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:

0=C0+t=1nCt(1+IRR)t0 = -C_0 + \sum_{t=1}^{n} \frac{C_t}{(1+IRR)^t}

Where:

  • C0C_0 is the initial investment (in this case, $76,940),
  • CtC_t is the annual cash flow ($18,120),
  • tt is the year, and
  • nn 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:

  1. What is the difference between IRR and NPV in evaluating projects?
  2. How do changes in cash flow patterns affect the IRR?
  3. What does it mean if the IRR is higher than the cost of capital?
  4. How is IRR used in decision-making for multiple projects?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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)