Question

Annual revenue for Corning Supplies grew by 5.5% in 2007; 1.1% in 2008; -3.5% in 2009; -1.1% in 2010; and 1.8% in 2011.

What is the mean growth annual rate over this period? Round your answer to four decimal places. Do not round intermediate calculations.

Answer 1

The objective is to compute the mean growth annual rate over the given period. Compute the geometric mean of the growth factors to determine the mean growth rate over some period of time.

The growth factor for each period is computed as

Growth Factor \(=1+.01 \times(\) percentage period return \()\)

The growth factor for the year 2007 is,

$$ \begin{aligned} G F_{2007} &=1+0.01(5.5) \\ &=1+0.055 \\ &=1.055 \end{aligned} $$

The growth factor for the year 2008 is,

$$ \begin{aligned} G F_{2008} &=1+0.01(1.1) \\ &=1+0.011 \\ &=1.011 \end{aligned} $$

The growth factor for the year 2009 is,

$$ G F_{2009}=1+0.01(-3.5) $$

$$ \begin{array}{l} =1-0.035 \\ =0.965 \end{array} $$

The growth factor for the year 2010 is,

$$ \begin{aligned} G F_{2010} &=1+0.01(-1.1) \\ &=1-0.011 \\ &=0.989 \end{aligned} $$

The growth factor for the year 2011 is,

$$ G F_{2011}=1+0.01(1.8) $$

$$ \begin{array}{l} =1+0.018 \\ =1.018 \end{array} $$

The mean annual growth factor over the years \(2007-2011\) is computed as

$$ \begin{aligned} \bar{x}_{g} &=\sqrt[5]{\left(x_{1}\right)\left(x_{2}\right) \cdots\left(x_{5}\right)} \\ &=\sqrt[5]{(1.055)(1.011)(0.965)(0.989)(1.018)} \\ &=\sqrt[5]{1.036275} \\ &=1.007152 \end{aligned} $$

Hence, the mean annual growth rate over the years \(2007-2011\) is,

$$ \begin{aligned} \text { Mean annual growth rate } &=\left(\bar{x}_{g}-1\right) \times 100 \% \\ &=(1.007152-1) \times 100 \% \\ &=0.007152 \times 100 \% \\ &=0.7152 \end{aligned} $$