Chapter 3, Problem 43QP

Summary Introduction

To calculate: The sustainable growth rate, the number of additional borrowings, and the growth rate without any outside financing.

Introduction:

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

Answer to Problem 43QP

The sustainable growth rate and the additional borrowing of Company E are 13.61% and $9,117.35 respectively. The internal growth rate is 7.41%.

Explanation of Solution

Given information:

The sales of Company E are $275,000, net income is $19,000, dividends are $8,100, total debt is $67,000, and the total equity is $91,000.

Formula to compute the retention ratio:

$\text{Retention ratio}=1-b$

Compute the retention ratio:

$\begin{array}{c}\text{Retention ratio}=1-b\\ =1-\left(\frac{\$8,100}{\$19,000}\right)\\ =0.5737\end{array}$

Hence, the retention ratio is 0.5737.

Formula of DuPont identity to compute ROE (Return on equity):

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

Compute ROE (Return on equity):

$\begin{array}{c}\text{ROE}=\frac{\text{Net income}}{\text{Total equity}}\\ =\frac{\$19,000}{\$91,000}\\ =0.2088\text{or }20.88\%\end{array}$

Hence, the ROE is 20.88%.

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 maximum sustainable growth rate:

$\begin{array}{c}\text{Sustainable growth rate}=\frac{\text{ROE}\times b}{1-\text{ROE}\times b}\\ =\frac{0.2088\times 0.5737}{1-0.2088\times 0.5737}\\ =0.1361\text{ or 13}\text{.61}\%\end{array}$

Hence, the sustainable growth rate is 0.1361 or 13.61%.

Formula to compute the net total assets:

$\text{New total assets}=\left(1+\text{Sustainable growth rate}\right)\left(\text{Total assets}\right)$

Compute the net total assets

$\begin{array}{c}\text{New total assets}=\left(1+\text{Sustainable growth rate}\right)\left(\text{Total assets}\right)\\ =\left(1+0.1361\right)\left(\$67,000+91,000\right)\\ =\$179,500.62\end{array}$

Hence, the new total assets are $179,500.62.

Formula to compute the net total debt:

$\text{New total debt}=\left[\frac{\text{Total debt}}{\left(\text{Total debt}+\text{Total equity}\right)}\right]\left(\text{New total assets}\right)$

Compute the net total debt:

$\begin{array}{c}\text{New total debt}=\left[\frac{\text{Total debt}}{\left(\text{Total debt}+\text{Total equity}\right)}\right]\left(\text{New total assets}\right)\\ =\left[\frac{\$67,000}{\left(\$67,000+\$91,000\right)}\right]\left(\$179,500.62\right)\\ =\$76,117.35\end{array}$

Hence, the new total debt is $76,117.35.

Formula to compute the additional borrowings:

$\text{Additional borrowing}=\text{New total debt}-\text{Current total debt}$

Compute the additional borrowings:

$\begin{array}{c}\text{Additional borrowing}=\text{New total debt}-\text{Current total debt}\\ =\$76,117.35322-\$67,000\\ =\$9,117.35\end{array}$

Hence, the additional borrowing is $9,117.35.

Formula to compute the ROA (Return on assets):

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

Compute the ROA (Return on assets):

$\begin{array}{c}\text{ROA}=\frac{\text{Net income}}{\text{Total assets}}\\ =\frac{\$19,000}{\left(\$67,000+\$91,000\right)}\\ =0.1203\text{ or }12.03\%\end{array}$

Hence, the ROA is 12.03%.

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:

$\begin{array}{c}\text{Internal growth rate}=\left[\frac{\left(\text{ROA}\right)\left(b\right)}{1-\left(\text{ROA}\right)\left(b\right)}\right]\\ =\left[\frac{0.120253164\left(0.57368421\right)}{1-0.120253164\left(0.57368421\right)}\right]\\ =0.0741\text{ or 7}.41\%\end{array}$

Hence, the internal growth rate is 7.41%.