The question is asking to calculate the Internal Rate of Return (IRR) for a project with the following details:

• Initial investment (cost): $700,000
• Annual cash flow: $160,000
• Project duration: 8 years
• Discount rate (for comparison): 15% (though this is not directly used in calculating IRR).

IRR Calculation:

The IRR is the rate $r$ that satisfies the Net Present Value (NPV) equation set to zero:

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

Where:

• $CF_t$ = Annual cash flow ($160,000 per year)
• $C_0$ = Initial investment ($700,000)
• $T$ = Project duration (8 years)
• $r$ = IRR (to be solved).

For projects with equal annual cash flows, we can simplify this using the annuity formula:

$700,000 = 160,000 \cdot \left[ \frac{1 - (1 + r)^{-8}}{r} \right]$

Solving this equation for $r$ (the IRR) requires numerical methods. Let me calculate this for you. scipy.optimize import fsolve

Define the parameters

initial_investment = 700000 # Initial cost annual_cash_flow = 160000 # Annual cash flow project_duration = 8 # Duration in years

Define the IRR equation

def irr_equation(r): return annual_cash_flow * (1 - (1 + r) ** -project_duration) / r - initial_investment

Solve for IRR (r)

initial_guess = 0.1 # Starting guess for IRR irr = fsolve(irr_equation, initial_guess)[0] irr_percentage = irr * 100 # Convert to percentage irr_percentageThe Internal Rate of Return (IRR) for this project is approximately 15.78%.

This means that the project breaks even at a discount rate of 15.78%. Since this is slightly higher than the given discount rate of 15%, the project would be considered financially viable.

Would you like to see the detailed steps, explore alternative examples, or clarify any specific parts?

Here are 5 related questions to expand on this:

1. How is IRR used in comparing multiple investment opportunities?
2. What are the advantages and limitations of IRR in decision-making?
3. How does IRR compare with other metrics like NPV or Payback Period?
4. How does the project's cash flow pattern affect the IRR?
5. How can irregular cash flows influence the calculation of IRR?

Tip: Always compare the IRR with the cost of capital or required rate of return to evaluate the project's profitability effectively.