How do you know if your investments are performing well? That’s a question I struggle with quite often. It’ll be easier if I show you an example.
Let’s assume I have an asset which I bought for $10,000 and then sold it for $15,000. During that time I received cash dividends totaling $500. I also incurred brokerage commissions on the buy and sell of $100 total. For the sake of simplicity we’ll assume this asset is in a tax-deferred account, like an IRA, so taxes will not matter. So, what’s my return?
If you said 53.5% then you would be right if you’re calculating total return. How did you get that? Easy.
[ (Ending Value + Dividends) / (Initial Investment + Costs) ] - 1
or
[ ($15,000 + $500) / ($10,000 + $100 ] -1 = 0.535
However, this calculation fails to account for a very important factor when dealing with money. Time.
If the asset was held for one year, then that’s an outstanding return! However, it’s not so hot if I held it for 10 years. Most people would simply take the 53.5% and divide it by 10 years and say that they averaged 5.35% per year over that time period. Unfortunately, that’s incorrect. Here’s why.
PV is Present Value at time 0
FV is Future Value at time n
i is the rate at which the investment will compound each period
n is the time, or number of periods
If we plug in our rate of 5.35% per year from our naive calculation, we get the following result:
FV = $10,100 x (1 + 0.0535)^10 = $17,008.53
That’s a few dollars more than the $15,500 that the investment actually produced! So how do we calculate the actual return so it accurately reflects the time value of money?
We begin by using the simple total return number we previously calculated. But before we subtract one, we need to account for the time value. To do so, we need to take the inverse of our time period, 1/n. In our case, 1/10 or 0.10. Now raise the total return figure by the inverse of the time period, subtract one and you have your compounded rate of return.
[ (Ending Value + Dividends) / (Initial Investment + Costs) ]^(1/n)
or
[ ($15,000 + $500) / ($10,000 + $100) ]^(1/10) - 1 = 0.0438
So, in reality our return was only 4.38% per year. That’s a big difference from the simple calculation of 53.5%! Now the investment doesn’t look so hot does it?
As my grade school math teachers would say, double check your answer. We do this my plugging in these numbers to the present value formula above:
FV = $10,100 x (1 + 0.0438)^10 = $15,505.80 (the difference is due to rounding error)
That checks out. So we know the math is correct. Go ahead and play with the time period. Increase it 15 or 20 years and see how time has an impact on your investment’s growth rate.
Things get more complicated when you begin to consider the consequences of taxes and when you choose to reinvest those dividends instead of receiving cash. That, my friend, is a whole other article!
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