# Present Value of Cash Flows Calculator

## Calculator Use

Calculate the present value (PV) of a series of future cash flows. More specifically, you can calculate the
**present value of uneven cash flows** (or even cash flows). To include an initial investment at time = 0 use
Net Present Value (NPV) Calculator.

- Periods
- This is the frequency of the corresponding cash flow. Commonly a period is a year or month. However, a period can be any repeating time unit that payments are made. Just be sure you are consistent with weeks, months, years, etc for all of your inputs.
- Rate per period
- This is your discount rate or your expected rate of return on the cash flows for the length of one period.
- Compounding
- is the number of times compounding will occur during a period. You might have a yearly rate and compounding is 12 times per yearly period, monthly.
- Payments at Period Beginning or End
- Choose if payments are made at the beginning of each period (like an annuity due in advance) or at the end of each period (like an ordinary annuity in arrears)
- Cash Flows
- The cash flow (payment or receipt) made for a given period or set of periods.

## Present Value of Cash Flow Formulas

The present value, PV, of a series of cash flows is the present value, at time 0, of the sum of the present values of all cash flows, CF.

We start with the formula for PV of a future value (FV) single lump sum at time n and interest rate i,

Substituting cash flow for time period n (CF_{n}) for
FV, interest rate for the same period (i_{n}), we calculate present value for the cash flow for that one period (PV_{n}),

If our total number of periods is N, the equation for the present value of the cash flow series is the summation of individual cash flows:

For example, i = 11% = 0.11 for period n = 5 and CF = 500.

Therefore,

PV_{5} = CF_{5} / (1 + i_{5})^{5 }

PV_{5} = 500 / (1 + 0.11)^{5 }

PV_{5} = 500 / (1.11)^{5 }

PV_{5} = 500 / 1.685058

PV_{5} = 296.73

When cash flows are at the beginning of each period there is one less period required to bring the value backward to a present value. Therefore, we multiply each cash flow by an additional (1 + i_{n}) giving division by one less.

With compounding m times per period we arrive at i_{n} and n by setting r as the periodic rate and t as the period number to calculate i_{n} = r/m and n = mt; we can now calculate the
PV starting with the future value formula

Calculating the PV for each cash flow in each period you can produce the following table and sum up the individual cash flows to get your final answer. If you wish to get a minimum return of 11% annual return on your investment you should pay, at most, $1,689.94 lump sum for this investment at the beginning of period 1 (time 0).

**1,689.94**

## Example Cash Flow Problem

Starting in year 3 you will receive 5 yearly payments on January 1 for $10,000. You want to know the present value of that cash flow if your alternative expected rate of return is 3.48% per year.

You are getting 5 payments of $10,000 each per year at 3.48% and paid in advance since it is the beginning of each year. Starting in year 3 there are 2 years of payments of $0. You would enter:

- Rate per Period: 3.48%
- Compounding 1 time per year
- Payments at Period : Beginning (in Advance)
- Number of Lines: 2
- Line 1 @ 2 periods with 0 cash flow
- Line 2 @ 5 Periods with 10,000 cash flow

You'll get the present value of $43,656.85 and cash flow table:

**43,656.85**