How To Calculate Incremental IRR On BA II Plus

IRR Formula:

\[ IRR = [CF_0 + \sum \frac{CF_t}{(1+IRR)^t}] = 0 \]

Initial Investment (CF₀):

Cash Flow Year 1 (CF₁):

Cash Flow Year 2 (CF₂):

Cash Flow Year 3 (CF₃):

Incremental IRR:

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1. What Is Incremental IRR?

Incremental Internal Rate of Return (IRR) is used to evaluate the additional return from choosing one investment over another. It represents the discount rate that makes the net present value of the difference between two cash flow streams equal to zero.

2. How To Calculate On BA II Plus

Step-by-step BA II Plus calculation:

BA II Plus Steps:

Press [CF] to enter Cash Flow worksheet
Clear previous data: [2nd] [CE/C]
Enter initial investment as negative: [amount] [+/-] [ENTER] [↓]
Enter subsequent cash flows: [amount] [ENTER] [↓]
For repeated cash flows: [amount] [ENTER] [↓] [frequency] [ENTER] [↓]
Calculate IRR: [IRR] [CPT]

Key Points:

Initial investment must be entered as negative (outflow)
Use [↓] arrow to navigate between periods
[IRR] [CPT] computes the internal rate of return
For incremental IRR, calculate difference between project cash flows first

3. IRR Formula Explanation

Mathematical Foundation: The IRR is the discount rate that satisfies the equation where the net present value equals zero:

\[ NPV = CF_0 + \frac{CF_1}{(1+IRR)^1} + \frac{CF_2}{(1+IRR)^2} + \frac{CF_3}{(1+IRR)^3} + \cdots = 0 \]

Where:

\( CF_0 \) — Initial investment (negative value)
\( CF_t \) — Cash flow at time period t
\( IRR \) — Internal Rate of Return
\( t \) — Time period (years)

4. Using The Calculator

Instructions: Enter the initial investment as a negative number if it's an outflow. Enter subsequent cash flows as positive for inflows. The calculator will approximate the IRR using iterative methods.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between IRR and incremental IRR?
A: IRR evaluates a single project, while incremental IRR compares two mutually exclusive projects by analyzing the difference in their cash flows.

Q2: When should I use incremental IRR?
A: Use when choosing between mutually exclusive projects with different scales or timing of cash flows, especially when IRR and NPV give conflicting results.

Q3: What are the limitations of IRR?
A: Multiple IRRs can occur with unconventional cash flows, and IRR assumes reinvestment at the calculated rate, which may not be realistic.

Q4: How accurate is the BA II Plus IRR calculation?
A: The BA II Plus uses sophisticated algorithms and provides highly accurate IRR calculations for most practical purposes.

Q5: Can I calculate IRR for more than 20 periods?
A: The BA II Plus can handle up to 24 uneven cash flows, which is sufficient for most investment analyses.