip G. Pardey
The sum is Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.
- $t$ represents the time so interval $0..N$ is the time period (in years) in which we calculate the economic effects. 0 is the start year.
- $B(t)$ and $C(t)$ represents the benefits and costs. The values are known for each year $t$
- $Z$ - Internal Rate of Return (IRR) is a metric used in capital budgeting to estimate the profitability of potential investments. The internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero.
Usually, $Z$ is a known variable and given all the other known values I can calculate the sum for any $t$ in interval $0..N$
What I want to know is what is the value of $Z$ for which the sum (NPV) is 0.
My background is in software engineering. And math is an important component in my background but I'm stuck on solving this equation.
$Z$ - Internal Rate Of Return cannot be calculated analytically. I checked different software implementations and "guess-and-check"/"trial-and-error" method is the common way to find it.