**What is the Present Value?**

Present value (PV) is defined as the current or present value of all future sums of cash flow or money at a specified rate of return. This rate of return is known as the discounted rate, which is essentially the interest rate, discounted over some time. The expected cash flows are discounted at a discount rate to compute the present value. The higher the discount rate, the higher the future value (FV), but the lower the present value.

PV is the measurement of the time value of money, where if a future value is expected today, it is said that the value of money held today is more valuable than its future value. The farther the expected future value, the lesser its present value is today.

## What is the Purpose of Present Value?

PV is commonly used in financial models, stock valuation, determination of capital projects, and new ventures. PV is important in measuring the cash flows in different periods within the same project while taking into account a discount rate, an interest rate, and in most cases, inflation as well.

Present value and future value computations are critical in business investment and acquisition decisions. Projections for year on year are computed based on the formula for PV and FV, based on conservative estimates while accounting for other critical factors such as inflation.

The sum of these discounted cash flows is then compared with the actual purchase price or acquisition cost. If the PV of cash flows (value of an investment) is higher, then the organization may go ahead with the investment.

If not, then the investor or organization may find it better to invest their money in something more worthwhile and desirable. PV and FV calculations are paramount in making decisions related to risk management and financial planning.

The interest rate is generally a part of the discount rate (besides the time value of money), and is subjective, based on several factors, including the period the interest is computed for. The interest rate is the value that will be gained in addition to the investment made.

If $1000 are invested today and could earn an interest of 10% per annum, then the value of the investment in a year would be $1100.

The discount rate is the converse of the interest rate. If one were to receive $1000 in a year, then today, the value will only be $909.10. While normally the market interest rates are computed, sometimes they may be adjusted given inflation and other economic factors.

Discount rates (also known as hurdle rates) may be compounded annually, quarterly, or semi-annually. Based on this, the number of periods varies and affects the present value calculation. The discount rate is the FV being discounted to today, whereas the interest rate is the rate at which the investor could have expected to earn more income. This essentially qualifies the meaning of â€˜time value of money which implies that money in hand today is more valuable than a future payment.

## What is the Formula for Present Value?

$\text{Present}\text{\xe2\u20ac\u2030}\text{Value}\text{\xe2\u20ac\u2030}=\text{\xe2\u20ac\u2030}\frac{FV}{{(1+r)}^{n}}$

**Present Value and Net Present Value (NPV)**

While the PV calculations account for the inflow of cash, NPV is a more comprehensive indicator of a business decision, which takes into account the initial capital outlay of the investment. This makes it easier to compute the future value of cash flows, and ascertain the interest rate and the return from the investment that would have been made possible.

PV assumes a standard cash stream for the period intended, NPV takes into account several other factors in determining future value such as ununiform revenues across the periods.

NPV considers the time value of money as a critical factor in determining the value of the project. APV is Adjusted Present Value which is similar to NPV, but considers financing through equity, but uses the cost of equity as opposed to the rate of discount.

**Let us understand PV and NPV with the help of an example:**

The project is expected to generate an income of $1000 at the end of 3 years. Assume the interest rate is 10% compounded annually. What is the present value?

$\begin{array}{l}\begin{array}{l}n\text{}=\text{}3\hfill \\ I\text{}=\text{}10\%\hfill \\ FV\text{}=\text{}\$1,000\hfill \end{array}\\ PV\text{}=\frac{1,000}{{(1+0.1)}^{3}}\end{array}$

In this case, the present value factor is 0.7513 which is multiplied by the income generated, giving us the present value of $751.31

**Therefore,**

Given that there is a positive NPV, the future value of the cash flows seems promising and this is an option worth pursuing the company.

## Common Mistakes and Pitfalls

While PV and NPV computations are straightforward, there may be some errors that may arise while making these computations. They are as follows:

- Taking the wrong interest rate or the discount rate.
- Not carefully noticing the number of periods and how they are compounded (annually, semi-annually, or quarterly).
- Incorrect calculation of present value by using the wrong future value and their related variables.
- Incorrect computation of present value factor.
- Incorrect computation of discounting (either by taking the wrong interest rate or wrong period or the present value factor)

## Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses that have accounting and commerce at their core. This may be especially applicable for

- B.Com
- M.Com
- MBA (Finance)

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