What Is an Uneven Cash Flow?
An uneven cash flow is a series of amounts that aren't all the same, such as a project that pays $1,500 one year and $2,100 a later year. Money today is worth more than the same money later, so you can't simply add the amounts up. Each one has to be moved to the same date first. This calculator finds:
- Present value: what all the cash flows are worth today.
- Future value: what they grow to by the last year.
- Interest rate: the yearly rate that makes them worth a given amount today.
Which calculator should I use?
- This calculator: for amounts that change from year to year.
- Time Value of Money calculator: for one lump sum.
- Annuity Present Value and Annuity Future Value calculators: for a series of equal payments.
- Net Present Value calculator: to subtract an investment from the value and see what a project is worth.
- Internal Rate of Return calculator: to judge an investment against the return you require.
How to Calculate the Value of Uneven Cash Flows
Each cash flow arrives at the end of its year. For present value, discount each one back to today and add them up:
For future value, grow each one to the last year and add them up. The last cash flow earns nothing, because it arrives at the end:
- Ct: the cash flow in year t.
- r: the yearly interest rate.
- n: the number of years.
The interest rate is the r that makes the PV equation equal your amount today. It can't be rearranged to give r directly, so it's found by trial and error, which the calculator does for you.
Example
Cash flows of $1,500, $1,850 and $2,100 at 7.25% a year:
- Present value: $1,500 ÷ 1.0725 + $1,850 ÷ 1.07252 + $2,100 ÷ 1.07253 = $1,398.60 + $1,608.34 + $1,702.27 = $4,709.20
- Future value: $1,500 × 1.07252 + $1,850 × 1.0725 + $2,100 = $1,725.38 + $1,984.13 + $2,100.00 = $5,809.51
- Interest rate: if the same cash flows cost $4,500 today, the rate is 9.65%.
How to Use the Uneven Cash Flow Calculator
"If I'll receive $1,500, $1,850 and $2,100 over the next three years and money earns 7.25% a year, what are they worth today?" This calculator answers that.
Let's enter the numbers for this example in each box. They are already filled in when the calculator opens, so you can follow along and then change any box to match your own numbers. Choose the tab for what you want to find.
- Interest Rate (Present Value and Future Value tabs): Enter 7.25, which is the yearly rate money earns. It must be from 0 to 99.99.
- Present Value (Interest Rate tab): Enter 4,500, which is what the cash flows are worth today, such as the price you'd pay for them.
- Number of Years: Choose 3, which is how many years of cash flows you have, from 1 to 12.
- Year 1 to Year 3: Enter 1,500, 1,850 and 2,100, which is the cash for each year. A year can be 0, or negative if it costs you money.
Calculate and Reset
Click Calculate to see your results. If a box has a problem, such as a rate of 100, a message pops up under that box instead. With the default numbers on the Present Value tab you get:
- Your Results: a short summary in words. On the Interest Rate tab it also tells you if there's no rate, or more than one.
- Present Value: the headline number, $4,709.20.
- Interest Rate, Total Cash Flows and Total Discount: 7.25%, $5,450.00 and $740.80.
- Chart: each year's cash flow beside what it's worth. Links under it open related calculators.
- Cash Flow Table: each year's cash flow, the rate and its value, with totals. Download Excel saves it with the formulas, so you can change a number and see the answer update.
- Share Results: a link that opens this calculator with your numbers filled in. Copy it, or share it on Facebook or X.
Amounts of $1 million or more are shortened, for example $1.25M. Click Reset to put the current tab's boxes back to their defaults and show the default results again.