A business owner is evaluating whether to buy a $180,000 piece of equipment that will generate $45,000 per year in savings over 6 years. Before taking on debt, they need to know the payback period and whether the NPV is positive at their cost of capital.
NPV & Payback Period
Investment
Your required return / cost of capital
Payback period = Initial investment ÷ Annual cash inflow
NPV = Σ [Cash flow ÷ (1 + r)ⁿ] − Initial investment
Decision rule: NPV > 0 means the investment creates value. NPV < 0 means you'd be better off investing elsewhere at your discount rate.
Reference: Finance Formulas Cheatsheet — Section 6 Investment Analysis & Section 8 Time Value of Money
Results are estimates for planning purposes. Verify with current standards and a qualified professional.
1 What this calculator does
Calculates Net Present Value (NPV) and simple payback period for an investment with annual cash inflows. NPV discounts future cash flows at the required rate of return to determine whether the investment creates or destroys value in today's dollars.
2 Formula & professional reasoning
Payback period = Initial investment / Annual inflow (simple)
NPV = -Investment + Sum[Annual inflow / (1 + Discount rate)^year] for year 1 to n
Positive NPV: investment creates value at the discount rate
Negative NPV: investment destroys value -- consider alternatives
The NPV framework captures the time value of money -- a dollar received today is worth more than a dollar received in 5 years because it can be invested in the interim. The discount rate (also called the required rate of return or hurdle rate) represents the minimum acceptable return for the investment, which may be the cost of borrowing or an opportunity cost rate. NPV > 0 means the investment generates more than the required return. The simple payback period ignores the time value of money but is useful as a quick risk measure.
3 Worked examples
⚠️ Illustrative example only — not clinical or professional instruction.
Basic
Equipment purchase -- positive NPV
Given: Investment: $180,000 | Annual inflow: $45,000 | Years: 6 | Discount rate: 8%
Working:
Payback: $180,000/$45,000 = 4.0 years | NPV: -$180,000 + $45,000/1.08 + $45,000/1.08^2 + ... + $45,000/1.08^6 | Sum of PV annuity: $45,000 x [(1-(1+0.08)^-6)/0.08] = $45,000 x 4.6229 = $208,030Answer: Payback: 4.0 years | NPV: +$28,030 | Investment creates value at 8% hurdle rate
💡 Positive NPV of $28,030 means this investment earns more than the 8% required return. The project clears the hurdle rate and should be accepted if no better alternative exists.
Standard
Marginal investment -- is 5% hurdle rate different?
Given: Same investment but discount rate: 12%
Working:
NPV: -$180,000 + $45,000 x [(1-(1.12)^-6)/0.12] = -$180,000 + $45,000 x 4.1114 = -$180,000 + $185,013Answer: NPV at 12%: +$5,013 -- barely positive
💡 At 8% discount rate NPV is $28,030. At 12% it is only $5,013. The Internal Rate of Return (IRR) is the rate where NPV = 0 -- in this case approximately 13%. The investment is acceptable at any hurdle rate below 13%.
Advanced
Comparing two mutually exclusive investments
Given: Project A: $200K invest, $55K/yr, 5 years, 8% | Project B: $150K invest, $40K/yr, 6 years, 8%
Working:
Project A NPV: -$200K + $55K x [(1-1.08^-5)/0.08] = -$200K + $219,508 = +$19,508 | Project B NPV: -$150K + $40K x [(1-1.08^-6)/0.08] = -$150K + $184,917 = +$34,917Answer: Project A NPV: +$19,508 | Project B NPV: +$34,917 | Select Project B
💡 Despite lower annual inflows, Project B has a higher NPV because it runs longer and requires less initial capital. Always use NPV (not payback period) when comparing mutually exclusive projects.
4 Sanity check
NPV decision rule
NPV > 0: accept | NPV = 0: neutral (earns exactly the hurdle rate) | NPV < 0: reject
Discount rate selection
Cost of debt: use the interest rate on the borrowing | WACC: use the weighted average cost of capital | Opportunity cost: use the return forgone on the best alternative
The discount rate selection significantly affects NPV -- always state which rate was used.
Payback period limitation
Payback ignores cash flows after payback -- a project paying back in 2 years then generating nothing more is ranked equally to one paying back in 2 years then generating large cash flows for 10 years
Simple vs discounted payback
Simple payback: investment / annual inflow | Discounted payback: accounts for time value of money -- is longer than simple payback
5 Common errors
| Error | Cause | Consequence | Fix |
|---|---|---|---|
| Using an unrealistically low discount rate to make NPV appear positive | Applying the risk-free rate (government bond yield) instead of the appropriate hurdle rate | Investment appears to create value when it is actually below the required return for the risk level | For business investments, use the Weighted Average Cost of Capital (WACC) or the return forgone on the next best alternative. A business borrowing at 8% should use at least 8% as the discount rate. |
| Using constant annual cash inflows when actual flows vary by year | Calculator assumes uniform annual inflows -- real investments often have variable cash flows | NPV significantly wrong if cash flows ramp up or down over the project life | For projects with variable annual cash flows, calculate each year's present value separately: PV = Cash flow in year t / (1+r)^t and sum them. This calculator is most appropriate for stable recurring savings or revenues. |
| Not including the salvage value of the asset at end of project life | Treating the terminal value as zero | NPV understated -- the asset may still have significant value at end of the analysis period | Add the present value of the salvage value as an additional cash inflow in the final year: Salvage PV = Salvage value / (1+r)^n. |
| Confusing payback period with profitability | Accepting projects with short payback regardless of NPV | Short payback projects may earn below the hurdle rate while long payback projects may create substantial value | Use NPV as the primary decision criterion. Use payback period as a secondary risk measure -- how long is capital at risk? A positive NPV project with a 5-year payback is still worth doing if NPV is substantial. |
6 Reference & regulatory links
7 Professional workflow
Common tools used alongside this one:
Depreciation Calculator
Depreciation Calculator provides annual depreciation on the asset, which reduces taxable income and affects after-tax cash flows used in NPV
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Break-Even Calculator
Break-Even Calculator shows the minimum annual volume to justify the investment; NPV shows whether the expected volume creates net value
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Profit Margin Calculator
Profit Margin Calculator shows the margin on operations funded by the investment; NPV shows whether the investment to generate those margins is worthwhile
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