Mastering Discounted Cash Flow
Time Value of Money
Why Money Has a Time Value
Would you rather have $100 today or $100 a year from now? Most people would choose today, and for good reason. A dollar in your hand right now is worth more than a dollar you'll receive in the future. This core idea is called the time value of money.
Two main factors drive this principle: opportunity cost and inflation.
Opportunity Cost: If you have money now, you can invest it and earn a return. By choosing to receive the money later, you miss out on the potential earnings you could have made in the meantime. That missed potential is an opportunity cost.
Inflation: This is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. The 💲100 you receive in a year will likely buy less than 💲100 buys today.
Understanding these forces allows us to calculate exactly how the value of money changes over time, using the concepts of future value and present value.
Future Value and Compounding
Future value (FV) tells you what a sum of money today will be worth at a specific point in the future, assuming it grows at a certain rate. The engine behind this growth is compounding.
Compounding
verb
The process where the earnings from an asset, such as interest or capital gains, are reinvested to generate additional earnings over time. It is essentially earning interest on your interest.
Let's say you invest $1,000 at a 5% annual interest rate. After one year, you'll have $1,050. In the second year, you don't just earn interest on your original $1,000; you earn it on the full $1,050. This is compounding in action. Your money starts to grow at an accelerating rate.
The formula to calculate future value is straightforward:
Where:
- is the Present Value (the initial amount of money)
- is the interest rate per period
- is the number of periods
So, if you invest that $1,000 for 5 years at a 5% annual rate, the future value would be:
Present Value and Discounting
Present value (PV) works in the opposite direction. It tells you the current worth of a future sum of money. To find the present value, we use a process called discounting, which is essentially the reverse of compounding.
Discounting helps answer questions like, "If I want to have $10,000 in five years, how much do I need to invest today?" It strips away the future interest to show you what that money is worth in today's dollars.
The formula for present value is a simple rearrangement of the future value formula:
Let's say you need $20,000 in 10 years for a down payment on a house, and you expect to earn a 6% annual return on your investments. How much do you need to invest today?
This means you would need to invest $11,167.92 today to reach your goal of $20,000 in ten years, assuming a consistent 6% return. This is the present value of your future goal.
Perhaps the most important concept in personal-finance is that money has a time value.
Now, let's test your understanding of these core concepts.
Which two factors are the primary drivers behind the principle that money available today is worth more than the same amount in the future?
The process of earning interest on both the original principal and the accumulated interest from previous periods is known as:
Mastering present value and future value is the first step toward making smarter financial decisions, from saving for retirement to evaluating investment opportunities.