Discounted Payback Period Calculator - Calculate NPV, DPP & IRR

How to Use This Calculator

Step-by-Step Instructions

1. Initial Investment: Enter the upfront cost of your investment project in dollars.
2. Cash Flow: Input the expected annual cash inflow from the investment.
3. Time Period: Specify the analysis period in years.
4. Cash Flow Growth:
   • Select "Increase" if cash flows are expected to grow over time
   • Select "Decrease" if cash flows are expected to decline
   • Enter the annual percentage change
5. Discount Rate: Enter your required rate of return or cost of capital as a percentage.
6. Click "Calculate Period" to generate results.

Formulas and Methodology

Discounted Payback Period Formula

The discounted payback period is calculated by finding when the cumulative discounted cash flows equal the initial investment:

Discounted Cash Flow = CF_t / (1 + r)^t

Where:

• CF_t = Cash flow in period t
• r = Discount rate
• t = Time period

Growing Cash Flow Formula

When cash flows grow at a constant rate:

CF_t = CF₁ × (1 + g)^t-1

Where:

• CF₁ = Initial cash flow
• g = Growth rate

Internal Rate of Return (IRR)

IRR is the discount rate that makes the Net Present Value (NPV) equal to zero:

NPV = Σ [CF_t / (1 + IRR)^t] - Initial Investment = 0

Methodology Notes

This calculator implements standard discounted cash flow analysis as taught in corporate finance courses and used by financial professionals worldwide. The calculations assume:

• Cash flows occur at the end of each period
• Discount rates remain constant throughout the analysis period
• Growth rates are applied consistently to future cash flows
• All cash flows are in nominal terms

Practical Applications

Common Use Cases

• Capital Equipment Purchases: Machinery, vehicles, technology upgrades
• Real Estate Investments: Rental properties, commercial buildings
• Energy Projects: Solar installations, energy efficiency improvements
• Business Expansion: New product lines, market entry strategies
• Research & Development: Innovation projects, patent development

Industry Benchmarks

References

Government and Academic Sources

• U.S. Department of Energy - Simple Payback and Internal Rate of Return
• Small Business Administration - Calculate Your Startup Costs
• Federal Reserve - Flow of Funds Data
• U.S. Treasury - Current Interest Rates