# Present Value

Present value (PV), also known as discounted value, is a financial calculation to find the current value of a future sum of money or cash stream in today at a specific rate of return. In simple terms, it compares the buying power of one dollar in the future to the purchasing power of one dollar today.

Present value is an indication of whether the money an investor receives today will be able to earn a return in the future. It’s a commonly used metric in stock valuation, bond pricing and financial modeling.

## Present Value Formula

$Present\: Value = \dfrac{FV}{(1 + r)^{n}}$

As financial formulas go, present value is a relatively simple one. To calculate it, you need the expected future value (FV). So let’s say you invest $1,000 and expect to see a 10% annual return for five years, the future value at the end of 5 years would be$1,610.51.

The rate of the return would obviously be the 10% in this example, and the number of periods is 5.

## Present Value Example

Ian is considering investment online publishing company and needs to work out the present value.

He expects to receive a cash flow of $100,000 after 4 years, at a 15% annual return. Let’s work out the present value of this investment: $Present\: Value = \dfrac{\100{,}000}{(1 + 15\%)^{4}} = \57{,}175.32$ The current, present value of this investment is$57,175.32. This means that if you invested this amount at 15% over four years, you’d have $100,000. So in this situation, if the investment into the company is less that$57k, then it could be considered a good investment because the cash flows will allow you to earn more than the money is currently worth.

If Ian had to invest $70,000 to get this cash flow in four years, it’s probably not a wise investment because he’s investing more than the present value of the cash flow. ## Present Value Analysis Present value is based on the time value of money concept – the idea that an amount of money today is worth more than the same in the future. In other words, the money that is to be earned in the future is not worth as much as an equal amount that is received today. In the most basic form, would you rather receive$1,000 today or $1,000 in five years time? You’d obviously take the money today, based on two factors: interest/return rate and inflation/purchasing power. ### Interest Rate or Rate of Return Investors measure the PV of a company’s expected cash flow to decide whether the stock is worth investing in. Investing$1,000 today would presumably earn a return on investment over the next five years. Present value allows you to take into account those expected returns to determine how much that investment is worth today.

If you had $1,000 today and could invest that to get 5% return per year, this is better than receiving$1,000 in five years time. By waiting five years, there are opportunity costs and you would miss out of the 5% returns that you could have by putting the money to use.

Inflation is the mechanism in which goods and services costs increase over time. You can buy goods at today’s prices if you receive money today. Inflation is likely to cause the price of goods to rise in the future, which would diminish your money’s purchasing power.

Any implied annual rate which could be inflation or the rate of return if the money was invested, money not spent today could be expected to lose value in the future. The Present Value equation compares the Future Value to today’s dollars by factoring either inflation or the rate of return that could be obtained if an amount were invested in the expected annual rate.

### Future Value Compared With PV

The best illustration of the theory of time value of money and the need to compensate or pay additional risk-based interest rates is a correlation of present value (PV) with future value (FV). Simply put, because of the passage of time, today’s money is worth more than the same money tomorrow.

People would prefer to have $1 today versus the same$1 tomorrow. Future value (FV) may be linked to potential cash inflows from investing the money today, or the potential payment required to repay the money borrowed today.

### Discount Rate for Finding PV

The discount rate is the rate of return on investment applied to the calculation of the Present Value (PV). In other words, if an investor chose to accept an amount in the future over the same amount today, the discount rate would be the forgone rate of return. The discount rate chosen for the calculation of the present value is highly subjective because it is the expected rate of return you would receive if you had invested the dollars of today for a period of time.

The discount rate is the sum of the time value and a related interest rate that, in nominal or absolute terms, mathematically increases future value. On the other hand, the discount rate is used to determine future value in terms of present value, enabling a lender or capital provider to settle any future earnings or obligations in relation to the present value of the capital on the fair amount. The word “discount” refers to the future value being discounted to the present.

In many financial calculations, determining the discounted or present value is extremely important. Net present value, bond yields, spot rates, and pension obligations, for instance, are all dependent on discounted or present value. Understanding how to make present value calculations using a financial calculator will help you decide whether to accept such incentives as a cash discount, 0% financing on a car’s purchase, or pay points on a mortgage.

### Future Value vs. Present Value

Future value (FV) is the future value of a current asset based on an expected rate of growth at a specified date. The FV formula assumes a steady growth rate and a single upfront payment remains untouched for the investment period. The FV calculation enables investors to estimate the amount of profit that can be produced by various investments, with varying degrees of accuracy.

Present Value (PV) is the current value given a specified rate of return of a future sum of money or cash flow. The Present Value takes the Future value and applies a rate of discount or interest that could be earned if it is invested.

Future Value tells you what an investment will be worth in the future, while Present Value tells you how much you would need to earn a specific amount in the future in today’s dollars.

### Limitations of Using PV

Calculating the Present Value, as stated earlier, involves making the assumption that a return rate could be earned on the funds over the period of time. In our example, we looked at one investment over the course of one year. Nevertheless, if a company decides to pursue a series of projects with a different return rate for each year and each project, the Present Value becomes less certain if the expected return rates are not achievable.

It is important to consider that no interest rate is guaranteed in any investment decision, and inflation may reduce any investment’s rate of return.

## Present Value Conclusion

When calculating present value, the below points are worth bearing in mind as a quick recap of what it is, why it’s used, and how to use it:

• Present value is the idea that is worth more than the same amount of money today in the future. In other words, the money that has been earned in the future is not worth as much as today’s equal amount.
• Any implied annual rate, which could be inflation or the rate of return if the money was invested, could be expected to lose value in the future.
• Calculating the present value means making the assumption that over the period of time, a return rate could be earned on the funds.
• The present value provides a basis for determining the fairness of any future assets or liabilities. For example, having a potentially higher purchase price may or may not be worth having a possible cash refund reduced to present value. When buying a vehicle, the same financial equation applies to 0% financing.
• It may be safer for the consumer to pay some interest on a lower sticker price than to pay zero interest on a higher sticker price. It only makes sense to pay mortgage points now in exchange for lower mortgage payments later if the present value of future mortgage savings is greater than the mortgage points paid today.

## Present Value Calculator

You can use the present value calculator below to work out your own PV by entering the future value, return rate, and number of periods.