Time value of money: Lotteries, growth and calculations

Say you had just won 1,000,000 dhs and were offered two options to get paid:

• Option A: Get a check for 1,000,000 dhs in 5 years
• Option B: Get a check for 800,000 dhs today

Which would you take? Let’s analyze the decision given what you know about interest and compounding so far.

Option A:

Getting 1,000,000 dhs in 5 years may sound attractive at first because 1,000,000 is more than 800,000. However, you need to also consider opportunity cost. What do you miss out on by waiting 5 years before receiving your winnings.

Say you received 1,000,000 dhs today, and invested it somewhere that gave you, say for argument’s sake, 5% interest. In 5 year’s time you’d have 1,276,281 dhs:

‍

‍

By waiting 5 years before you receive your winnings, you would have missed out on 276,282 dhs in potential interest payments.

Option B:

At first glance, 800,000 dhs is significantly less than 1,000,000 dhs. Let’s do the math again. Where would you end up in 5 years time with this option? Assuming you had invested the money somewhere that also gave you 5% interest, then by the end of the 5th year you’d have 1,021,026 dhs:

‍

‍

Comparing this to Option A, it becomes clear that even if you get only 800,000 dhs today and invest it at 5% interest, this yields a better result than simply getting paid 1,000,000 dhs in 5 years.

An important point to note is that the calculations above may yield different results depending on the interest rate you can realistically get. If you assumed a rate of 10% instead of 5%, then Option B would be even more correct. If you assumed a rate of 3% instead of 5%, Option B becomes incorrect. This is because 800,000 dhs invested at 3% is worth only 927,419 dhs in 5 years — less than 1,000,000 dhs.

‍

‍

This concept is easier to visualize in the chart above. Look at each bar. Notice how the higher the interest rate you assume, the more correct it becomes to receive 800,000 dhs today and invest it. Also note that any interest rate below 5% makes it better for you to receive 1,000,000 dhs in 5 years.

So once again, interest & compounding remain two critical concepts that when combined, help us define what we call the Time Value of Money. And the Time Value of Money should be the basis of all your mental calculations when dealing with financial decisions.