Chapter 3, Problem 13QP

External Funds Needed The Optical Scam Company has forecast a sales growth rate of 15 percent for next year. The current financial statements are shown here:

1. a. Using the equation from the chapter, calculate the external funds needed for next year.
2. b. Construct the firm’s pro forma balance sheet for next year and confirm the external funds needed that you calculated in part (a).
3. c. Calculate the sustainable growth rate for the company.
4. d. can the company eliminate the need for external funds by changing its dividend policy? What other options are available to the company to meet its growth objectives?

Summary Introduction

To calculate: The external funds that are essential for next year.

External Funds:

External funds refer to the funds that are being 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 based on the need of the funds.

Explanation of Solution

Solution:

Given,

Percentage change in sales is 15%.

Total projected sales are $29,187,000.

Total assets are $24,800,000.

Short term debts are $5,200,000.

Dividend payout percentage is $\frac{\$786,450}{\$2,247,000}=35\%$

Profit margin is $\frac{\$2,247,000}{\$25,380,000}=8.8\%$

The formula to calculate external funds to be needed is,

$\text{External funds needed}={\text{A}}_0\times \frac{\Delta \text{S}}{{\text{S}}_0}-{\text{L}}_0\times \frac{\Delta \text{S}}{{\text{S}}_0}-{\text{S}}_1\times \text{PM}\times \left(1-\text{d}\right)$

Where,

• A₀ is current value of assets.
• L₀ 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
• S₁  is the projected sales.
• PM is the profit margin.
• d is the dividend payout percentage

Substitute $24,800,000 for A₀, $5,200,000 for L₀, $\frac{15}{100}$ for $\frac{\Delta \text{S}}{{\text{S}}_0}$, 8.8% for PM, $29,187,000 for S₁ and 35% for d in the above formula.

$\begin{array}{c}\text{External funds needed}={\text{A}}_0\times \frac{\Delta \text{S}}{{\text{S}}_0}-{\text{L}}_0\times \frac{\Delta \text{S}}{{\text{S}}_0}-{\text{S}}_1\times \text{PM}\times \left(1-\text{d}\right)\\ =\$24,800,000\times \frac{15}{100}-\$5,200,000\times \frac{15}{100}\\ -\$29,187,000\times 8.8\%\times \left(1-35\%\right)\\ =\$3,720,000-\$780,000-\$1,669,496.4\\ =\$1,270,503.6\end{array}$

The external funds needed are$1,270,503.6.

Conclusion

Thus, the external funds needed are $1,270,503.6.

Summary Introduction

To construct: The per forma balance sheet for the company by using the projected sales figures.

Explanation of Solution

The construction of current balance sheet is,

O.S Company. Balance Sheet ($ in millions)
Assets	Amount
Current Assets $\left(\$7,200,000\times 115\%\right)$	8,280,000
Fixed Assets $\left(\$17,600,000\times 115\%\right)$	20,240,000
Total Assets	28,520,000
Liabilities and Owners’ Equity
Current Liabilities
Short Term Debts $\left(\$5,200,000\times 115\%\right)$	5,980,000
Long Term Debts	6,000,000
Owner’s Equity
Common Stock	3,200,000
Retained Earnings (working note)	12,069,496.4
Total liabilities and owners’ equity	27,249,496.4

Table (1)

The formula to calculate additional funds needed is,

$\text{External funds needed}=\text{Total assets}-\text{Total liabilities and equity}$

Substitute $28,520,000 for total assets and $27,249,496.4 for total liabilities and equity in the above formula.

$\begin{array}{c}\text{External funds needed}=\text{Total assets}-\text{Total liabilities and equity}\\ =\$28,520,000-\$27,249,496.4\\ =\$1,270,503.6\end{array}$

External funds needed are $1,270.503.6.

Working notes:

Calculation of net income is,

$\begin{array}{c}\text{Net income}=\text{Profit margin}\times \text{Projected sales}\\ =8.8\%\times \$29,187,000\\ =\$2,568,456\end{array}$

Calculation to the addition to the retained earnings is,

$\begin{array}{c}\text{Addition to the retained earnings}=\text{Net income}\times \left(1-\text{d}\right)\\ =\$2,568,456\times \left(1-35\%\right)\\ =\$1,669,496.4\end{array}$

Calculation of the accumulated retained earnings is,

$\begin{array}{c}\text{Accumulated retained earnings}=\left(\begin{array}{l}\text{Current year's retained earnings}\\ +\text{Addition to the retained earnings}\end{array}\right)\\ =\$10,400,000+\$1,669,496.4\\ =\$12,069,496.4\end{array}$

Conclusion

Thus, external funds needed are $1,270.503.6.

Summary Introduction

To calculate: The sustainable growth rate of the company.

Sustainable Growth Rate:

Sustainable growth rate refers to the maximum growth that a company can have without using external funds or increasing the financial leverage of the company.

Explanation of Solution

Given,

ROE of the company is 16.52% (working note).

Dividend payout ratio is 35%.

The formula to calculate sustainable growth rate is,

$\text{Sustainable growth rate}=\frac{\left(\text{ROE}\times \text{b}\right)}{\left[\left(\text{1}-\text{ROE}\right)\times \text{b}\right]}$

Where,

ROE refers to Return on Equity

d refers to the dividend payout ratio.

Substitute 16.52% for ROE and 35% for d in the above formula.

$\begin{array}{c}\text{Sustainable growth rate}=\frac{\left(\text{ROE}\times \text{b}\right)}{\left[\left(\text{1}-\text{ROE}\right)\times \text{b}\right]}\\ =\frac{16.52\%\times \left(1-35\%\right)}{1-16.52\%\left(1-35\%\right)}\\ =12.03\%\end{array}$

The sustainable growth of the company is 12.03%.

Conclusion

Thus, the sustainable growth of the company is 12.03%.

Summary Introduction

To explain: Whether the company can exclude the necessity for external funds by changing the dividend policy and other options that are obtainable to the firm to meet its growth objective.

Answer to Problem 13QP

No, the company cannot exclude the necessity for external funds by changing its dividend policy. The decrease in dividend payout ratio and increase in ROE are the other options that the company can use to meet its growth objective.

Explanation of Solution

• As the amount of dividend is $786,450, the requirement of additional or external funds is more than that the amount of dividend. Hence, the company cannot eliminate the need of external funds but it can surely reduce it by changing its dividend policy.
• As in the part (c), it can be seen that the sustainable growth rate of a company is dependent on the ROE of the company and the dividend payout ratio of the company.
• The increase in ROE or return of equity will also decrease the value in the denominator and increase the value in numerator, which will increase the value of overall growth rate.

Conclusion

Thus, the company cannot exclude the need for external funds by making a change in its dividend policy. The decrease in dividend payout ratio and increase in the ROE are the other options that the company can use to meet its growth objective.