The Internal Rate of Return (IRR) is the rate that makes the net present value (NPV) of a series of cash flows equal to zero. For this project, we are solving for $r$ in the equation:

$NPV = -C_0 + \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t} = 0$

Where:

• $C_0 = 9,000$ (initial outlay)
• $C_t = 1,583$ (cash inflow per year)
• $n = 11$ (number of years)

This results in the equation:

$9,000 = \sum_{t=1}^{11} \frac{1,583}{(1 + r)^t}$

To compute $r$, we use numerical methods (e.g., trial-and-error, financial calculators, or software tools). Let’s solve this step-by-step:

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Step 1: Use the IRR formula in an approximate method (trial-and-error or solver)

We will estimate $r$ by testing different values.

1. For $r = 10\%$: $NPV = \sum_{t=1}^{11} \frac{1,583}{(1.10)^t} \approx 9,663 \, (\text{too high})$

2. For $r = 12$]