Douglas has two master's degrees (MPA & MBA) and a PhD in Higher Education Administration.
$100 today is not worth the same as $100 was 50 years ago, nor is it worth the same as $100 will be in 50 more years. In this lesson, we'll discuss the time value of money and how it influences the present and future values of cash.
The Time Value of Money (a.k.a. Inflation)
The value of cash changes over time; that is simply an economic fact. Did you ever hear a grandparent talk about 'the good ole days' when candy cost a penny and a soda cost a nickel? Now, that same candy and soda - instead of costing a total of six cents - would cost you around $2. Why is that? Has soda and candy become scarcer, and therefore, more valuable? No. But, the cash you use to pay for that soda and candy has lost some of its value. This idea is known as the time value of money.
The time value of money is an important concept, that refers to the economic fact that money generally loses its value over time and the idea that money can potentially be invested in other ways for a more valuable return in the same period. The lost opportunity to invest money differently is called opportunity cost. Inflation, on the other hand, is actually a measurement. Inflation is the rate at which money loses its value due to increases in the costs of goods and services. So the amount of groceries you could buy a year ago with 50 dollars was likely more than what you can buy today with 50 dollars.
Present and Future Value of Cash Flow
The time value of money is an important concept to understand, especially when it comes to investing today's cash into something that will earn cash in the future. Since the money in the future isn't worth as much as the money being invested today, it is necessary to adjust the future amounts for the time value of money. Basically, it is essential to calculate how much money an investment will return, expressed in today's dollars, so that the cost of the investment can be compared to the expected return in an apples-to-apples way.
The future value of a lump-sum of money is calculated using the formula FV = PV(1+i)^n. In this formula, FV is the future value, PV is the lump sum, i is the rate at which it grows, and n is the number of periods into the future. An important issue with this formula is to make sure that the i and n are consistent. If you are measuring n in years, for example, make sure that i is a yearly rate. If you are measuring n in quarters, make sure that i is a quarterly rate.
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To calculate the present value, or PV, of a future cash payment, the same formula applies in reverse. It's PV = FV / (1 + i)^n. Now if you are calculating the PV of a series of unequal cash payments to be received in the future, you will need to use the formula for each payment and calculate the PV for each unequal payment FV, and sum them. The formula for this looks like:
Present Value: Multiple Cash Flows
This formula also allows you to use different rates (i) for different cash payments. If the payments in the future are of equal amounts, it's called an annuity. The formula shown here is the most accurate way to calculate the PV of amount C, which is the equal payment amount.
This may look like a lot of work, and it certainly is if using paper, pencil, and a calculator. However, with spreadsheet applications, an investor can easily automate these formulas and even set them up so that by changing the variables, the entire answer updates.
Individuals and companies make investments that are paid back over time - sometimes a few months and sometimes over many years. A critical part of making an investment decision is the time value of money. This is the economic fact that money loses its value over time, so if you invest $100 now and get $100 back in three years, you've actually lost money…or rather, lost purchasing power.
To make sure you are comparing apples-to-apples when making investment decisions, it's important to calculate the present value of future cash flow. If you only consider the future value of your payments, you will overstate the value of the money you receive. Really, all of that is essentially taking future payments and equating it into today's dollars. This concept is a critical part of understanding investments, economics, accounting, and financial markets.
For multiple cashflows, it's important to account for each payment's future value. And with multiple payments, the calculation can be complicated. Luckily, you can use the formula to avoid many tedious individual calculations.
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