NPV Calculator

What Is NPV?

Net Present Value (NPV) discounts every future cash flow back to today's dollars using a chosen rate, then sums them up. A positive NPV means the project is expected to create value above your required return; a negative NPV means it would destroy value.

\[ NPV = \sum \frac{CF_t}{(1 + r)^{t}} \]

Where \(CF_t\) is the cash flow at period \(t\) (\(CF_0\) is typically the initial outlay, not discounted) and \(r\) is the per-period discount rate.

Why Discount?

A dollar today is worth more than a dollar tomorrow because:

1. Today's dollar can be invested and earn a return.
2. Inflation erodes tomorrow's purchasing power.
3. There is risk that future cash flows may not materialise.

The discount rate r should reflect both the time value of money (risk-free rate) and the riskiness of the project.

Worked Example

A project costs $10,000 today and returns $3,000 / $4,200 / $6,800 over the next three years. Discount rate 10% annually:

\[ NPV = -10000 + \frac{3000}{1.1} + \frac{4200}{1.1^{2}} + \frac{6800}{1.1^{3}} = -10000 + 2727.27 + 3471.07 + 5104.59 \approx \text{\$1,302.93} \]

Positive NPV → accept at a 10% hurdle rate.

Choosing the Discount Rate

• Cost of capital: WACC (weighted average cost of capital) is the textbook choice for corporate finance projects.
• Required return: equity investors often use a hurdle rate (e.g. 12-15%) reflecting their opportunity cost.
• Risk-adjusted rate: higher-risk projects demand higher rates (venture capital, emerging markets).

Using a too-low discount rate makes bad projects look good; a too-high rate makes good projects look bad. Be deliberate.

Profitability Index (PI)

PI measures value created per dollar invested:

\[ PI = \frac{PV \text{ of Inflows}}{|PV \text{ of Outflows}|} \]

• PI > 1: project creates value.
• PI < 1: project destroys value.
• PI = 1: NPV is zero (break-even).

PI is especially useful when comparing projects with different scales — a $1M project with PI=1.5 creates more value than a $100k project with PI=2.

Compounding Frequency

Converting annual rates to per-period rates:

\[ \text{per-period rate} = \frac{\text{annual rate}}{\text{compounding frequency}} \]

For 10% annual, monthly compounding → 0.833% per month. Daily compounding → 0.0274% per day. Higher compounding at the same nominal rate gives slightly higher effective annual rates.

NPV vs. IRR

• NPV measures value created (a dollar amount), depends on the discount rate you choose.
• IRR is the rate that makes NPV = 0; doesn't depend on a discount rate.

NPV is generally the preferred metric in capital budgeting because it directly measures value added. IRR is most useful for quick screening and communication.

Limitations

• NPV is sensitive to the discount rate. Small changes can flip the accept/reject decision.
• It assumes you can reinvest intermediate cash flows at the discount rate.
• It depends on accurate cash-flow forecasts — garbage in, garbage out.

About This Tool

NPV is computed as the sum of discounted cash flows at the chosen rate and frequency. PV of inflows (positive PV) and PV of outflows (absolute value of negative PV) feed the Profitability Index. The chart shows each period's cash flow as a coloured bar (green positive, red negative) and the discounted present value as an amber line — when the amber line sits above the red outflows and the cumulative net is positive, the project is creating value.