Chapter 3, Problem 24QP

EFN and Internal Growth Redo Problem 21 using sale growth rates of 15 and 25 percent in addition to 20 percent. Illustrate graphically the relationship between EFN and the growth rate, and use this graph to determine the relationship between them.

Summary Introduction

To determine: The relationship between external fund needed and the internal growth rate of the firm through graph using sales growth rate of 15%, 20% and 25%.

External Funds:

External funds refers to the funds that are been provided to the business or company from outside. These funds could be short term that is for the period of less than 1 year or long term that is for the period of more than 1 year which is decided on the basis of the need of the funds.

Explanation of Solution

Given,

Percentage change in sales is 15%,25%,

Total projected sales are $865,375,$940,625.

Total assets are $483,851.

Accounts payables are $58,140.

Dividend payout percentage is $\frac{\$27,331}{\$91,104}=30\%$

Profit margin is $\frac{\$91,104}{\$752,500}=12.11\%$.

The formula to calculate external funds to be needed is,

$\text{External Funds Needed}={\text{A}}_0\times \frac{\Delta \text{S}}{{\text{S}}_0}-{\text{L}}_0\times \frac{\Delta \text{S}}{{\text{S}}_0}-{\text{S}}_1\times \text{PM}\times (1-\text{d})$

Where,

• ${\text{A}}_0$ is current value of assets.
• ${\text{L}}_0$ is current value of liabilities.
• $\frac{\Delta \text{S}}{{\text{S}}_0}$ is the percentage increase in sales that is change in sales divided by current sales.
• ${\text{S}}_1$ is the projected sales.
• $\text{PM}$ is the profit margin.
• $\text{d}$ is the dividend payout percentage.

Substitute $483,851 for ${\text{A}}_0$, $58,140 for ${\text{L}}_0$, $\frac{15}{100}$ for $\frac{\Delta \text{S}}{{\text{S}}_0}$, 12.11% for PM, $865,375 for ${\text{S}}_1$ and 30% for d in the above formula to calculate EFN at sales growth of 15%.

$\begin{array}{c}\text{External Funds Needed}=\left[\begin{array}{l}\left(\$483,851\times \frac{15}{100}\right)-\left(\$58,140\times \frac{15}{100}\right)\\ -\left(\$865,375\times 12.11\%\times (1-30\%)\right)\end{array}\right]\\ =\$72,577.65-\$8,721-\$73,357.84\\ =-\$9,501.19\end{array}$

The external funds needed at sales growth of 15% are $-\$9,501.19$.

Substitute $483,851 for ${\text{A}}_0$, $58,140 for ${\text{L}}_0$, $\frac{20}{100}$ for $\frac{\Delta \text{S}}{{\text{S}}_0}$, 12.11% for PM, $903,000 for ${\text{S}}_1$ and 30% for d in the above formula to calculate EFN at sales growth of 20%.

$\begin{array}{c}\text{External Funds Needed}=\left[\begin{array}{l}\left(\$483,851\times \frac{20}{100}\right)-\left(\$58,140\times \frac{20}{100}\right)\\ -\left(\$903,000\times 12.11\%\times (1-30\%)\right)\end{array}\right]\\ =\$96,770-\$11,628-\$76,547\\ =\$8,595\end{array}$

The external funds needed at sales growth of 20% are $8,595.

Substitute $483,851 for ${\text{A}}_0$, $58,140 for ${\text{L}}_0$, $\frac{25}{100}$ for $\frac{\Delta \text{S}}{{\text{S}}_0}$, 12.11% for PM, $940,625 for ${\text{S}}_1$ and 30% for d in the above formula to calculate EFN at sales growth of 25%.

$\begin{array}{c}\text{External Funds Needed}=\left[\begin{array}{l}\left(\$483,851\times \frac{25}{100}\right)-\left(\$58,140\times \frac{25}{100}\right)\\ -\left(\$940,625\times 12.11\%\times (1-30\%)\right)\end{array}\right]\\ =\$120,962.75-\$14,535-\$79,736.78\\ =\$26,690.97\end{array}$

The external funds needed at sales growth of 25% are $26,690.97.

The formula to calculate internal growth rate is,

$\text{Internal Growth Rate}=\frac{\text{Net Income}}{\text{Total Assets}}\times 100$

Substitute $\left(\$865,375\times 12.11\%\right)=\$104,796.91$ for net income and $\left(\$483,851\times 115/100\right)=\$556,428.65$ for total assets to calculate internal growth rate at sales growth of 15% in the above formula.

$\begin{array}{c}\text{Internal Growth Rate}=\frac{\$104,796.91}{\$556,428.65}\times 100\\ =18.83\%\end{array}$

The internal growth rate at sales growth of 15% is 18.83%.

Substitute $\left(\$903,000\times 12.11\%\right)=\$109,353.3$ for net income and $\left(\$483,851\times 120/100\right)=\$580,621.2$ for total assets to calculate internal growth rate at sales growth of 15% in the above formula.

$\begin{array}{c}\text{Internal Growth Rate}=\frac{\$109,353.3}{\$580,621.2}\times 100\\ =18.83\%\end{array}$

The internal growth rate at sales growth of 20% is 18.83%.

Substitute $\left(\$940,625\times 12.11\%\right)=\$113,909.69$ for net income and $\left(\$483,851\times 125/100\right)=\$604,813.75$ for total assets to calculate internal growth rate at sales growth of 15% in the above formula.

$\begin{array}{c}\text{Internal Growth Rate}=\frac{\$113,909.69}{\$604,813.75}\times 100\\ =18.83\%\end{array}$

The internal growth rate at sales growth of 25% is 18.83%.

The relationship between external fund needed and internal growth rate is,

Fig.1

The internal growth is constant at 18.83% while the external fund required is increasing with increase in sales growth rate.

• The figure shows that the external fund needed is increasing with the increase in the sales growth rate while the internal growth rate is same irrespective of the sales growth rates.
• In the above figure it can be seen that before the internal growth rate the company is able to have additional funds but after achieving its internal growth, every increase in sales will require more additional funds.

Conclusion

Thus, the internal growth is constant at 18.83% while the external fund required is increasing with increase in sales growth rate.