Time Value of Money is an important financial concept and primarily refers to the value of money at different points in time. Two methods of finding the time-adjusted value of money are compounding and discounting. Though both these methods are useful, they work differently to find the value of money at two different points in time. So, it is quite important to understand the concept as well as understand and appreciate the differences between Compounding vs Discounting.
Before we detail the differences, let’s understand the two terms.
Compounding vs Discounting – Meaning
The primary difference between the two is that we use discounting to express the value of a future amount of money in present dollars. While compounding is exactly the opposite of that wherein we try to get a value of current dollars in the future point of time.
Compounding is the process of earning interest on the principal amount, as well as on the interest portion year after year. In compounding, we assume that the interest earned gets reinvested in every period, leading to the earning of interest on interest over the term of the investments.
Finance experts and analysts use both compounding and discounting to analyze investments. Since time is the basic factor and the value of money changes with time, it is important that we have the values for the same period to compare the investment options.
For instance, a project requires an upfront investment of $60,000. And it will give a $20,000 return for the next three years. Now, if we discount the revenue of three years and add it up, obviously, it would be less than $60,000 in today’s value. This implies that the project is not profitable because the net present value of future earnings is less than today’s investment.
On the other hand, a project can give revenue of $60,000 now but will need an investment of $60,000 in three years from now. This project will be profitable. This is because the present value of $60,000 cost to be paid after 3 years will be less than the PV of the revenue that the project is giving today.
Compounding vs Discounting – Differences
Following are the differences between Compounding vs Discounting:
The compounding concept basically helps us to understand the amount we will get at a future date if we invest a specific sum of money today. That means here, we look for the accumulation or increase in today’s value over the years. On the other hand, through the concept of discounting, we would like to estimate what would be the worth of the future sum of money receivable in today’s value. Or what would be the amount of investment today needed to fetch that kind of future earnings.
Compounding uses the compound interest rate, while discounting uses the discount rate.
Formula for compounding is FV = PV (1 + r)^n, while for discounting is PV = FV / (1 + r)^n. In discounting, we divide the future values by the interest factor. And in compounding, we multiply the present value by the interest factor.
In compounding, we refer to the future value factor table to get the future value. On the other hand, in discounting, we use the present value factor table to get the present value.
Read the Present Value Table for more detail.
In the case of compounding, we already have the present value amount. And, in the case of discounting, we already have the future value.
Impact of Increase/Decrease in Rate
If we drop the rate, the present value goes up in discounting. And, if we raise the rate, the present value goes down. A lower rate lowers the future value in compounding, while a higher rate raises the future value.
In the case of compounding, we start with the present investment value and determine the future value at the given interest rate after a given period of time. However, in discounting, we start with the future earnings values, and those are discounted to get the present value at the given interest rate (discount rate).
Assume we have to calculate the present value of $50,000 if the discount rate is 10% and the time is 10 years. For this, we need to put these values in the present value formula:
PV = FV/(1+r)n or = 50000/(1+0.1)10 = $19277.16.
Now, let us take the example of compounding. Assume we want to find the future value of $10,000 from 10 years from now at a 10% interest rate. Suppose compounding is done half-yearly.
Putting the values in the FV formula: FV = PV * (1 + r/f)fn
= $10000 * (1 + 0.05)^20
We can say that compounding and discounting are two sides of the same coin. One gives us the present value, and the other gives us the future value. So, it will not be wrong to say that if we reverse one, it becomes another, and vice versa.
Continue reading – Discount Factor Formula.
Frequently Asked Questions (FAQs)
Compounding is the process of earning interest on the principal amount, as well as on the interest portion year after year. We use compounding to get the future value of present money.
In discounting, if the rate decreases, the present value increases. And, if the rate increases, the present value decreases. In compounding, a decrease in the rate reduces the future value, while a higher rate raises the future value.