Discounting is simply applying the time value of money, but backwards. It allows us to calculate the value today of a payoff at sometime in the future.
In our Compounding example, we used 1.75% as our interest rate (r). This interest rate is also called our Required Rate of Return.
For lower-risk investments, we will accept a lower interest rate: our required rate of return is lower. For higher-risk investments, we require a higher rate of return. This is why Treasury Bonds (investments issued by the U.S. Government) have such a low interest rate: the payments are backed by the full faith and credit of Uncle Sam (i.e. they will never default).
When compounding, we multiply our capital base by (1 + r) to get our ending investment value. Remember to move the decimal to the left two spaces to convert a percentage into decimal format (1.75% = 0.0175). In our previous example, the value of our $100 investment at the end of the year is equal to $101.75.
$100 x (1 + 1.75%) =
$100 x (1.0175) =
If discounting is the reverse of compounding, then we can find the value today of some payoff in the future, given a required rate of return, by division instead of multiplication. Instead of multiplying our beginning value by (1 + interest rate) to get our ending value, we divide our ending value by (1 + interest rate) to get our beginning value.
Beginning value x (1 + r) = Ending value
Ending value / (1 + r) = Beginning value
$101.75 / (1.0175) = $100
We can use this formula to answer the question, “how much do I need to save today in order to have X dollars in the future?”
For example, if I know that I need to have $5,000 for a large payment next year, what do I need to save today? I’ll assume that I’m investing in a riskier investment that has a 6% interest rate.
$5,000 is our ending value
6% is our interest rate
$5,000 / 1.06 =
Given a 6% interest rate, I’ll need to save (invest, rather) $4,717 today in order to meet my goal.
We’ll look at compounding and discounting for multiple years in our next lesson, Present Value and Future Value.