1.2 Proportions
Another way to analyze the performance of branches A, B, and C described above is to take the view that all of the percent margins should be equal – or, equivalently, that the ratio of profit to sales should be the same for each branch.
When the ratio of quantities should be the same in all circumstances, the quantities are said to be proportional to one another.
Example 1.2.1
Assume that the profit should be proportional to sales, and that this proportion should be that of the company totals (20.5%). Then you could calculate the appropriate profits for branches A, B and C individually.
For branch A:
[latex]Ratio = \frac{20.5}{100} = 0.205[/latex]
[latex]0.205 = \frac{Amount}{Base}= \frac{Profit}{\$12,500}[/latex]
Thus Profit = [latex]0.205 \times \$ 12,500 = \$ 2,562.50[/latex]
Similarly for branches B and C, the proportional profits would be $9,532.50 and $12,956 respectively. The analysis would proceed as follows:
| Profits | A | B | C |
| Actual | $2,950.00 | $7,750.00 | $14,350.00 |
| Proportional | 2,562.50 | 9,532.50 | 12,956 .00 |
| Difference | +387.50 | -1,782.50 | +1,394.00 |
Again you can see the branch B’s performance was the least effective.
Ratios are generally used as in the above exercises – sometimes to eliminate the effect of size, and sometimes “in reverse” to make sure the quantities are appropriate.
Knowledge Check 1.2
- Will’s Coffee Shops expect to earn a percent net margin of 14% of sales.
- Find the expected profit and expenses of a shop that will have sales of $29,000 a month.
- If a shop hopes to earn a net profit of $5,000 a month, what should be its sales target?
- As a guide to restaurant pricing, it is often assumed that the price of a meal should be proportional to the cost of the food in the meal. Suppose that a restaurant decided to make that ratio 2.8.
That is:
[latex]\frac{\text{Meal Price}}{\text{Food Price}}=2.8[/latex]
Use this guide to estimate the price of meals for which the food cost is (a) $3.50; (b) $8.00; (c) $14.00.
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