Question

Sawyer Corporation's 2015 sales were $6 million. Its 2010 sales were $3 million.

(a) At what rate have sales been growing? Round your answer to two decimal places.
(b)Suppose someone made this statement: "Sales doubled in 5 years. This represents a growth of 100% in 5 years, so, dividing 100% by 5, we find the growth rate to be 20% per year." Is the statement correct?

Answer 1

The growth rate of Sawyer Corporation's sales from 2010 to 2015 is 100%, but the compound annual growth rate (CAGR) is approximately 14.87% per year, not the simple 20% per year as incorrectly suggested in the statement.

Step-by-step explanation:

To calculate the growth rate of Sawyer Corporation's sales from 2010 to 2015, we compare the increase in sales to the original amount in 2010. Since sales increased from $3 million to $6 million, the growth rate is calculated as ($6 million - $3 million) / $3 million = 1 or 100% over the 5-year period. However, this percent represents the total growth over 5 years, not the annual growth rate.

To find the compound annual growth rate (CAGR), we use the formula:

CAGR = (Ending Value/Beginning Value)^(1/Number of Years) - 1

Here, CAGR = ($6 million / $3 million)^(1/5) - 1 Approximately = 0.1487 or 14.87% per year.

The statement that calculates a straight division of 100%/5 is incorrect because it assumes simple, not compound growth. Instead, the compound rate we've calculated shows that the sales grew by approximately 14.87% per year over the 5 years.