This question is asking to calculate the Internal Rate of Return (IRR) for a project. Here's how we can calculate it:

IRR Formula

The IRR is the discount rate ($r$) that makes the Net Present Value (NPV) of the project zero. The general equation for IRR is:

$0 = -C_0 + \frac{C_n}{(1 + r)^n}$

Where:

• $C_0 = 11,500$ (initial outlay, or the cost of investment),
• $C_n = 27,116$ (cash inflow after $n$ years),
• $n = 9$ (the number of years),
• $r$ is the IRR (to be calculated).

Rearranging the Formula:

$11,500 = \frac{27,116}{(1 + r)^9}$

Solving for $r$:

1. Divide both sides by 27,116: $\frac{11,500}{27,116} = \frac{1}{(1 + r)^9}$

2. Take the reciprocal: $(1 + r)^9 = \frac{27,116}{11,500}$

3. Simplify the fraction: $(1 + r)^9 = 2.35878$

4. Take the 9th root (or raise both sides to the power of $1/9$): $1 + r = (2.35878)^{1/9}$

5. Subtract 1 to find $r$: $r = (2.35878)^{1/9} - 1$

Let me calculate this. Calculating IRR using the formula initial_outlay = 11500 # C0 cash_inflow = 27116 # Cn years = 9 # n

Step-by-step calculation

ratio = cash_inflow / initial_outlay # Cn / C0 irr = (ratio ** (1 / years)) - 1 # (Cn/C0)^(1/n) - 1

Converting IRR to percentage and rounding

irr_percentage = round(irr * 100) # Rounding to the nearest whole percent irr_percentageThe IRR (Internal Rate of Return) for the project is 10%.

Would you like further details on how the calculation was done or how IRR applies in decision-making? Let me know!

Here are 5 related questions you might find useful:

1. How does IRR compare to NPV in evaluating investments?
2. What are the limitations of IRR for multi-period cash flows?
3. How do you compute IRR for more complex cash flow patterns?
4. What does a higher IRR signify about a project?
5. Can a project have multiple IRRs?

Tip: If you’re working on financial analysis often, learning to use Excel’s =IRR() function can save time for complex cash flows!