## Calculator Use

Calculate the existing value (PV) of a series of future cash flows. More specifically, you deserve to calculate the present worth of uneven cash flows (or also cash flows). To include an initial investment at time = 0 use Net current Value (NPV) Calculator.

durations This is the frequency of the matching cash flow. Generally a duration is a year or month.However, a period can be any type of repeating time unit that payments room made. Simply be certain you are consistent with weeks, months, years, etc for every one of your inputs. Price per duration This is your discount price or your expected rate of return ~ above the cash flows because that the size of one period. Absorption is the variety of times compounding will occur throughout a period. You might have a yearly rate and compounding is 12 times every yearly period, monthly. Payments at duration Beginning or End choose if payments room made in ~ the start of each duration (like one annuity early out in advance) or in ~ the finish of each period (like an ordinary annuity in arrears) Cash flows The cash flow (payment or receipt) made for a given duration or set of periods.

## Present worth of Cash FlowFormulas

The current value, PV, the a series of cash operation is the current value, in ~ time 0, that the sum of the present values of all cash flows, CF.

We begin with the formula because that PV of a future worth (FV) solitary lump amount at time n and also interest rate i,

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Substituting cash flow for time duration n (CFn) because that FV, interest rate for the same period (in), we calculate present value for the cash flow for that one period (PVn),

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

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For example, ns = 11% = 0.11 for duration n = 5 and CF = 500. Therefore, PV5 = CF5 / (1 + i5)5 PV5 = 500 / (1 + 0.11)5 PV5 = 500 / (1.11)5 PV5 = 500 / 1.685058 PV5 = 296.73

When cash flows are at the beginning of each duration there is one less duration required to bring the value backward come a existing value. Therefore, us multiply each cash flow by secondary (1 + in) giving department by one less.

With compounding m times per duration we arrive at in and n by setup r together the routine rate and t as the period number to calculate in = r/m and n = mt; we can now calculation the PV starting with the future worth formula

Calculating the PV because that each cash flow in each period you can develop the following tableand sum up the separation, personal, instance cash operation to gain your final answer. If you great to gain a minimum return the 11% yearly return ~ above your invest you have to pay, in ~ most, \$1,689.94 lump amount for this investment at the beginning of duration 1 (time 0).