Question

Sawyer Corporation's 2020 sales were $5 million. Its 2015 sales were $2.5 million. At what rate have sales been growing? Round your answer to two decimal places. % 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 annual growth rate of Sawyer Corporation's sales over 5 years from 2015 to 2020 is approximately 14.87%, calculated with the compound annual growth rate formula instead of a simple division by the number of years.

Step-by-step explanation:

The question pertains to calculating the growth rate of Sawyer Corporation's sales over a 5-year period (from 2015 to 2020). To determine the growth rate, we need to use the formula for percentage change, which is (Change in Quantity) / (Original Quantity) × 100. In this case, the Change in Quantity is $5 million - $2.5 million = $2.5 million, and the Original Quantity is $2.5 million. Therefore, the percentage change or growth rate is ($2.5 million / $2.5 million) × 100 = 100%. However, the growth rate per year is not simply 20% as one might erroneously conclude by dividing 100% by 5. Instead, the annual growth rate should be calculated using the compound annual growth rate (CAGR) formula, which is [(Ending Value / Beginning Value)^(1 / Number of Years)] - 1.

Using the formula, the CAGR is [(5/2.5)^(1/5)] - 1. After calculating, we find that the accurate annual growth rate is approximately 14.87%. This figure is more precise than the simplistic division by 5, which does not account for the compound nature of growth over multiple years.