Present value formula and PV calculator in Excel

This tutorial answers three key questions: What is the present value of an annuity? What is the present value formula? And what discount or interest rate should be used for present value calculations?

Most people prefer receiving money now rather than later. This preference is explained by the time value of money concept. Future value (FV) and present value (PV) are two key terms describing how money's value changes over time. FV calculations determine an investment's future worth, while PV calculations determine its current worth. This tutorial focuses on calculating present value in Excel.

Present Value of an Annuity

An annuity is a series of equal payments (inflows or outflows) at regular intervals (weekly, monthly, quarterly, or yearly). The present value of an annuity is the current worth of these future cash flows, considering a specific discount rate (or rate of return). Higher discount rates result in lower present values. The PV concept is rooted in the time value of money: money today is worth more than the same amount tomorrow due to its earning potential. PV calculations are crucial in financial analysis for investment decisions, project evaluations, and more. They also help in everyday decisions, such as comparing lump-sum payments versus annuities.

Present Value Formulas

For a single cash flow, the present value formula is:

Where:

• FV = Future Value
• r = Discount or Interest Rate

For a series of cash flows, the formula is more complex:

Where:

• r = Discount or Interest Rate
• n = Number of Time Periods
• i = Cash Flow per Period

Calculating Present Value in Excel

Excel's PV function simplifies present value calculations. The function's syntax is: PV(rate, nper, pmt, [fv], [type])

Present Value for a Single Payment:

Example: Choosing between $10,000 now or $11,000 in one year with a 7% interest rate. The Excel formula would be: =PV(C2, C3, ,C4) where C2 contains the interest rate, C3 the number of years, and C4 the future value. The result (a negative value) represents the investment required to reach the future value.

The calculation changes if interest compounds monthly: =PV(C2/12, C3*12, ,C4).

Present Value for an Annuity:

For a series of equal payments, adjust the rate and nper arguments in the PV function according to the compounding frequency (monthly, quarterly, etc.). For example, for annual payments: =PV(B2, B3, B4) where B2 is the annual interest rate, B3 the number of years, and B4 the annual payment (negative for outflow). For monthly payments: =PV(B2/B5, B3*B5, B4), where B5 represents the number of periods per year (12).

Annuity Types:

The optional type argument specifies the annuity type: 0 for ordinary annuity (payments at the end of the period), and 1 for annuity due (payments at the beginning).

Creating a Present Value Calculator in Excel:

By using input cells for all PV function arguments, a flexible calculator can be created. The formula would be: =PV(B2/B7, B3*B7, B4, B5, B6), where B7 represents periods per year. Remember to use negative values for outflows and positive for inflows. The Periods per year cell (B7) must not be blank or zero.

This tutorial provides a comprehensive guide to calculating present value in Excel, covering single payments and annuities of various types. A practice workbook is available for download.

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