## What is the present value (PV)?

Present value, often referred to as **discounted value**, is a financial formula that calculates the value of a particular amount of money to be received in the future, reduced to the **present value** of that amount. In other words, it calculates the amount of money that must be invested **today** to equalize the payout or the amount of money received in the **future**.

This concept is based on the **time value of money** principle that dictates that $ 1 today is worth more than $ 1 tomorrow. Today’s money is always worth more than tomorrow for three main reasons: interest, inflation, and opportunity costs.

The price of money is **not free**. Debtors must pay an interest rate to creditors in order to be able to borrow funds. Likewise, creditors’ funds never standstill. They always make money in the form of interest, making cash an expensive commodity. Moreover, inflation devalues the purchasing power of today’s currency as time goes on.

## How to calculate present value?

You may use this Present Value Calculator to determine the present value of a certain sum of money in the future or the present value of periodic annuity payments. The present value is estimated by discounting the projected future cashflows back to the present day. To do so, the investor will require three essential pieces of information: the projected cashflows, the number of years over which the cashflows will be paid, and their discount rate. The discount rate significantly impacts the present value, with greater discount rates resulting in a lower present value and vice versa.

## Present value formula

We calculate the present value through the formula by dividing the cash flow of one period by one plus the rate of return to the nth degree.

*PV = C1 / (1 + r) n*

Here’s what each symbol means:

C1 – Cash flow of 1 period

r – A return rate

n – number of periods

As you can see from the present value equation, several different variables need to be **estimated**. Cash flow from one period is simply the **amount of money received** at a future date. This is also called the future value of the lump sum.

The rate of return is the estimated annual interest rate that will receive in the future. The number of periods is simply the number of interest periods.

Note that this equation uses annual interest. It means both the rate and the number of periods in years. If you want to calculate the semi-annual interest, you have to divide these numbers in half.

The present value formula is often redesigned to reflect the future value of the lump sum payment received for the following week:

*PV**= FV * 1 / (1 + r) n*

Here’s what each symbol means:

FV – Future value of money received in the future

r – A return rate

n – number of periods

## Present value or future money (the time value of money)

The time value of money is based on the idea that money received in the **present** is more valuable than the same amount in the **future**. The higher value arises from the possibility of its further investment, resulting in earnings, i.e., interest or yield. In short, money is worth more in the present than in the future because of the opportunity cost of not using it.

In practice, if you lend money to someone for a certain period of time, you expect to get a more significant amount back than you gave.

Therefore, from the above, it is clear that** $ 1,000** received today has a higher value than **$ 1,000** in the future. Of course, everyone will intuitively decide to take **$ 1,000** today rather than in a year without overthinking. There are several reasons for this, and not all of them are financial.

However, what if someone offers you **$ 1,100** or **$ 1,200**? How will you then evaluate the offer? Assuming you trust the person or institution that gives it to you (which is another story), a yield of **10** or **20%** per year should interest you. If you are able to earn more on your own, then **$ 1,000** is worth more to you today than in a year. Otherwise, take that offer. And also due to the fact that such a high yield is often brought only by illegal activities.

## How does present value calculator work?

The present value calculator computes the present value (PV) of a sum you will receive in the future. You must use the following mathematical formula:

PV = C / (1+r)^n

PV = Present Value

C = Cash Flow at a period

n = number of period

r = rate of return

You understand the idea of the time value of money, which demonstrates how money received now is worth more in the future. Assume you want $ 1.000,000 exactly six years from now. You anticipate a return of 5% on your investment. There would be a total of six sessions.

C = $ 1.000,000

n = 6

r = 5%

PV = 1.000,000 / (1+0.05)^6

PV = $ 746.268,65

## Present value of periodical deposits

The present value of an annuity formula calculates the present value of a series of future monthly payments at a particular point in time. The present value of an annuity formula is based on the notion of the time value of money, which states that a dollar today is worth more than a dollar tomorrow.

Money obtained now is worth more than the same amount of money received in the future due to the time value of money since it may be invested in the meanwhile. A discount rate is used to calculate the future worth of money. The discount rate is the interest rate or anticipated rate of return on other assets over the same time period as the payments.

## Present value application

Both investors and creditors use a present value calculator to estimate **potential investments** and measure returns on current projects. The concept of the time value of money is **essential** because it allows investors to measure how much their investment returns are worth today and whether there are better options.

Most lotteries will provide winners with two additional payment methods. Today they can get a smaller lump sum, or they can get the total amount of winnings in equal amounts for the rest of their lives. This theory is based on the time value of money. A small lump sum today is worth a more significant lump sum in the future.

Company management also uses this theory when investing in projects, expansions, or the purchase of new **equipment**. Using the net present value formula, management can assess whether a potential project is worthwhile and whether the company will make money on the job.

## Net present value

An investment pays off if it creates value for its owner, and value is created by finding that investment in the market that is** worth more **than the cost of the purchase.

For example, buy a house for **$ 25,000**, spend an extra** $ 25,000** to decorate it. After that, the market sold for** $ 60,000**. Thus, the market value exceeds the investment of **$ 10,000**.

When deciding on such a venture, the first challenge is to find out in advance if it is a** $ 50,000** investment is a good idea or whether the earnings it will bring will be worth it more than invested.

The difference between the market value of an investment and its costs is called the net present the value of **NPV** and answering questions about how much value has been created today by undertaking investment activities.

## How to assess NPV?

We are thinking of starting a company and producing and selling a new product – an organic fertilizer. We can estimate **start-up** costs because we know what we all need to start a business. Do we wonder if this is a good investment? The answer depends on whether the value of the new business is greater than the cost required to take action to get it up and run. That is, the question arises, will the net present value be positive.

To develop an answer, do a **DCF – discounted cash flow valuation**, a method consisting of estimating future cash flow and discounting it at present value.

## Discount rate for finding present value

The discount rate is the investment rate of return used in calculating the present value. In other terms, the discount rate is the rate of return foregone if an investor chooses to take some amount in the future rather than the same amount today. The discount rate used in the present value calculation is very subjective since it represents the projected rate of return if you invested today’s cash for a length of time.

Many financial calculations rely heavily on the computation of discounted or present value. Net present value, bond yields, and pension liabilities, for example, all rely on discounted or present value. Learning how to use a financial calculator to calculate current value will help you determine whether to accept offers such as a cash refund.

## Examples of present value

### Example 1

You need **400** to be able to buy the book next year. You can earn **7%** of your money. How much do you need to invest today?

Solution:

PV = 400 * 1.07^{-1}

**= 373.83**

### Example 2

The car costs **$ 68,500**. How much do you have to invest today to buy a car in **2 years?** The interest rate is **9%.**

Solution:

PV = 68,500 * 1.09^{-2}

**= 57,655.08**

### Example 3

You need **$ 1,000** for a year and another **$ 2,000** for two years. The interest rate is** 9%**. How much do you need to invest today, or what is the present value for both amounts?

Solution:

PV = 1,000 * 1.09-1

+ 2,000 * 1.09-2

**PV = 2,600.79**

### Example 4

The initial cost of starting a business is **$ 30,000**. It is estimated that the cash inflow will be **$ 20,000** and the outflow** $ 14,000** per year. We are talking about a period of **8 years**. At the end of the 8th year, the equipment will be worth **$** **2,000**. The interest rate is **15%**. Is it a good investment?

Solution:

PV = 6,000 * [(1-1,15-7) / 0,15] + 8,000 * 1.15-8

= **27,577.73**

NPV = 27,577.73-30,000 = **-2,422.27**

## FAQ

### What is the NPV method?

The net present value (NPV) technique calculates the current worth of all future cash flows generated by a project, including the initial capital expenditure. It is frequently used in capital planning to determine which projects are most likely to provide the most profit.

### Is a higher or lower NPV better?

NPV discounts each input and outflow to the present and then adds them to see how the value of the inflows compares to the value of the outflows. A positive NPV indicates that the investment is profitable. An NPV of 0 indicates that the inflows equal the outflows. A negative NPV indicates that the investment is not beneficial to the investor.

### At what discount rate, is the NPV just equal to zero?

The internal rate of return is the discount rate at which the NPV equals zero (IRR).

### What is the formula for the present value of an annuity?

The present value of a due annuity formula is the same as the present value of a regular annuity, except that the immediate cash flow is added to the present value of the remaining future monthly cash payments.

### How to calculate the net present value?

It is computed by subtracting the present value of cash inflows from the current value of cash withdrawals over time.

### How to calculate present value factor?

The PV Factor is 1 (1 +i)n, where i is the rate and n is the number of periods.

## Other calculators

*Be sure to check out our Future Value Calculator to find out how to calculate the future value of money (investment or saving). Also, you can find out what is money and what kind of money ancient people used and how money developed throughout history and different cultures. You can find some interesting examples that can help you to better understand the calculation of future value. For more calculators in math, physics, finance, health, and more, visit our CalCon Calculator official page.*