## Profit and Loss

Profit and Loss accounting is a fundamental way to measure the financial performance of a business. A firm grasp of the basics is essential.

There are two distinct kinds of profit and loss problems - those in which profit or loss is based on cost and those in which profit or loss is based on selling price. Before such a prolem can be solved it must be known in which of these classes it belongs. Bear in mind, though, that profit or loss is always to be considered as based on cost unless it is stated or otherwise known that it is based on selling price.

### Profit and Loss Based on Cost

When a percent of profit or loss is given, it is understood, unless stated to the contrary, that this percent is bsed on the cost. Thus, if someone states simply that he or she sold something at a profit of 10%, it is understood to mean that it was sold for an amount equal to its cost plus 10% of its cost. In modern business, however, it is customary to figure profit and loss as a percent of selling price. This is because commissions, discounts, certain taxes and other items of expense are commonly based on selling price, and in a complicated business it makes for simplicity in accounting to base profit and loss also on selling price.

 To find the percent gain or loss, divide the amount gained or lost by the cost. Example: A toy that cost 80 cents is sold at a profit of 20 cents. Find the percent or rate of profit. Gain / cost = % profit. 20 / 80 = 25%. - Answer Example: A book that cost \$1.00 is sold for 80 cents. Find the percent loss. Cost - selling price = loss. \$1.00 - \$.80 = \$.20 loss. Loss / cost = % loss. \$.20 / \$1.00 = 1/5 or 20%. - Answer To find the loss and the selling price when the cost and the percent loss are given, multiply the cost by the percent and subtract the product from the cost. Example: A damaged chair that cost \$110 was sold at a loss of 10%. Find the loss and the selling price. Cost x percent loss = loss. \$110 x 1/10 = \$11, loss. - Answer Cost - loss = selling price. \$110 - \$11 = \$99, selling price. - Answer To find the cost when the profit and the percent profit are given or To find the cost when the loss and the percent loss are given, divide the profit or loss by the percent profit or loss. Example: A bracelet was sold at a profit of \$9,000. The rate of profit was 30%. What was the cost of the bracelet? 30% of the cost = \$9,000. Cost = \$9,000 / .30 = \$30,000. - Answer To find the cost when the selling price and the percent loss are given, divide the selling price by 1 minus the percent loss. Example: A vase was sold for \$168; the loss was 4%. How much did the vase cost? Loss = 4% of cost. Total cost = \$100%. Selling price = 100% - 4% = 96% 96% of cost = \$168. Cost = \$168 / .96 = \$175. - Answer

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### Profit and Loss Based on Selling Price

Modern accounting practice favors the basing of profit and loss on selling price rather than on cost. This is because commissions and other selling expenses are figured as percentages of selling price, and it also simplifies accounting to base profit and loss on selling price.

To find the percent profit or loss, divide the amount gained or lost by the selling price.

Example: A candy bar sells for \$1.30 at a profit of 65 cents. What percent of profit on selling price does this represent?

Gain / selling price = % profit.
\$.65 / \$1.30 = .5 or 50% profit. - Answer

Example: On every radio selling for \$40 a merchant lost \$8. What was his rate of loss on selling price?

Loss / selling price = % loss.
\$8 / \$40 = .20 or 20% loss. - Answer

To find the profit and the cost when the selling price and the percent profit are given, multiply the selling price by the percent profit and subtract the result from the selling price.

Example: A toy sells for \$6.00 at a profit of 25% of the selling price. Separate this selling price into cost and profit.

Selling price x % profit = profit.
Selling price = profit = cost.
\$6.00 x .25 = \$1.50, profit. - Answer
\$6.00 - \$1.50 = \$4.50, cost. - Answer

To find the loss and the cost when the selling price and the percent loss are given, multiply the selling price by the percent loss and subtract the result from the selling price.

Example: At a sale, neckties selling at \$50.00 are sold at a loss of 60% of selling price. What is the loss and the original cost?

Selling price x % loss = loss.
Selling price + loss = cost.
\$50.00 x .60 = \$30.00, loss. - Answer
\$50.00 - \$30.00 = \$20.00, cost. - Answer

To find the selling price when the profit and the percent profit are given, or to find the selling price when the loss and the percent loss are given, divide the profit or loss by the percent profit or loss.

Note: This rule should be compared with the one under Profit and Loss Based on Cost. The two rules are exactly similar except that in one case 100% represents cost while in the other case 100% represents selling price.

Example: A kind of tape is selling at a profit of 12% of selling price, equal to 18 cents per yard. What is the selling price of the tape?

Profit / % profit = selling price.
\$.18 / .12 = \$1.50 selling price. - Answer

Example: A loss of \$13.50 on a book represents 15% loss on the selling price. What is the selling price?

Loss / % loss = selling price.
\$13.50 / .15 = \$90.00, selling price. - Answer

To find the selling price when the cost and the percent loss are given, add the percent loss to 100% and divide the cost by this sum.

Example: Socks that cost \$7.00 per pair were sold at a loss of 25% of selling price. What was the selling price?

Cost / ( 100% + % loss ) = selling price.
\$7.00 / 1.25 = \$5.60, selling price. - Answer

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### Mark-up

When profits are based on cost, profit is commonly referred to as mark-up over selling price, and the percent profit on cost is called percent mark-up to distinguish it from percent profit (i.e., on selling price).

To reduce percent profit on selling price to percent mark-up (percent profit on cost), divide profit on selling price by 100% minus percent profit on selling price.

Example: A 20% profit on selling price is what percent mark-up (percent profit on cost) ?

% profit on selling price / (100% - % profit on selling price) = % profit on cost.
.20 / .80 = .25 or 25% profit on cost. - Answer

To reduce percent mark-up (percent profit on cost) to percent profit on selling price, divide percent mark-up by 100% plus percent mark-up.

Example: A coat marked up 60% carries what percent of profit on selling price?

% profit on cost / ( 100% + % profit on cost ) = % profit on selling price.
.60 / 1.60 = .375 or 37.5% on selling price. - Answer

To reduce percent loss on selling price to percent loss on cost, divide percent loss on selling price by 100% plus percent loss on selling price.

Example: 20% loss on selling price is what percent loss on cost?

% loss on selling price / ( 100% + % loss on selling price ) = % loss on cost.
.20 / 1.20 = .16666 or .16.67% loss on cost. - Answer

To reduce percent loss on cost to percent loss on selling price, divide percent loss on cost by 100% minus percent loss on cost.

Example: 20% loss on cost is what percent loss on selling price?

% loss on cost / ( 100% - % loss on cost ) = % loss on selling price.
.20 / 80 = .0025 or 25% loss on selling price. - Answer

The four mark-up examples may appear confusingly difficult, but they can be more easily remembered, if you ask yourself whether the percent required in the answer is to be larger or smaller than the one that is given. Where profits are concerned, the percent of selling price is smaller than the percent of cost. Where losses are concerned, the percent of selling price is larger than the percent or cost. If a smaller percent is required in the answer, the given percent is divided by 100% (or 1) plus the given percent. If a larger percent is required in the answer, the given percent is divided by 100%, minus the given percent. It should also be noted in these examples that when the given percent is added to 100% the sum represents a cost or a selling price corresponding exactly with the kind of percent wanted in the answer.