To calculate NPV and IRR on the TI BA II Plus: Press CF ➔ Press 2ND + CLR WORK ➔ Input CF0 (negative outflow) & press ENTER ➔ Use ↓ to enter cash inflows C01, C02 and frequencies F01, F02 ➔ Press NPV, enter discount rate I, press ENTER, ↓, then CPT ➔ Press IRR, then press CPT.
1. Understanding NPV & IRR Fundamentals
Evaluating multi-year investment projects or corporate capital budgets requires analyzing cash flows that occur across different points in time. Money received today is worth more than money received in the future due to opportunity costs, inflation, and financial risk. In financial decision-making, Net Present Value (NPV) and Internal Rate of Return (IRR) represent the two gold-standard capital budgeting metrics tested extensively in the CFA, CPA, and FRM curricula.
The Texas Instruments BA II Plus (and BA II Plus Professional) calculator features a dedicated Cash Flow (CF) Worksheet designed specifically to solve complex discounted cash flow (DCF) models with uneven cash flows and variable frequencies in seconds.
Mathematical Definitions
- Net Present Value (NPV): The sum of all present values of incoming cash flows minus
the initial investment outlay ($CF_0$).
$$\text{NPV} = \text{CF}_0 + \sum_{t=1}^{n} \frac{\text{CF}_t}{(1 + r)^t}$$ Where $r$ is the required rate of return (hurdle rate / cost of capital) and $t$ is the time period. If NPV > 0, the investment adds value and should be accepted. - Internal Rate of Return (IRR): The exact discount rate ($r^*$) that equates the
present value of future cash inflows to the initial cash outflow, driving the NPV to
zero.
$$0 = \text{CF}_0 + \sum_{t=1}^{n} \frac{\text{CF}_t}{(1 + \text{IRR})^t}$$ If IRR > Hurdle Rate ($r$), the project yields a return exceeding its cost of capital.
2. Key Functions of the BA II Plus Cash Flow Worksheet
Before diving into our real-world case study, let's clarify the specific keys on your calculator that govern the Cash Flow worksheet:
| Key / Symbol | Calculator Screen Prompt | Function & Practical Purpose |
|---|---|---|
| CF | CF0 = |
Opens the Cash Flow Worksheet starting at initial outlay ($CF_0$). |
| 2ND + CLR WORK | CF0 = 0.00 |
Clears all previous cash flows stored in memory registers. Crucial first step! |
| ENTER | ▶ (Triangle Indicator) |
Saves the currently typed number into the active cash flow register. |
| ↓ / ↑ | C01, F01, C02... |
Navigates down and up through cash flow registers ($C_{01}$) and frequencies ($F_{01}$). |
| +/− | -150,000.00 |
Toggles positive (inflow) vs negative (outflow) sign. Initial outlay $CF_0$ must be negative! |
| NPV | I = ➔ NPV = |
Switches to NPV mode. Prompts for discount rate $I$, then calculates NPV upon pressing CPT. |
| IRR | IRR = 0.00 |
Switches to IRR mode. Solves for IRR via bisection algorithm upon pressing CPT. |
3. Step-by-Step Capital Budgeting Case Study
Let's evaluate a realistic multi-year corporate expansion project (Project Apex). This example demonstrates how to handle uneven cash flows and cash flow frequency multipliers ($F_k$) to save keystrokes.
Apex Logistics Inc. is considering purchasing a fleet of autonomous electric delivery vans. The financial model details the following cash flow projection:
- Initial Upfront Outlay ($CF_0$): $150,000 (Equipment purchase & installation)
- Year 1 Cash Inflow ($C_{01}$): $35,000
- Years 2, 3, and 4 Cash Inflow ($C_{02}$): $45,000 per year (3 consecutive equal annual cash flows)
- Year 5 Cash Inflow ($C_{03}$): $55,000 (Includes equipment salvage value)
- Company Hurdle Rate / Cost of Capital ($I$): 10.0%
Tasks:
1. Calculate the Net Present Value (NPV) of Project Apex.
2. Calculate the Internal Rate of Return (IRR).
3. Determine whether Apex Logistics should accept or reject the project.
4. Full Keystroke Execution & Solutions
Follow this exact keystroke-by-keystroke sequence on your BA II Plus calculator or on our BA II Plus Online Simulator.
Step 1: Clear Existing Cash Flow Memory
Always clear the worksheet memory before starting a new problem. Pressing CE/C alone does not clear stored memory registers!
Open CF Register & Clear Memory
Press CF ➔ Press 2ND ➔ Press CLR WORK (the bottom-left key).
Step 2: Enter Initial Outflow ($CF_0$) and Inflow Series ($C_{01}$–$C_{03}$)
Remember: Expenditures ($CF_0$) are cash outflows and must be entered with a negative sign using the +/− key!
| Step / Entry | Keystroke Sequence | Display Screen Output | Notes & Logic |
|---|---|---|---|
| Initial Outlay $CF_0$ | 150000 ➔ +/− ➔ ENTER | CF0 = -150,000.00 |
Outflow must show negative sign. Press ENTER to store. |
| Year 1 Cash Flow $C_{01}$ | ↓ ➔ 35000 ➔ ENTER | C01 = 35,000.00 |
First year cash inflow of $35,000. |
| Year 1 Frequency $F_{01}$ | ↓ | F01 = 1.00 |
Occurs once. Leave default frequency as 1. |
| Years 2–4 Cash Flow $C_{02}$ | ↓ ➔ 45000 ➔ ENTER | C02 = 45,000.00 |
Cash flow amount for Years 2, 3, and 4. |
| Years 2–4 Frequency $F_{02}$ | ↓ ➔ 3 ➔ ENTER | F02 = 3.00 |
Pro Tip: Set frequency $F_{02} = 3$ since $45,000 repeats for 3 consecutive periods! |
| Year 5 Cash Flow $C_{03}$ | ↓ ➔ 55000 ➔ ENTER | C03 = 55,000.00 |
Final year cash inflow. |
| Year 5 Frequency $F_{03}$ | ↓ | F03 = 1.00 |
Occurs once in Year 5. |
Step 3: Compute Net Present Value (NPV)
Now that all cash flows are stored in memory, calculate NPV at a 10% discount rate:
- Press NPV. Screen shows
I = 0.0000. - Type 10 and press
ENTER (Note: Enter 10 for 10%, do not enter 0.10!). Screen
shows
I = 10.0000. - Press ↓ down arrow. Screen shows
NPV = 0.0000. - Press CPT (Compute button).
Result: The NPV = $17,703.71.
Step 4: Compute Internal Rate of Return (IRR)
To compute IRR, you do not need to re-enter any cash flow data! The calculator retains all entries in memory:
- Press IRR. Screen shows
IRR = 0.0000. - Press CPT. (The calculator screen will show a small
COMPUTINGindicator for 1–2 seconds as it runs the numerical root-finding algorithm).
Result: The IRR = 14.37% (or 14.3678%).
Decision: ACCEPT Project Apex.
- NPV Criterion: NPV is +$17,703.71, which is greater than $0. Accepting the project increases shareholder wealth by $17,703.71 in present-value terms.
- IRR Criterion: IRR is 14.37%, which exceeds the company's 10.0% hurdle rate / cost of capital by 437 basis points.
5. Advanced Incremental Insights & Pitfalls
Most standard online guides skip the nuanced pitfalls that cause candidates to fail questions in exam settings or produce flawed corporate valuation models. Here are crucial technical insights every BA II Plus user must master:
Pitfall #1: How to Fix "Error 5" on the BA II Plus
If you press CPT IRR and your calculator screen displays
Error 5, do not panic! Error 5 means "No Solution Found" or mathematically invalid
cash flow sign pattern.
- Cause 1: Forgetting the negative sign on $CF_0$. If all cash flows (including
$CF_0$) are entered as positive numbers, there is no mathematical rate of return that can
discount positive numbers to zero.
Fix: Press CF, check $CF_0$, re-enter as negative using +/−, and press ENTER. - Cause 2: Forgetting to clear previous worksheet data. Residual cash flows
stored deep in higher registers (e.g. $C_{08}$) from a prior problem can corrupt your current
calculation.
Fix: Always execute CF ➔ 2ND + CLR WORK before typing new values.
Pitfall #2: The Reinvestment Rate Assumption Paradox (NPV vs. IRR Conflict)
When evaluating two mutually exclusive projects (where accepting Project A means rejecting Project B), the NPV and IRR methods can sometimes yield conflicting rankings. Why?
- NPV Assumption: Assumes intermediate cash inflows are reinvested at the Opportunity Cost of Capital / Hurdle Rate (e.g., 10%). This is realistic and conservative for corporations.
- IRR Assumption: Mathematically assumes intermediate cash inflows are reinvested at the project's own IRR (e.g., 14.37% or 35%). This assumption is often unrealistically high for highly profitable projects.
When NPV and IRR conflict for mutually exclusive projects, ALWAYS choose the project with the higher positive NPV! NPV measures absolute dollar wealth creation, whereas IRR measures percentage rate of return.
Pitfall #3: Non-Normal Cash Flows & Multiple IRRs
A project with normal cash flows has exactly one sign change (an initial negative outflow followed by positive inflows: $-, +, +, +$).
However, projects involving decommissioning costs, environmental remediation, or nuclear power plants often have non-normal cash flows with multiple sign changes (e.g., $-, +, +, -$). According to Descartes' Rule of Signs, a cash flow series can have as many real IRRs as there are sign changes. The BA II Plus algorithm will compute only one root (or throw Error 5), making NPV the only reliable metric for non-normal cash flows.
6. How to Calculate Modified IRR (MIRR) on the BA II Plus
To overcome the unrealistic reinvestment assumption of standard IRR, corporate finance professionals use Modified Internal Rate of Return (MIRR). MIRR assumes cash inflows are reinvested at the company's actual cost of capital ($r$).
While the standard TI BA II Plus does not have a single "MIRR" button, you can compute MIRR in 3 quick steps using the calculator's TVM Keys and memory registers:
Compound Inflows to Terminal Value ($TV_n$)
Calculate the Future Value (FV) at Year $N=5$ of each inflow compounded at the cost of capital ($10\%$):
- Year 1 ($35,000$): $35,000 \times (1.10)^4 = \$51,243.50$
- Year 2 ($45,000$): $45,000 \times (1.10)^3 = \$59,895.00$
- Year 3 ($45,000$): $45,000 \times (1.10)^2 = \$54,450.00$
- Year 4 ($45,000$): $45,000 \times (1.10)^1 = \$49,500.00$
- Year 5 ($55,000$): $55,000 \times (1.10)^0 = \$55,000.00$
Total Terminal Value ($TV_5$) = $270,088.50
Use TVM Keys to Solve for MIRR
Input values into TVM registers:
- 5 ➔ N
- 150000 ➔ +/− ➔ PV
- 0 ➔ PMT
- 270088.50 ➔ FV
- Press CPT ➔ I/Y
Comparison Summary:
- Standard IRR: 14.37% (Assumes reinvestment at 14.37%)
- Modified IRR (MIRR): 12.48% (Assumes realistic reinvestment at 10.0% cost of capital)
Practice NPV & IRR Calculations Online Right Now
Launch BA II Plus Calculator ➔7. CFA Exam Speed Checklist & FAQs
⚡ Exam Day Checklist for CFA & FRM Candidates
- Check Decimals: Ensure your calculator displays 4 to 6 decimal places (Press 2ND ➔ FORMAT ➔ Type
4➔ Press ENTER). - Clear Worksheets First: Always press CF ➔ 2ND ➔ CLR WORK before entering data for a new problem.
- Double Check Frequencies ($F_k$): When entering consecutive identical cash flows, use $F_{01}, F_{02}$ to save precious exam seconds.
- Verify Signs: Cash outflows ($CF_0$) must be negative (+/−), cash inflows positive.
Frequently Asked Questions (FAQ)
A: CF0 represents the initial cash outflow at time period $t=0$.
C01 is the dollar amount of the first subsequent cash flow stream at $t=1$.
F01 is the frequency (number of consecutive periods) that the cash flow amount
C01 repeats.
A: Simply press NPV, type the new interest
rate (e.g. 12), press ENTER, press ↓ down arrow, and press CPT to re-compute NPV instantaneously.
A: Yes! Our online simulator matches the internal algorithms and LCD display output of the physical Texas Instruments BA II Plus calculator with 100% mathematical precision.