Present Value

Present Value definition

Whenever undertaking important financial decisions, individuals and investors consider the benefits of the project and weigh the benefits against the opportunity cost of investing their money. Investors are highly cautious when making long-term investments. They carefully calculate the future investment income by translating it into an equivalent amount in today's money.

How do they equate future income with the value of that money in today's terms? They use a very important concept called present value.

Basically, it measures how much your future money is worth today.

To account for the difference between today's money and future money, the calculation of present value makes use of a discount rate. The discount rate is the interest rate in the economy. It provides the rate of return an investor could be guaranteed to get by putting their money in a risk-free alternative, like depositing it in a bank. In the U.S. personal bank deposits are insured by the FDIC (up to a point).

The higher this discount rate, the lower the current value of that future income will be.

It helps to keep in mind that money loses value daily, monthly, and yearly. This percentage value loss over time compounds upon itself continuously, just as interest in your bank compounds. That means you earn interest not only on the principal amount that you originally invested, but also on the interest that you have been earning.

The purchasing power of $100 a year ago is not typically equivalent to the purchasing power of $100 now, and that's not typically equal to the purchasing power of $100 one year from now. This is because of inflation and other economic circumstances that contribute to the value loss of money, like increased uncertainty.

Present value is beneficial in accounting for inflation while calculating the current value of expected future income.

Present Value formula

The formula for the present value of income received n periods in the future, with discount rate r is:

$PresentValue=\frac{FutureValue}{{(1+r)}^n}$

To understand this, consider how interest compounds over time. If you earn interest rate r on an investment of $100, then at the end of one year you have$\$100(1+r).$If r was 10%, then you now have $110. If you keep the money invested for another year, you are earning interest rate r on the total amount$\$100(1+r).$At the end of the second year you have $\$100(1+r)(1+r)$ and each additional year that earns r multiplies the investment by 1+r. If there are n periods total, then you earn $\$100{(1+r)}^n$.

Present value discounts future income in the same way, but reversed. If you know the income is arriving n periods in the future, then you divide the future amount by ${(1+r)}^n$ to get the equivalent amount in terms of present value. Let's discuss the individual components of the present value formula to understand it better.

Future Value

Future value is just the nominal amount of money that you are expecting to receive at some time in the future. If you receive income of $100 in one year from now, then the future value of that income is $100. It is just the future amount of expected income or cash flow. This is the amount that needs to be discounted back to the present in order to account for the time value of money.

Discount Rate (r)

Is it better to receive $10,000 now or to receive $1,000 every year for the next ten years? Regardless of the interest rate, receiving money now is better than later, but how much better? It depends on how quickly money loses value over time. Your $10,000 could retain its purchasing power if it is invested in an asset that generates a return, or interest, without any risk of losing the principal amount.

The rate at which money loses value can be very subjective since it represents the projected rate of return you would earn if you had invested today's cash for an extended period. However, in many circumstances, a risk-free rate of return is used as a proxy for the discount rate. A risk-free rate of return means that it is guaranteed that you will have the return on your investment bank, and there will not be a default. If one was to hold cash instead of investing it in an asset, the discount rate is the opportunity cost of holding cash.

Because the government of the United States guarantees U.S. Treasury bonds and U.S. bank deposits, the interest rate on one of these assets is often used as the risk-free rate.

Number of Periods (n)

The number of periods refers to the time duration considered for the longevity of the investment. It could be daily, monthly, yearly. It basically shows how much money is growing throughout the considered period. If the number of a period is ten years, it shows how much worth $1000 is worth today vs. ten years from now.

A period can generally be a day, a month, a year, or almost any interval at all. The important factor is that the interest rate r must be the rate for one period of time using the same interval that is measured by n. For instance, if r is an annual rate of return on a U.S. Treasury bond, then n must count the number of years from the initial investment. If the investment pays an annual rate r in 18 months, then n would be 1.5, the number of intervals counted in years.

Similarly, if r is a monthly rate of return, then n must count the number of months instead. If the rate is 1% per month over the course of 3 years, then n would be 3x12 = 36. Then discount rate and the number of intervals must agree with each other.

Present Value example

Present value examples include assessing the current value of an investment based on its return.

Imagine you’re joining a company as a financial analyst at KKR, the leading global investment firm. As one of your first tasks, your manager asks whether you recommend purchasing a particular piece of real estate. You find out that it is a piece of land that costs $85,000, and after analyzing trends in the real estate market, you predict that the piece of land will increase in value to a price of $91,000 in the next year, a $6,0000 gain. If the interest rate earned on a certificate of deposit with the bank is currently 10%, should KKR invest in the land?

To decide whether to buy the land, the KKR investment team should calculate the present value of the future income, which is $91,000 one year from now, if the land is sold after one year. Considering that the interest rate on bank certificates of deposit is 10%, what does that $91,000 equate to in terms of present value? We use the present value formula for that.

$PV=\frac{FV}{{(1+r)}^n}=\frac{91,000}{{(1+.10)}^1}=\frac{91,000}{1.1}=82,727.27$

Basically, if we invest $85,000 today, we would have $82,727.27 in income one year from now. We would lose money!

That is of course based on the fact that we can instead put the same $85,000 in the bank and earn 10% risk-free. Then, one year from now we would have $85,000 + $8,500 = $93,500. This is more than the $91,000 we would get for the land. At this discount rate, the land purchase does not measure up.

This means that it wouldn’t be a wise decision for KKR to invest the money in the piece of land.

Present Value vs. Future Value

Just as we calculate the present value of future income, we can also calculate the future value of current income.

When calculating future value, we consider the worth of a current asset at a particular time n periods into the future. With present value, we use a discount rate to account for money losing value of time--the further in the future the income arrives, the lower its present value. With future value, we compound interest over time that can be earned from the same guaranteed risk-free opportunity that we use as the discount rate when calculate present value.

When calculating future value, we are starting with money today, which is most valuable because money today can be invested at the same guaranteed risk-free rate. The future value of that money is the amount we can expect to have from this baseline activity of depositing it in the bank at the guaranteed risk-free interest rate r.

From the formula for present value (PV), we can derive the equation for calculating the future value (FV) of a certain amount of dollars today projected n periods into the future at baseline rate r, as follows:

$FV=PV{\hspace{0.17em}(1+r)}^n$

The FV equation is based on the assumption of a constant growth rate over time and a single initial amount of money today. This is the future value of today's money.

This equation can also be used to determine exactly how much money a given investment will provide. If we know that an investment returns, say, a 9% dividend in each year, then we can plug in 9% for the variable r in the equation for future value. When n = 1, this formula gives the income that will be received after one year. When n = 2, it gives the income that this investment will provide after two years, and so on.

investors may use this formula to forecast the amount of profit that different types of investment opportunities can earn with differing degrees of accuracy. In order to do that, investors use the concept of Net Present Value.

Hopefully, you are beginning to see how helpful the concepts of present value and future value can be!

Importance of using Present Value

One of the most important aspects of using present value is to account for inflation and loss in purchasing power. If an economy experiences a 10% increase in inflation, meaning that the price of goods and services increased by that particular percentage, the money in your pocket will also lose value. $1000 would buy you $900 worth of goods and services in the following year after the prices have increased by 10%. The present value captures the impact of the inflation rate and helps calculate the current value of your money as well as inform you how much your $1,000 should be worth next year to have the same purchasing power under the inflation rate.

Additionally, it is very important in valuing assets and bonds in the financial market. Present value helps inform investors about the value of an asset in today’s terms. Also, it helps investors navigate through the various assets and securities they can invest in, and make apples-to-apples comparisons between them.

Present Value principles

Present value is based on certain key principles as seen in Figure 1 about the value of money over time and how to compare options. These principles, or assumptions, include:

1. Money loses value over time. That means that the value of today’s money is not the same as its value a year from now. This is due to both inflation as well as impatience. Prices tend to increase over time, and people tend to prefer consumption now to consumption at any point in the future.

2. Investment options can be characterized by a constant rate of return. This is the idea that there is a reliable average rate of return that is stable over time for any given investment option. Since many investment returns follow a random walk, their average rate of return may not be constant over time, or even follow a constant trend. Nevertheless, for simplicity, present value analysis assumes a constant rate of return.

3. There is a guaranteed risk-free rate of return. Another principle is that you can guarantee a certain rate of return. In the U.S., depositing money in a bank is generally considered to be risk-free because bank deposits are insured by a federal agency called the FDIC (although there is a per-person limit on the amount that is insured).