We often hear people say that 'a dollar today is worth more than a dollar tomorrow', but why is that the case if you are holding that same $1 coin in your hand?
Many of those with basic understandings in economics and finance may attribute this to inflation because that dollar today will have more buying power than in the future hence it is 'worth' more. This is only half correct because under the concepts of corporate finance it is a little bit more complicated than that. To explain this, we must first understand the time value of money. If someone asks you whether you want
- $10,000 lump sum upfront
- $10,000 lump sum in 5 years
- or $10,000 in 5 installments of $2,000 per year
What would you choose?
To compare the three choices, you cannot simply sum up the total amount received because the value of money is constantly changing with time. To decide which option would give you the highest gain, you must first convert everything to its present value or future value.
Why is present value different from future value? This is due to a number of factors such as:
- Inflation
- Interest rate
- Opportunity cost of time
Inflation and interest are pretty obvious, but what is the opportunity cost of time?
Let me put it this way: If you receive $10,000 now, you can immediately invest this amount and earn some profit in 1 year's time. Assuming rate of return of 5% per annum, by next year you would have $10,500. If you receive $10,000 in 1 year's time however, all you would have is the same $10,000 and the $500 return foregone is your opportunity cost.
Now back to the above example, assuming an interest rate of 3% per annum the present values are:
- $10,000
- $$$10,000 * (1+0.03)^{-5} = $8626.$$
- $$$10,000\times\frac{1-{{(1+0.03)}^{-5}}}{0.03}=\$9159.$$
Simple annuity formula
Through the above comparison, we can see that receiving the lump sum will give us the highest present value while receiving it in 5 years time will give us the lowest value. Why is the value of installments higher? That is due to receiving some of the payments sooner which gave it higher present value than the second option. The same concept applies if we change the interest rate to rate of inflation because the fundamental idea is still the same.
Generally speaking, it is always better to receive money early because the time value of money can make a huge difference.
