Time Value of Money Explained Part III
Calculating Present Value to Get to the Country of Kilts and Golf
As I was going through college, my first opportunity to travel overseas took me to the country of Scotland. While my cousin was studying abroad in Edinburgh, he found a great deal switching cable companies and got me a free ticket to fly over. Although my ticket was free, I still needed to save what I projected to be about $1000 for the rest of the trip. Since it was about a year out, I needed to figure out how much I had to save at that time so I would have the $1000 available when it was time to get on the plane. To figure out this problem, we’ll work through calculating present value of the $1000 in the future.
Essentially, when someone talks about the present value, they are talking about how much money we would need to invest now to have a certain amount in the future. In this case, I needed to find how much I would have to save today to have $1000 in one year.
For this problem, let’s assume that I could invest in a savings account that gave me 5% interest. To calculate the total that I would have to save today, I have to divide by the interest rate that I could get plus 1:
$1000 / (1+5%) = $1000 / (1 + 0.05) = $1000 / 1.05 = $952.38
So if I want to have exactly $1000 by the time I step on the plane to go to Scotland in one year, I need to invest $952.38 today at 5% interest. Therefore, the present value of $1000 one year in the future is $952.38 if I can invest at a 5% interest rate.
Heighten my Interest Calculating Present Value in Another Example
Taking my savings plan to get to Scotland as another example, let’s say that I could invest at 7% instead of 5%. To make sure that I had $1000 in one year, I’d have to invest the following amount at 7%:
$1000 / (1+7%) = $1000 / (1+0.07) = $1000 / 1.07 = $934.58
As the interest rate that I could get increased in the savings account, the amount that we would have to invest decreased. This makes sense since we’ll be able to get more interest on what I initially invested at a higher interest rate. What this shows is that as the interest rate increases, the present value of money in the future decreases.
Calculating Present Value – Another Small Business Financial Management Example
Let’s go through one more example to make sure we understand the concept of the present value. Say that we wanted to save a total of $35,000 in a year for a house down payment in that nice neighborhood across town. If we were able to save at 3%, how much would we have to invest today to have $35,000 one year from now?
When calculating present value, we need to divide the amount we want to have by 1 plus the interest rate:
$35,000 / (1 + 3%) = $35,000 / (1 + 0.03) = $35,000 / 1.03 = $33,980.58
So, this means that we’ll have to invest $33,980.58 in our 3% savings account today if we want to have $35,000 in one year. Said another way, the present value of $35,000 one year from now is $33,980.58 if the interest rate is 3%.
Key Takeaway: Calculating present value is finding the amount of money that we would have to invest today to have a certain amount of money in the future. For the next lesson, we’ll see how the present value and the future value can be used to calculate each other.