Chapter 3, Problem 45QP

Internal and Sustainable Growth Rates. Best Buy reported the following numbers (in millions) for the years ending February 1, 2014, and January 31, 2015. What are the internal and sustainable growth rates? What are the internal and sustainable growth rates using ROE × b and (ROA × b) and the end of period equity (assets)? What are the growth rates if you use the beginning of period equity in this equation? Why aren’t the growth rates the same? What is your best estimate of the internal and sustainable growth rates?

	2014	2015
Net income		$ 1,233
Dividends		251
Total assets	$14,013	15,256
Total equity	3,986	4,995

Summary Introduction

To discuss: The internal growth rate and sustainable growth rate and calculate the rates, growth rate by using the starting of period equity, the reason for the similar growth rates and the best estimate the internal and sustainable growth rates.

Introduction:

The rate of internal growth is the highest growth rate which can be achieved without any kind of external financing. The rate of sustainable growth is the highest growth rate which can be achieved without external equity financing.

Answer to Problem 45QP

The ROA in the beginning is 8.80% and in the end is 8.08% respectively. The ROE in the beginning is 30.93% and the ROE in the end is 24.68%.

Explanation of Solution

Given information:

The net income of Company B for the year 2015 is $1,233. The dividend in the year 2015 is 251. The total assets for the year 2014 and 2015 are $14,013 and $15,256 respectively. The total equity for 2014 and 2015 are $3,986 and $4,995 respectively.

Formula to compute the ROA in the beginning:

${\text{ROA}}_{\text{Begin}}=\frac{\text{Net income}}{\text{Total assets}}$

Compute the ROA in the beginning:

$\begin{array}{c}{\text{ROA}}_{\text{Begin}}=\frac{\text{Net income}}{\text{Total assets in 2014}}\\ =\frac{\$1,233}{\$14,013}\\ =0.0880\text{ or 8}\text{.80\%}\end{array}$

Hence, the ROA in the beginning is 8.80%.

Compute the ROA in the end:

$\begin{array}{c}{\text{ROA}}_{\text{End}}=\frac{\text{Net income}}{\text{Total assets in 2015}}\\ =\frac{\$1,233}{\$15,256}\\ =0.0808\text{ or 8}\text{.08\%}\end{array}$

Hence, the ROA in the end is 8.08%.

Formula to compute the ROE using the starting period equity:

${\text{ROE}}_{\text{Begin}}=\frac{\text{Net income}}{\text{Total equity}}$

Compute the ROE using the starting period equity:

$\begin{array}{c}{\text{ROE}}_{\text{Begin}}=\frac{\text{Net income}}{\text{Total equity in 2014}}\\ =\frac{\$1,233}{\$3,986}\\ =0.3093\text{ or }30.93\%\end{array}$

Hence, the ROE in the beginning is 30.93%.

Compute the ROE using the end of period equity:

$\begin{array}{c}{\text{ROE}}_{\text{End}}=\frac{\text{Net income}}{\text{Total equity in 2015}}\\ =\frac{\$1,233}{\$4,995}\\ =0.2468\text{ or 24}.68\%\end{array}$

Hence, the ROE in the end is 24.68%.

Formula to compute the retention ratio:

$b=1-\frac{\text{Dividends}}{\text{Net income}}$

Compute the retention ratio:

$\begin{array}{c}b=1-\frac{\text{Dividends}}{\text{Net income}}\\ =1-\frac{\$251}{\$1,233}\\ =0.7964\text{ or }79.64\%\end{array}$

Hence, the retention ratio is 79.64%.

Formula to compute the internal growth rate:

$\text{Internal growth rate}=\left[\frac{\left(\text{ROA}\right)\left(b\right)}{1-\left(\text{ROA}\right)\left(b\right)}\right]$

Where,

ROA denotes the return on assets.

b denotes the retention or plowback ratio.

Calculate the internal growth rate:

$\begin{array}{c}\text{Internal growth rate}=\left[\frac{\left(\text{ROA}\right)\left(b\right)}{1-\left(\text{ROA}\right)\left(b\right)}\right]\\ =\left[\frac{0.0808\left(0.7964\right)}{1-0.0808\left(0.7964\right)}\right]\\ =0.0688\text{ or 6}\text{.88}\%\end{array}$

Hence, the internal growth rate is 6.88%.

Formula to calculate the sustainable growth rate:

$\text{Sustainable growth rate}=\frac{\text{ROE}\times b}{1-\text{ROE}\times b}$

Where,

ROE denotes the return on equity.

b denotes the retention or plowback ratio.

Compute the sustainable growth rate:

$\begin{array}{c}\text{Sustainable growth rate}=\frac{\text{ROE}\times b}{1-\text{ROE}\times b}\\ =\frac{0.2088\times 0.7964}{1-0.2088\times 0.5737}\\ =0.2447\text{ or 24}\text{.47}\%\end{array}$

Hence, the sustainable growth rate is 24.47%.

Formula to compute the internal growth rate using ROA at the end:

$\text{Internal growth rate}={\text{ROA}}_{\text{END}}\times b$

Compute the internal growth rate using ROA at the end:

$\begin{array}{c}\text{Internal growth rate}={\text{ROA}}_{\text{END}}\times b\\ =0.0808\times 0.7964\\ =0.0644\text{or 6}\text{.44\%}\end{array}$

Hence, the internal growth rate is 6.44%.

Formula to compute the sustainable growth rate using ROE at the end:

$\text{Sustainable growth rate}={\text{ROE}}_{\text{END}}\times b$

Compute the sustainable growth rate using ROE at the end:

$\begin{array}{c}\text{Sustainable growth rate}={\text{ROE}}_{\text{END}}\times b\\ =0.2468\times 0.7964\\ =0.1966\text{or }19.66\text{\%}\end{array}$

Hence, the sustainable growth rate is 19.66%.

Formula to compute the internal growth rate using ROA at the beginning:

$\text{Internal growth rate}={\text{ROA}}_{\text{Begin}}\times b$

Compute the internal growth rate using ROA at the beginning:

$\begin{array}{c}\text{Internal growth rate}={\text{ROA}}_{\text{Begin}}\times b\\ =0.0880\times 0.7964\\ =0.0701\text{or }7.\text{01\%}\end{array}$

Hence, the internal growth rate is 7.01%.

Formula to compute the sustainable growth rate using ROE at the beginning:

$\text{Sustainable growth rate}={\text{ROE}}_{\text{Begin}}\times b$

Compute the sustainable growth rate using ROE at the beginning:

$\begin{array}{c}\text{Sustainable growth rate}={\text{ROE}}_{\text{Begin}}\times b\\ =0.3093\times 0.7964\\ =0.2464\text{ or }24.64\text{\%}\end{array}$

Hence, the sustainable growth rate is 24.64%.