PRESENT VALUE: CHARACTERISTICS, FORMULAS AND EXAMPLES - DUDAS - 2024

The current value (VA) is the present value of a future amount of money or cash flow, taking into account a specific rate of return, beginning at the time of valuation. In accounting, it is the indicator concept so that assets and liabilities are measured at the current value at which they could be sold or settled as of the current date.

Future amounts have to deal with inflationary or deflationary pressures, with opportunity costs and also other risks that affect the value of the final amount. The actual equivalent value of an amount in the future will not be the same amount as having a sum of money today. That's where current value comes into play.

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If you have an estimate of the return on what you could earn from an investment today, you can easily estimate how much that future value would be worth. Alternatively, the present value also indicates the amount that would need to be invested today if one wanted to end up with a final lump sum, assuming a given return.

characteristics

An investor who has money has two options: spend it now or save it. The financial trade-off for keeping it and not spending it is that the monetary value will accumulate through compound interest you will receive from a borrower or bank.

Therefore, to evaluate the real value of a quantity of money today after a certain period of time, economic agents combine the quantity of money at a certain interest rate.

The operation of evaluating a present value in future value is called compounding. For example, how much will the current $ 100 be worth in 5 years?

The inverse operation, which evaluates the present value of a future amount of money, is called a discount. For example, how much will the $ 100 received in 5 years be worth today, in a lottery?

Present value in accounting

Present value is useful when there has been a prolonged period of excessive inflation. Under these conditions, the historical values ​​at which the assets and liabilities were recorded will likely be much lower than their current values.

However, there is not a high degree of acceptance of the present value concept in accounting. It presents the following problems:

Accounting cost

It takes time to accumulate current value information. Therefore, this increases the cost and time associated with generating the financial statements.

Information availability

It may be difficult or impossible to obtain current value information on some assets and liabilities.

Information accuracy

Certain present value information may be based less on facts and more on ill-founded assumptions or estimates, affecting the reliability of the financial statements when this information is included.

Formulas

Present value is a formula used in finance that calculates the present value of an amount that will be received at a future date. The premise of the equation is that there is a "time value of money."

The time value of money is the concept that indicates that receiving something today is worth more than receiving that same item at a future date.

The presumption is that it is preferable to receive $ 100 today than to receive the same amount of money one year from today. However, what if the options were between receiving $ 100 in the present or $ 106 in a year from today?

You need a formula that can provide a quantifiable comparison between a current amount and an amount at a future time, in terms of its present value.

VA = Fn / (1 + r) ^ n, where

Fn = Future value in period n.

r = Rate of return or profitability.

n = number of periods.

Using the formula

The present value formula has a wide range of uses. Therefore, it can be applied to various areas of finance, including corporate finance, banking, and investment. It is also used as a component of other financial formulas.

How is the present value calculated?

Suppose you currently have $ 1000 and 10% annual interest. This means that money grows 10% every year, in such a way:

$ 1000 x (10% = 100) = $ 1100 x (10% = 110) = $ 1210 x (10% = 121) = $ 1331, etc.

-Next year, $ 1100 will be the same as $ 1000 now.

-In two years, $ 1210 will be the same as $ 1000 now.

-In three years, $ 1331 will be the same as $ 1000 now.

In fact, all these amounts will be the same over time, considering when they occur and with 10% annual interest.

Instead of adding 10% each year, it is easier to multiply by 1.10. In this way, the following is obtained: $ 1000 x 1.10 = $ 1100 x 1.10 = $ 1210 x 1.10 = $ 1331, etc.

Calculate future value back to now

To find out what the money in the future is currently worth, it is calculated backwards, dividing by 1.10 each year, instead of multiplying.

For example, let's say you promise to pay $ 500 next year. The interest rate is 10%. To find out what the value of that amount is today, divide the future value of $ 500 by 1.10, being equal to $ 454.55 as the present value.

Now suppose you promise to pay $ 900 in three years. To find the value of that amount currently, divide that future amount by 1.10 three times. Thus, $ 900 in 3 years would currently be: $ 900 ÷ 1.10 ÷ 1.10 ÷ 1.10 = $ 900 ÷ (1.10 × 1.10 × 1.10) = $ 900 ÷ 1.331 = $ 676.18 now.

Examples

Example 1

An individual wants to determine how much money they would need to put into their money market account to get $ 100 in a year from today, if they earn 5% interest on their account.

The $ 100 you would like to receive in a year denotes the F1 portion of the formula, 5% would be r, and the number of periods would simply be 1. Putting this in the formula, you would have VA = $ 100 / 1.05 = $ 95.24. You should deposit $ 95.24 today to get $ 100 one year from now, at a 5% interest rate.

Example 2

Suppose that today an amount is being deposited into an account, which earns 5% interest annually. If the goal is to have $ 5,000 in the account at the end of six years, you want to know how much to deposit in the account today. For this, the current value formula is used:

present value = future value / (1 + interest rate) ^ number of periods.

Inserting the known information, we have:

VA = $ 5,000 / (1 + 0.05) ^ 6 = $ 5,000 / (1.3401) = $ 3,731.

References

1. Steven Bragg (2018). Current value accounting. Accounting Tools. Taken from: accountingtools.com.
2. Finance Formulas (2019). Present Value. Taken from: financeformulas.net.
3. Mathsisfun (2019). Present Value (PV). Taken from: mathsisfun.com.
4. Dqydj (2019). Present Value Calculator and Explanation of the Present Value Formula. Taken from: dqydj.com.
5. Pamela Peterson (2019). Present Value Example. James Madison University. Taken from: educ.jmu.edu.
6. Wikipedia, the free encyclopedia (2019). Present value. Taken from: en.wikipedia.org.