The Future and Present Value of Money

Present Value Future Value Money

Money today worth more than money tomorrow. That’s the first principle you learn in finance at the academy. Yet, you don’t have to be an academic to understand why. With a simple story, we’ll demonstrate the difference between money in the past and money in the future, and how we can calculate that difference.

#Take the Money Now or Later?

Let’s assume you’re planning a trip around the world next year. You don’t have enough money for the trip, so you ask your wealthy and generous friend for a $10,000. He agrees, and asks you when would you like to receive the money?

  1. Today
  2. Next year, right before to the trip

What would you do? Would you take it today, although you don’t need the money today and you probably waste it? Or maybe you would take it next year, right before the trip?

If you picked option 2, as a rational, responsible person, you picked the wrong choice, and I’ll explain why.

The simplest explanation would be that the money you have today should make more money in the future. If we want to know the future value of today’s money, we need to calculate the alternative we could have done with that money.

#”Risk-Free” Rate

The most basic alternative that has usually been used for calculations, is called the “risk-free” rate. What is this “risk-free” rate? It is the theoretical rate of return on investment with zero risk. Of course, you can argue that there is no such thing as a truly risk-free investment. You are probably right, but usually it is the governments’ bonds for short-term, which is considered “risk-free”. Although it is subject to changes between countries, for U.S. based investors, the interest rate on a three-month U.S. Treasury bill is often used as the risk-free rate. The reason behind it is the belief that the government has no chance of defaulting on its obligation.

Task 1

Check

https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=billrates

Look for the three-month U.S. Treasury bill and check its interest. Write it because we’ll use it next.

Currently, for 14/08/2019, a 3 Month Treasury Bill Annual Rate is at 1.96%, which means our annual risk-free rate is 1.96%.

After we understood that by getting the money now we can make 1.96% on it until our vacation next year, we can get back to our question: Whether we would like to receive the money now, or a year from now? The answer is we would like to get the money today. Because money today can be worth at least (1.96%)^number of years in the future. In our example, we would get $10,196 after one year. Keeping that in mind, let’s continue exploring the Present Value of money.

#Worth Investing?

Let’s have another example; Your friend suggests you invest with him $10,000 in a real- estate investment. He thinks this investment will triple itself over 10 years period. Theoretically, it is a great deal: 200% return over 10 years ((3*10,000/10,000)-1) = 2.

Now that we know how to calculate the future value of money, we can estimate if this investment worth investing or not. As we did before, we need to know the alternatives for our money. To know that, we take the “risk-free” rate we found before, and add to it the risk-premium we take for investing in such investment. 

Task 2

Assuming the risk-premium for these kinds of investments with similar risk is 6%. What is the rate of return we expect to get on the investment our friend has offered us?

After that, calculate the amount we expect to get after 10 years.

Does this investment worth your investing?

The Answer

Knowing our risk-free rate and the risk-premium for these kinds of investments, we can calculate the rate of return we expect to get:

1.96% + 6% = 7.96%.

The amount we expect to get after 10 years will be:

$10,000 * (1 + 7.96%)^10 = $21,509. This is the minimum amount we expect to get for our investment. If we can get a higher amount, we should consider the opportunity. In our case, $30,000 after 10 years for this investment is worth investing.

 

#How Much Do Money I Need Right Now?

We can get the solution the other way around. Knowing the future value of our money (10,000*3=30,000) after 10 years – we can calculate how much money does it take now to reach that 30,000 in 10 years. Looking at our equation, we can see that:

Future Value = Present Value * (1 + rate of return) ^ no. of periods

So if we know all the other variables, we can get the Present Value:

Present Value = Future Value(1 + rate of return) ^ no. of periods

 

If we look back at our friend’s offer, we can see that in order to reach $30,000 on investments as ours, the money we need to invest today is $13,947. This is $3,947 more than what we were asked to invest, which makes our investment worth investing.

 

Summary

  • Money today worth more than money tomorrow.
  • To calculate the value of money in the future, you should know the “risk-free” rate.
  • To calculate whether an investment is worthy or not, we should add to the risk-free rate the premium risk we take for investing and risking our money.
  • To know that premium risk, we look at similar investments.
  • The formula to calculate the future value of money is:

Future Value = Present Value * (1 + rate of return) ^ no. of periods

  • If we know the future value, we can get the present value we must have in order to reach that future value.

Present Value = Future Value(1 + rate of return) ^ no. of periods

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