INVESTOR CLINIC

Thanks to everyone who took last week’s investing quiz and experienced what may well be the most thrilling and rewarding 10 minutes of their lives.

If you haven’t done the quiz yet, great news! You can still take it here and find out what all the fuss is about.

As promised, today – in response to feedback from readers – I’ll be explaining some of the more challenging questions.

If an investment posts a total return of 30 per cent over five years, the annual compound rate of return is:

a. 6.00 per cent

b. 5.39 per cent

c. 4.85 per cent

d. 3.93 per cent

If your investment grows by a total of 30 per cent over five years, you will end up with 1.3 times your initial principal. To calculate the annual compound rate of return, you must determine what number raised to the power of five equals 1.3. The answer (I used a calculator to find the fifth root of 1.3) is about 1.0539, which is equivalent to an annual growth rate of 5.39 per cent. So the correct answer is b. You can test the answer by calculating 1.0539 to the fifth power, which produces a result very close to 1.3.

Acme Anvil Co. has a trailing price-to-earnings multiple of 21. Its earnings yield is:

a. Unknown based on information provided

b. 12/21 or about 57 per cent

The price-to-earnings or P/E multiple is the current price per share divided by the earnings per share over a specified 12-month period (in this case, it’s the previous 12 months). The earnings yield is the reciprocal of the P/E – it’s the earnings per share divided by the price per share. Since 1/21 equals about 0.048, the correct answer is c: About 4.8 per cent.

The next question I’ll discuss, No. 11, was one of the most difficult based on the feedback I received from readers:

Justin buys 100 shares of U.S.-based Big Oil Corp. for \$75 (U.S.) each when the Canadian dollar is trading at 98 cents. He later sells the shares at \$68 each when the loonie is at 75 cents His total capital loss, or gain, in Canadian dollars, is:

a. Capital loss of \$700

b. Capital loss of \$933.33

c. Capital gain of \$714.29

d. Capital gain of \$1,413.61

For tax purposes, capital gains must be calculated in Canadian dollars using the exchange rates that were in effect on the purchase and sale dates. Justin’s cost to purchase the 100 shares was \$7,500 (U.S.). Because \$1 (Canadian) was worth 98 cents (U.S.) at the time, his cost in Canadian dollars was \$7,500/\$0.98, or \$7,653.06 (Canadian). The proceeds of the sale were \$6,800 (U.S.) which, when divided by the exchange rate of 75 cents (U.S.), works out to \$9,066.67 (Canadian). The capital gain was therefore the Canadian dollar proceeds of \$9,066.67 minus the Canadian dollar cost of \$7,653.06, or \$1,413.61. Correct answer: d.

Finally, we’ll look at question No. 15:

Fred buys 100 shares of Slate Rock and Gravel Co. for \$45 each. He later buys 200 shares at \$75 each. Finally, he sells 100 shares at \$80 each. His adjusted cost base per share on his remaining 200 shares is:

a. \$67

b. \$65

c. \$57.50

d. \$52.50

Many readers chose c. – and fell into my dastardly trap! They arrived at the answer by starting with Fred’s total cost of \$19,500 for purchasing the 300 shares, subtracting the \$8,000 proceeds from selling 100 shares and then dividing the net amount of \$11,500 by the remaining 200 shares to get \$57.50. But this is not the correct way to calculate the adjusted cost base (ACB). When you sell a portion of your shares, the ACB per share of your remaining shares does not change. Fred paid a total of \$19,500 for the 300 shares, so his ACB was \$65 a share. The fact that he sold 100 of those shares doesn’t affect his average cost for the remaining 200 shares, which is still \$65 a share. So answer b. is correct.

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