A firm's sales rise from 100 to 150 units (+50%) in one year and fall to 120 (−20%) the next. What are the average annual growth rate and the CAGR? (Take $\sqrt{1.2} = 1.0954$ .)

Average 15%, CAGR 15%Correct answerYour answerAverage 10%, CAGR about 9.54%Correct answerYour answerAverage 15%, CAGR 10%Correct answerYour answerAverage 15%, CAGR about 9.54%Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Average growth $= \frac{50\% + (-20\%)}{2} = 15\%$ .
CAGR $= \left(\frac{120}{100}\right)^{1/2} - 1 = 1.0954 - 1 \approx 9.54\%$ : the steady rate that actually gets from 100 to 120.

Worth noting

The simple average overstates growth: 15% a year would take 100 to over 132, not 120.

Concept: CAGR against the average growth rate
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsRate of return and CAGR

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Ten questions from EMI, CAGR & Depreciation, at your own pace.

A firm's sales rise from 100 to 150 units (+50%) in one year and fall to 120 (−20%) the next. What are the average annual growth rate and the CAGR? (Take 1.2=1.0954\sqrt{1.2} = 1.09541.2​=1.0954.)

Explanation

A firm's sales rise from 100 to 150 units (+50%) in one year and fall to 120 (−20%) the next. What are the average annual growth rate and the CAGR? (Take $\sqrt{1.2} = 1.0954$ .)