Calculating Irr By Hand

IRR Approximation Formula:

\[ IRR \approx L + \frac{NPV_L}{NPV_L - NPV_H} \times (H - L) \]

L (low rate, %):

H (high rate, %):

NPV_L ($):

NPV_H ($):

Approximate IRR:

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1. What is IRR Approximation?

The Internal Rate of Return (IRR) approximation using linear interpolation estimates the discount rate that makes the net present value (NPV) of cash flows equal to zero. This method provides a close approximation when exact calculation is complex.

2. How Does the Calculator Work?

The calculator uses the linear interpolation formula:

\[ IRR \approx L + \frac{NPV_L}{NPV_L - NPV_H} \times (H - L) \]

Where:

$ L $ — Low discount rate (%) where NPV is positive
$ H $ — High discount rate (%) where NPV is negative
$ NPV_L $ — Net Present Value at the low rate ($)
$ NPV_H $ — Net Present Value at the high rate ($)

Explanation: This method linearly interpolates between two discount rates where NPV changes sign to estimate the rate where NPV equals zero.

3. Importance of IRR Calculation

Details: IRR is a crucial metric in capital budgeting and investment analysis. It helps determine the profitability of potential investments and compare different investment opportunities.

4. Using the Calculator

Tips: Enter the low rate (L) and high rate (H) as percentages, and their corresponding NPV values in dollars. Ensure NPV_L is positive and NPV_H is negative for accurate interpolation.

5. Frequently Asked Questions (FAQ)

Q1: Why use linear interpolation for IRR?
A: Linear interpolation provides a quick approximation of IRR when exact calculation through iterative methods is not feasible manually.

Q2: What are typical IRR values for good investments?
A: Generally, an IRR higher than the cost of capital or hurdle rate indicates a good investment opportunity.

Q3: When is this approximation most accurate?
A: The approximation is most accurate when the two selected rates are close to each other and the NPV function is approximately linear between them.

Q4: What are limitations of this method?
A: This method assumes linearity between the two points, which may not hold for all cash flow patterns, especially those with multiple sign changes.

Q5: How should I choose the two discount rates?
A: Choose rates where one gives a positive NPV and the other gives a negative NPV, and they are reasonably close to each other for better accuracy.