Time is money, as the old adage says

One of the most fundamental principles in finance is the Time Value of Money. It basically says that the money (e.g., dollar) you have today is worth more than the money you will have in the future.

First of all, there is inflation, which erodes the value of your money. Today, you may pay $5 for a meal, but in five years that meal may cost $6. So, $5 today isn’t the same as it will be in 5 years from now.

Second, the dollar today is worth more because you can invest it and earn interest, or capital gains and dividends. Let’s say you invest $1,000 and earn 5% interest. In 5 years, your investment will be worth $1,276.28. That’s Future Value of Money.

But, what if someone promised you $1,000 in 5 years? What would be the Present Value of this amount if you used 5% interest? What you need to do is calculate the Present Value of Money. You arrive at it by discounting $1,000 for 5 years at 5%.

The Present Value of future $1,000 then becomes $783.53. You could theoretically sell the future $1,000 for $783.53 today to someone who’s willing to wait 5 years while earning 5%.

Now, let’s assume that inflation rose and you can earn 7% interest rather than 5% as in the case above. After 5 years, your $1,000 will grow to $1,402.55. On the other hand, the promised $1,000 in 5 years would be worth $712.99.

The higher the rate at which you discount the Future Value of Money, the lower is its current worth (Present Value). When it comes to investment valuation, the riskier (more uncertain) the future cash flow, the lower is the Present Value of the investment, thus investors are willing to pay less for it and demand higher return..

There’s a similar concept when it comes to borrowing. The riskier borrowers are charged higher interest rates.

Let’s continue and assume that now you can invest $1,000 at 7% interest for 10 years. In this case, in the future your investment will grow to $1,967.15. On the contrary, if someone promises you $1,000 in 10 years, the Present Value of that money, discounted at 7%, would be $508.35.

Thus, the longer you have to wait for money, the lower is its Future Value.

In summary:

  • The higher the discount rate on future cash flow (due to risk or higher inflation), the lower its Present Value
  • The longer you need to wait for money, the lower is its Present Value
  • The higher the interest rate (or required return on investment), the higher is the Future Value of Money (and vice versa)
  • The longer the period over which the investment is compounded, the higher is its Future Value (and vice versa)
  • When calculating the Present Value, you discount (divide) the Future Value by the rate and number of years
  • When calculating the Future Value, you compound (multiply) the Present Value by the rate and number of years 

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Introduction to Time Value of Money

This part discusses Time Value of Money, one of the most fundamental principles in finance every investor should know and understand. It is the basis for understanding investment valuation as well as other concepts in finance.