NPV and IRR calculator

1. Calculator

2. The formulas

NPV(r) = Σ_{t=0..T} CF_t / (1 + r)^t

IRR: r such that NPV(r) = 0

Payback = (t* − 1) + (−C_(t*−1)) / CF_t*

3. Worked example

1. A project costs €10,000 today and returns €2,000, €2,600, €2,800, €3,000 and €2,600 at the end of years 1 to 5.
2. At 8%: 2,000 / 1.08 = 1,851.85; 2,600 / 1.1664 = 2,229.08; 2,800 / 1.259712 = 2,222.73; 3,000 / 1.36048896 = 2,205.09; 2,600 / 1.4693280768 = 1,769.52. They sum to €10,278.27, so NPV = +€278.27: accept.
3. At 10% the same flows are worth €9,734.06 and NPV = −€265.94: reject. The IRR lies between, at 9.0016%, so the project clears any cost of capital below 9.00%.
4. Payback: the running total is −8,000, −5,400, −2,600 after three years, and year 4 brings 3,000, so payback = 3 + 2,600 / 3,000 = 3.87 years.
5. Discounted payback at 8%: the present values leave −1,491.25 after four years and year 5 adds 1,769.52, so 4 + 1,491.25 / 1,769.52 = 4.84 years.

Payback says the money comes back in under four years; only the NPV says whether it comes back with the 8% return it needed, and how much is left over. The glossary NPV page continues this example with a terminal value.

4. The Python behind it

import numpy as np
from scipy.optimize import brentq

cf = np.array([-10_000, 2_000, 2_600, 2_800, 3_000, 2_600])   # t = 0, 1, ..., 5
t = np.arange(cf.size)

def npv(rate):
    return (cf / (1 + rate) ** t).sum()

irr = brentq(npv, -0.99, 10)          # the rate where NPV crosses zero

def payback(flows):
    cum = np.cumsum(flows)
    j = np.argmax(cum >= 0)           # first period the total turns non-negative
    return j - 1 + -cum[j - 1] / flows[j]

print(f"NPV at 8%: {npv(0.08):.2f}")                         # 278.27
print(f"IRR: {irr:.4%}")                                     # 9.0016%
print(f"Payback: {payback(cf):.2f} years")                   # 3.87
print(f"Discounted payback: {payback(cf / 1.08 ** t):.2f}")  # 4.84

5. Reading the result

• When NPV and IRR disagree, for example between two projects of different size, follow the NPV: it is measured in money, the IRR in a rate.
• Cash flows that change sign more than once can have several IRRs or none. The calculator warns you and the NPV still decides.
• Payback ignores everything after the payback date. It measures how fast the outlay comes back, not whether the project is worth doing.
• The rate must match the period of the flows: monthly flows need a monthly rate, and the IRR comes out per month.