Net Present Value Converter
Convert between present value, future value, and discount rate using time-value-of-money relationships.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
NPV = -Initial Investment + Sum of [Cash Flow(t) / (1 + r)^t]
Where Cash Flow(t) is the net cash flow in period t, r is the discount rate per period, and t is the period number. The initial investment is subtracted as a cash outflow at time zero. The profitability index equals Total PV of future cash flows divided by Initial Investment. Simple payback period is the time it takes for cumulative undiscounted cash flows to equal the initial investment.
Worked Examples
Example 1: Business Expansion NPV Analysis
Problem:A company invests $10,000 upfront. Expected cash flows: $3,000 (Y1), $4,000 (Y2), $5,000 (Y3), $4,000 (Y4), $3,000 (Y5). Discount rate: 8%.
Solution:PV of Y1: $3,000 / (1.08)^1 = $2,777.78\nPV of Y2: $4,000 / (1.08)^2 = $3,429.36\nPV of Y3: $5,000 / (1.08)^3 = $3,969.16\nPV of Y4: $4,000 / (1.08)^4 = $2,940.12\nPV of Y5: $3,000 / (1.08)^5 = $2,041.75\nTotal PV = $15,158.17\nNPV = $15,158.17 - $10,000 = $5,158.17\nPI = $15,158.17 / $10,000 = 1.5158
Result:NPV = $5,158.17 (positive, accept the project) | PI = 1.52
Example 2: Equipment Purchase Decision
Problem:Purchase equipment for $25,000. Expected annual savings: $8,000 per year for 4 years. Discount rate: 10%.
Solution:PV of Y1: $8,000 / (1.10)^1 = $7,272.73\nPV of Y2: $8,000 / (1.10)^2 = $6,611.57\nPV of Y3: $8,000 / (1.10)^3 = $6,010.52\nPV of Y4: $8,000 / (1.10)^4 = $5,464.11\nTotal PV = $25,358.93\nNPV = $25,358.93 - $25,000 = $358.93\nThe equipment barely meets the required return threshold.
Result:NPV = $358.93 (marginally positive) | PI = 1.014 | Payback: 3.13 years
Frequently Asked Questions
What is Net Present Value and how is it calculated?
Net Present Value (NPV) is a financial metric that calculates the difference between the present value of all future cash inflows and the initial investment outflow. It uses a discount rate to convert future cash flows back to their present-day equivalent, reflecting the time value of money. The formula sums each future cash flow divided by (1 + discount rate) raised to the power of the period number, then subtracts the initial investment. A positive NPV indicates the investment is expected to generate value above the required return rate, while a negative NPV suggests the investment would destroy value. NPV is widely considered the most theoretically sound method for evaluating investment decisions.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy