What Is NPV
NPV (Net Present Value) is the present value of future cash flows discounted to today using a discount rate. If the npv project is greater than zero, the project returns more than the required rate.
NPV formula:
\[
NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} - I_0
\]
where \( CF_t \) is the cash flow in period \( t \), \( r \) is the discount rate, and \( I_0 \) is the initial investment.
What Is IRR
IRR (Internal Rate of Return) is the internal rate of return, i.e. the discount rate at which npv equals 0. IRR is convenient to compare with the required rate of return or WACC.
IRR formula:
\[
\sum_{t=1}^{n} \frac{CF_t}{(1 + IRR)^t} - I_0 = 0
\]
If the irr project is higher than the discount rate, the project is efficient.
NPV and IRR Together
| Metric | When to Use |
|---|---|
| NPV | Comparing projects of different scale and duration |
| IRR | Assessing profitability as a percentage |
NPV > 0 and IRR > discount rate at the same time is a good sign. If the metrics contradict each other, prefer NPV, because it reflects absolute profit.
Calculating NPV and IRR in Excel
Use the following functions:
=NPV(rate, CF1, CF2, ...)— future cash flows only, subtract investment manually.=IRR(range_of_flows)— internal rate of return.
Step-by-step example of npv in excel:
- Enter the initial investment in cell A1 with a minus sign.
- Enter cash flows by year in A2:A5.
- In cell B1 enter
=NPV(rate,A2:A5)+A1. - In cell B2 enter
=IRR(A1:A5).
Practical Example
Investment \( I_0 = \$100,000 \). Cash flows over 3 years: \( CF_1 = \$40,000 \), \( CF_2 = \$50,000 \), \( CF_3 = \$60,000 \). Discount rate \( r = 12\% \).
\[
NPV = \frac{40{,}000}{1.12} + \frac{50{,}000}{1.12^2} + \frac{60{,}000}{1.12^3} - 100{,}000
\]
\[
NPV \approx 35{,}714 + 39{,}860 + 42{,}707 - 100{,}000 = 18{,}281
\]
The project is profitable. IRR in this example is approximately 23% — higher than 12%, so the project is efficient.
Interpreting the Results
- NPV positive — the project increases company value.
- NPV equals 0 — the project gives exactly the required return.
- NPV negative — the project destroys value, it is better to reject it.
- IRR greater than discount rate — accept the project.
- IRR less than discount rate — the project does not cover the required return.
Common Mistakes
- Using the wrong discount rate — usually WACC or the investor's required return.
- Ignoring irregular cash flows.
- Comparing NPV of projects with different durations without adjustment.
- Choosing a project with a high IRR but a small NPV.
- Forgetting about reinvestment — the classic IRR assumes reinvestment at the IRR rate.
Frequently Asked Questions
What is more important — NPV or IRR?
For comparing projects of different scales, use NPV. IRR is useful for assessing return as a percentage.
What discount rate should I use?
Company WACC, the investor's required return, or the rate of an alternative investment.
Can NPV be positive while IRR is below the discount rate?
No. When the discount rate is below the IRR, NPV is positive.
How to calculate NPV with uneven cash flows?
Sum the discounted cash flows for each period separately.
What is Modified IRR?
MIRR fixes the classic IRR assumption of reinvesting at the IRR rate and is more realistic.
Calculate NPV and IRR for your project in the APF Dashboard planning calculator or build a financial model for detailed scenario analysis.