Math Problem Statement
A project with an initial cost of $76,940 is expected to generate annual cash flows of $18,120 for the next 8 yearsWhat is the project's internal rate of return
Solution
The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of a series of cash flows equal to zero. In this case, the initial cost (outflow) is $76,940, and the project generates annual cash inflows of $18,120 for 8 years.
To calculate the IRR, we use the following equation:
Where:
- is the initial investment (in this case, $76,940),
- is the annual cash flow ($18,120),
- is the year, and
- is the number of years (8 years in this case).
Let me calculate the IRR for this project.
The internal rate of return (IRR) for this project is approximately 16.71%.
Would you like more details on the calculation, or do you have any further questions?
Here are 5 related questions to explore:
- What is the difference between IRR and NPV in evaluating projects?
- How do changes in cash flow patterns affect the IRR?
- What does it mean if the IRR is higher than the cost of capital?
- How is IRR used in decision-making for multiple projects?
- What are the limitations of relying solely on IRR for project evaluations?
Tip: If a project’s IRR exceeds the required rate of return, it is generally considered a good investment.
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Math Problem Analysis
Mathematical Concepts
Finance
Internal Rate of Return (IRR)
Net Present Value (NPV)
Formulas
0 = -C_0 + Σ (C_t / (1 + IRR)^t)
Where C_0 = initial cost, C_t = annual cash flow, t = year, IRR = Internal Rate of Return
Theorems
IRR Theorem
NPV Theorem
Suitable Grade Level
College/University (Finance, Business Studies)
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