Example 6.1.10 Te n years ago I invested $2,000 in a dividend reinvestment plan
offered by my local electric utility company. The value of my original investment,
including reinvested dividends, has grown to $3,525.18. What was my total rate of
return?We do not need to look at capital gains and dividends separately; the values we are given
include everything. Applying the compound rate of growth formula once again gives:i (^) _PVFV (^)
1/n
1
i
$3,525.18____
$2,000
1/ (^10)
1
i 0.0583154 5.83%
Of course, if I invested additional money along the way (which people often do with
these plans) we would once again be dealing with an unpleasantly complicated situation.
The most efficient way to find the rate of return in those situations would probably be
to set up a spreadsheet reflecting the payments, and then use guess and check to find the
rate.
Volatility and Risk
If you put your money in a bank certificate to earn compound interest, the value of your
account can be expected to grow steadily and consistently, with essentially no risk of losing
money on your investment.^2 Investments in stocks carry much greater risks. No matter
how solid a company might look when you first invest in it, there is always the real pos-
sibility that things will go badly for the business and your stock decline in value, or even
become worthless. This risk is present whether you are looking at a publicly traded stock
like Zarofire Systems, or looking at the stock of a small business like Jason and Dave’s Dry
Cleaning. Even good businesses can fall on hard times or fail. While money invested in
owning a business has the potential to offer much greater gains than money snugly depos-
ited in a bank account, it also has the potential for loss. When you deposit money in a CD,
you know the rate of return on your money; when you buy stock in a company, you’re not
even certain of the return of your money.^3
Even if all works out well and you earn a good return on your investment, though, there
is another important difference in how that growth occurs. In Example 6.1.5 we found that
your investment in Zarofire Systems paid off handsomely, earning a 21.90% rate of return.
It would be a mistake, though, to think of this as happening smoothly. When we calculate
a rate of return on a stock investment, we are saying that the end result was equivalent to
earning that rate of compound growth. It should never be assumed that the journey looked
like a smooth and even rate though. Over the years, the price of Zarofire’s stock may have
gyrated wildly up and down, and in fact it probably did. This variation in the price along
the way is referred to as volatility. Volatility is not necessarily a bad thing, especially if you
have the judgment and courage to buy on the lows and sell on the highs, but it can make
for a bumpy ride. As you watch the stock price swing up and down from day to day it is not
hard to fall victim to greed or fear and make unwise decisions, buying on greed at the highs
and selling on fear at the lows as a result.
The route taken from your original $12.50 investment to the eventual $50 sale in a
stock might look quite a bit different than the route at a steady 21.90% compound interest
rate. The graph on the next page illustrates how Zarofire’s stock price may have actually
behaved over time, contrasted with a 21.90% compound interest rate. Notice that the stock
price, instead of going up smoothly, goes up, and down, at varying rates.
(^2) Even in the unlikely event that the bank collapses, most accounts are covered by FDIC insurance, through which the
federal government guarantees your accounts at the bank up to $100,000. Of course, it is possible that both the bank
and the federal government could collapse, but if that happened we’d all have much bigger worries than our CDs.
(^3) With apologies to Mark Twain.
258 Chapter 6 Investments