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John Heinzl will review a few of the questions that gave readers the most trouble from last week’s Investor Clinic back-to-school quiz.Igor Smichkov/Getty Images/iStockphoto

I won't lie: When I was creating last week's Investor Clinic back-to-school quiz, my goal was to lay a few traps that would ensnare unsuspecting readers.

Mission accomplished.

Today and next week, I'll review a few of the questions that gave readers the most trouble. Let's start with question No. 1, which elicited, by far, the most feedback from flummoxed readers. A couple of people even accused me of providing the wrong answer.

That's ridiculous. I never make mistakes. Well, at least in this case I didn't. Here's question No. 1 again:

If you purchased 200 shares of XYZ for $21 each, sold 100 shares of XYZ for $24 each, then bought 200 shares of XYZ for $27 each, the adjusted cost base (ACB) per share of your 300 shares (ignoring commissions) would be:

a) $24

b) $25

c) $25.33

d) $25.67

Many readers chose a) $24, but the correct answer was actually b) $25. Let's do that math, first correctly and then incorrectly, so people can see where they went wrong.

Calculating the ACB of the initial 200 shares is straightforward – it's $4,200 (200 times $21) or $21 a share.

If you then sell 100 shares – regardless of the price – the ACB of your remaining 100 shares doesn't change. It's still $21 a share (or $2,100 in total). After all, that's what you paid in the first place.

Now, if you purchase an additional 200 shares at $27 each, you would add the cost of $5,400 to the $2,100 you already spent, for a total cost of $7,500 for the 300 shares you own. The ACB per share would therefore be $7,500 divided by 300, or $25, which is the correct answer.

Some people got tripped up because they forgot a key rule about calculating the ACB – namely that selling a portion of your shares doesn't affect the ACB per share. (The ACB per share only changes when you purchase shares.)

Specifically, some readers calculated the ACB of the initial 200 shares as $4,200 (which is correct), then subtracted the sale proceeds of $2,400 (100 shares at $24) to arrive at a new ACB of $1,800 or $18 a share (which is incorrect). They then added $1,800 to $5,400 for a total cost of $7,200, or $24 a share.

To see why this calculation is flawed, consider a more extreme case. Say you bought 200 shares at $10 each (total cost $2,000), and the price then doubled to $20. If you sold 100 shares at $20 (total proceeds: $2,000) the ACB of your remaining 100 shares would not be zero (i.e. $2,000 minus $2,000). It would be $1,000 or $10 a share – the same price you paid originally.

For more on calculating the ACB, see my previous columns here and here.

Let's move on to question No. 4:

With exchange-traded funds (ETFs) and mutual funds, reinvested or "phantom" distributions:

a) are paid in cash but not identified on a T3 slip

b) are not paid in cash but are identified on a T3 slip

c) increase the adjusted cost base (ACB) of the investment

d) decrease the ACB of the investment

Phantom distributions are not paid in cash and are not identified on a T3 slip, which rules out answers a) and b). These amounts, which are broken out on the ETF provider's website (look under "distributions"), are automatically reinvested in the fund, and as such they increase the ACB of the unit-holder's investment, as answer c) states. Failing to add these amounts to the ACB can result in an investor paying more capital-gains tax than necessary when the units are sold.

You can read more about phantom distributions here and here.