Time Value of Money
We’re going to be answering the question, “Should we accept this investment or should we reject it?” When we talk about these tools, the concept of the time value of money is essential. The time value of money says that a dollar today is worth more than a dollar tomorrow.
These decision-making tools focus on the future cash flows that we get for investing today. Since these are cash flows that happen in the future, we need to calculate them back to what their present value is. This helps us to see how much our future cash flows are worth today, and we use what is called the discount rate to bring future cash flows to their present value.
There are four key terms to understand for the time value of money. The first one is the present value of a lump sum. This is for when you receive a one-time payment in the future, and you’re trying to figure out how much it is worth today.
Study Tip 😀
A lump sum is a one-time payment in the future
Let’s say that in five years you’re going to receive $100,000. Using a discount rate of 5%, how much is it worth today? It would be worth $78,300. When you have to calculate the time value of money for the CPA exam, the problems provide you with the specific factors you need to use.
The next type is for the present value of an ordinary annuity. Annuity means that you’re not just getting a one-time payment, but you’re getting a payment every year. We’re trying to figure out the present value of all of those payments. For example, let’s say that you’re going to receive $20,000 in payments for the next five years using a discount rate of 5%. The question is, how much are all of those future payments worth today? The answer is $86,000. Notice that this was called an ordinary annuity. Ordinary means that we get the payment at the end of the period. At the end of every year, we’re getting the $20,000 in our example.
Study Tip 😀
An annuity is an annual payment for the same amount each year.
The third term is for the present value of an annuity due. Whereas the ordinary annuity makes the payment at the end of each period, the annuity due makes the payment at the beginning of each period. For example, let’s say that you receive a rent payment of $1,000 at the beginning of each month. Since it happens at the beginning, this would be an annuity due. Using a discount rate of 5%, what would the present value be? It would be $11,700.
These first three terms look at future amounts and calculate their present value. The next term, future value, does the opposite. It looks at an amount today to see how much it will be worth in the future.
For example, if you invest $5,000 into a retirement account today, how much is that $5,000 going to be worth in 30 years if we use a discount rate of 5%? It would be worth $21,600.