Proctor & Gamble Company is a Cincinnati-based company that produces household p

Question

Proctor & Gamble Company is a Cincinnati-based company that produces household products under brand names such as Gillette, Bounty, Crest, Folgers, and Tide. The company's 2008 income statement showed the following (in millions): Net Sales $83, 503 Costs of products sold 40, 695 Selling, general, and administrative expenses 25,725 Operating income $17, 083 Suppose that the cost of products sold is the only variable cost; selling, general, and administrative expenses are fixed with respect to sales. Assume that Procter & Gamble had a 20% decrease in sales in 2009 and that there was no change in costs except for decreases associated with the lower volume of sales. Compute the predicted 2009 operating income for Proctor & Gamble and its percentage decrease. Explain why the percentage decrease in income differs from the percentage decrease in sales.

Explanation / Answer

Many people, including some financial advisors, would answer the question in the affirmative; they would say your stock would still be valued at $100,000. But let's compute the result before we answer the question. Since the stock first decreased by 20%, we take 20% of $100,000, which is $20,000. So, the value of the stock would then be $80,000. The 20% increase would be on the $80,000. Taking 20% of $80,000, we obtain $16,000, which means the stock increases in value by $16,000. Therefore, the stocks final value is $96,000. The answer to the question is no since the value has had a net decrease of $4,000. This answer seems counterintuitive since we had a 20% decrease and a 20% decrease. But note that the 20% decrease was on a greater value than the 20% increase. The changes were not on the same stock values. The 20% increase on $100,000 would be an increase of $20,000. So, the new value would be $120,000. We find the 20% of $120,000 is $24,000. Therefore, we would have a decrease of $24,000 for a net value of $96,000. Note that we have obtained the same result. The order of the increase and decrease did not matter, again because the 20% decrease was taken on the greater value than the 20% increase. The Commutative Property of Multiplication may be used to show that the above two problems will have the same result. First note that 100% of $100,000 is $100,000. A decrease of 20% of the value would mean that the final value would be 80% of the original value since 100% – 20% = 80%. Also, an increase of 20% of the value would mean that the final value would be 120% of the original value since 100% + 20% = 120%. Reword the problems: Find 120% of 80% of $100,000 or find 80% of 120% of $100,000. Translate the problems: 1.20(0.80)(100,000) = 0.80(1.20)(100,000). The commutative property shows that the two problems are equivalent. Multiplying either side of the equation we obtain our solution of $96,000. Further note that $96,000 is a 4% decrease from the original $100,000 since we had a decrease of $4,000. The above problem is a illustration of a common type of problem involving percentages where percents are used to describe how prices, salaries, and other monetary situations change. For instance, the TV you want to buy is on sale for 30% off or you get a 3.5% increase in your salary starting July 1. Knowing what these phrases mean and knowing how to compute the values is important to everyone in our society.

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