The Time Value of Money (TVM) is a key concept in understanding how to appraise investments. In its purest form TVM means that a dollar we have today is worth more than that same dollar if we receive it in the future, but why is that? In this blog post, we’ll break down what TVM is, why it matters, and why you should be factoring it into investment decisions.
Why does the Time Value of Money exist?
The answer lies in a combination of key basic economic principles including opportunity costs, inflation, interest, risk, present value, future value and compounding, but put simply, not all dollars are created equal; if we have a dollar today (which has a present value of $1) then we can invest that dollar, thus making a return plus keeping the original dollar (giving us the future value), whereas a dollar in the future is just a dollar (or actually less than a dollar, as we’ll see).
This is where we need to understand opportunity cost, i.e. what we are missing out on by doing something else. There are 3 things we know about a dollar today; it can be invested (earning us a guaranteed, or more risky rate of interest), it will suffer from inflation, and no matter how solid a return seems, future money always has at least a degree of risk associated with it. Our future dollar is therefore worth less than our dollar today because not only can it not be invested (so cannot raise additional value) but it will also lose value because of inflation (so its purchasing power is less than that of our dollar today), plus there is a chance that it won’t be paid back at all.
The impact of Compounding
These impacts are exacerbated by the concept of compounding of both interest and inflation. If we have a monthly interest rate of 2% on a $10,000 investment, then in the first month the interest earned will be 2% * $10,000 (giving $200), but the second month is no longer just 2% * $10,000, instead, it is 2% * $10,200 (as we are building on the return from the previous month), giving $204. Although this seems small when considering a single month of a $10,000 investment, over the course of a year a 2% compounded investment will give a 26.87% return compared to the 24% of simple interest, i.e. a 12% higher return than simple interest alone. On a large investment, over a longer timeframe, these compounding increments can really add up.
How is the TVM calculated?
When calculating the TVM, what we are actually doing is quantifying how the value of money will change over a future period of time. We do this by applying a discount rate to our future cashflows, therefore we are concerned with 2 main concepts; Future Value (FV) and Present Value (PV).
FV = PV * [ 1 + ( i / n ) ] ^ ( n * t )
while
PV = FV / [1 + i / n ] ^ (n * t)
where:
i = the interest rate the money can earn
t = the number of years
n = the number of compounding periods per year
Example
Using our $10,000, 2% monthly compounded interest example from earlier, we can see that after three years the Future Value will be:
$10,000 * [ 1 + ( 2% / 12 ) ] ^ [ 12 * 3 ]
= $10,617.84 (Future Value)
while solving for the Present Value, we can see that by discounting the future cashflows of the investment, if we wanted to receive $10,617.84 in 3 years time, we would require that same initial $10,000 investment, as:
$10,617.84 / [ 1 + ( 2% / 12 ) ] ^ [ 12 * 3 ]
= $10,000 (Present Value)
Not all dollars are created equal
To summarise, a dollar today is worth more than a dollar in the future. Once we understand this, we are on the road to successfully evaluating and comparing different investment opportunities, as factoring in the value of money over time means that we are able to more accurately evaluate projects of different lengths. The TVM is also a key element in Net Present Value calculations, plus it assists with capital budgeting, risk management and is central to Discounted Cash Flow analysis.
