investor clinic

I’ve been trying to figure out how to calculate the compound annual growth rate for stocks that I have enrolled in a dividend reinvestment plan. The problem I am running into is deciding what to use as the beginning value. Should I use the initial purchase value of the shares? Or should I use the average purchase price, which would include the cost of shares purchased through the DRIP?

The easiest way to explain this is with an example.

Let’s assume you purchased \$10,000 of Royal Bank shares on Oct. 15, 2011. You then enrolled them in the company’s DRIP, which lets you reinvest every penny of your dividends because it supports purchases of fractional shares. We’ll further assume that you did not contribute any new cash after that, apart from reinvesting all of your dividends in additional shares.

Ten years later, on Oct. 15, 2021, your \$10,000 investment would have grown to about \$40,500. Calculating your gross total return is straightforward: You would simply divide your gain of \$30,500 by your starting value of \$10,000. The answer, 3.05, is equivalent to a total return of 305 per cent. You don’t include the cost of your reinvested dividends in the starting value because that money didn’t come out of your pocket – it was paid out of the earnings of Royal Bank and represents part of your return.

Now, expressing that gross return as a compound annual growth rate takes a bit more work. One method is to use an online annual rate of return calculator such as the one at www.dinkytown.net (look under “investment calculators”). If you enter the starting and ending dollar values and their respective dates, the calculator will determine that the annualized return in our example is about 15 per cent. (Make sure you set the “periodic deposit or withdrawal” to zero, as our example assumes no money is added or withdrawn after the initial deposit.)

There’s an even quicker way to determine a stock’s annualized total return for a specific period. If you use the “Compound Returns Calculator” at canadastockchannel.com, you would simply enter the stock symbol and the start and end dates. There’s no need to enter dollar amounts because, whether you started with \$1,000, \$10,000 or \$100,000, the annualized return for Royal Bank over the 10-year period in question would be the same, 15 per cent.

The calculator at canadastockchannel.com also lets you compare a stock’s total annualized return to the S&P/TSX Composite Index. However, the index’s return does not include dividends, so it’s not an apples-to-apples comparison. As a workaround, you could instead enter XIC – the symbol for the iShares Core S&P/TSX Capped Composite Index ETF. XIC’s management expense ratio is just 0.06 per cent, so it is a good proxy for the S&P/TSX Composite Index’s total return, with dividends.

Again, the above analysis assume no money was added after the initial \$10,000 investment, but real life isn’t always so straightforward. Sometimes, people add cash to a portfolio or sell some shares and withdraw the funds. In such cases, calculating the rate of return is more complicated. There are two broad methods: the “time-weighted return,” which controls for the effects of cash inflows and outflows, and the “money-weighted return,” which includes the impact that contributions and withdrawals have on performance. For example, buying more Royal Bank shares right before a spike in the share price would improve the money-weighted return but would not affect the time-weighted return.

The details of each method are beyond the scope of this column, but when you see a total return for a mutual fund, exchange-traded fund, market index or individual stock, that’s a time-weighted return. The performance reports that advisers send their clients use money-weighted returns. I recently checked the performance of my accounts with my discount broker, BMO InvestorLine, and it provides both measures.