## The Time Value of Money

The Time Value of Money is a core concept in finance. If you are in the early stages of your studies in the field of finance then this is a concept that you want to ensure that you understand well. In your Finance 101 class your professor might have asked you, “Would you prefer \$1.00 today or would you prefer a dollar tomorrow?”. This is when students shout out “A \$1.00 today is more valuable assuming no negative rates”.

They would be absolutely correct as a dollar today could be immediately deposited in a bank account to earn interest. Just to avoid adding unnecessary complications we are assuming that any payments in the future are guaranteed so there is no element of uncertainty in the expected payment; both payments are guaranteed so the only differentiator here between a dollar today and a dollar tomorrow is the opportunity cost of losing out in interest payments. So, when you are presented with this question, remember to think of what you could be doing with the money in hand. Interest earned from a bank account was just an example but what if you have a valuable project that you could invest in today to double your cash?

The Relationship Between Future Value and Present Value

So how about \$0.97 today or a \$1.00 in a year, which would you prefer? Now the answer to this question isn’t as obvious. We first need to make a very important remark as \$0.97 and \$1.00 are not two quantities that we can compare. We need to compare apples to apples. We can do this in two ways: (1) find what \$0.97 would be in terms of Future Value or (2) We can find out how much \$1.00 is expressed in Present Value terms. The second method is more common, especially if we think of projects which require immediate cash outlays. I call the option of getting \$0.97 today Option A and the option of getting \$1.00 in a year Option B.

Assuming you get 3% interest rate for depositing your cash in a bank account, you can calculate how much you would end up with in a year’s time.

FV = Deposit + Interest or 0.97 + (0.97 * 0.03) = 0.9991

A more generic way of calculating future value is:

FV = (1+r)^n * PV

where, r is the interest rate and n is the compounding frequency, in this case 1 year so n = 1. Via the above formula you can calculate the Present Value of your \$1 in a year’s time.

FV = PV/(1+r)^n

therefore, 1.00/(1+0.03)^1 = 0.97087

Now we can compare like for like, for Present Value we can summarise our findings in the below table:

 Present Value Future Value Option A 0.97 0.9991 Option B 0.97087 1

We can see that both in Present Value Terms and Future Value Terms Option B, or getting \$1.00 in a year, results in us being better off.

Time Value of Money is a very powerful concept that comes up everywhere in finance. Whether it is in the form of evaluating companies and projects or finding the fair value of a complex derivative trade, we must always take into account the Time Value of Money in our models.

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