Chapter 8, Problem 69C

Keep or Drop a Division

Jan Shumard, president and general manager of Danbury Company, was concerned about the future of one of the company’s largest divisions. The division’s most recent quarterly income statement follows:

Jan is giving serious consideration to shutting down the division because this is the ninth consecutive quarter that it has shown a loss. To help him in his decision, the following additional information has been gathered:

• The division produces one product at a selling price of $100 to outside parties. The division sells 50% of its output to another division within the company for $83 per unit (full manufacturing cost plus 25%). The internal price is set by company policy. If the division is shut down, the user division will buy the part externally for $100 per unit.
• The fixed overhead assigned per unit is $20.
• There is no alternative use for the facilities if shut down. The facilities and equipment will be sold and the proceeds invested to produce an annuity of $100,000 per year. Of the fixed selling and administrative expenses, 30% represent allocated expenses from corporate headquarters. Variable selling expenses are $5 per unit sold for units sold externally. These expenses are avoided for internal sales. No variable administrative expenses are incurred.

Required:

1. 1. Prepare an income statement that more accurately reflects the division’s profit performance.
2. 2. Should the president shut down the division? What will be the effect on the company’s profits if the division is closed?

To determine

Make an income statement which shows the profit performance of the division.

Explanation of Solution

Income Statement:

The statement that shows revenue and expenses incurred over a period of time (usually one year) is called an income statement. It is used for external financial reporting as it helps the outsiders and investors in evaluating the firm’s financial health.

The following table represents the income statement of Company D:

Company D
Income Statement
	Amount ($)
Sales revenue	3,751,500
Less: Variable expenses1	2,004,900
Contribution margin	1,746,600
Less: Direct fixed expenses2	1,518,250
Divisional margin	228,350
Less: Common fixed expenses3	299,250
Operating income (loss)	(70,900)

Table (1)

The amount of operating loss for Company D is $70,900.

Working Notes:

1.

First, calculate the number of units:

$\begin{array}{c}\text{Number of units}=\frac{\text{Sales revenue}}{\left(\begin{array}{l}\text{Sales per unit to another division}+\\ \text{Purchase price if the part is purchased externally}\end{array}\right)}\\ =\frac{\$3,751,500}{\$83+\$100}\\ =\frac{\$3,751,500}{\$183}\\ =20,500\text{ units}\end{array}$

Hence, the number of units is 20,500 units.

Calculate variable cost per internal unit:

$\begin{array}{c}\text{Variable cost per internal unit}=\left(\frac{\text{Sale per unit to aother division}}{100\%+\text{Markup percentage}}\right)-\\ \text{Fixed overhead per unit}\\ =\left(\frac{\$83}{100\%+25\%}\right)-\$20\\ =\$66.4-\$20\\ =\$46.4\end{array}$

Hence, the variable cost per internal unit is $46.4.

Calculate the variable cost per external unit:

$\begin{array}{c}\text{Variable cost per external unit}=\left(\begin{array}{l}\text{Variable cost per internal unit}\\ +\text{Selling expense per unit}\end{array}\right)\\ =\$46.4+\$5\\ =\$51.4\end{array}$

Hence, the variable cost per external unit is $51.4.

Now, calculate the amount of variable cost:

$\begin{array}{c}\text{Variable cost}=\left(\text{Variable cost per internal unit}\times \text{Number of units}\right)+\\ \left(\text{Variable cost per external unit}\times \text{Number of units}\right)\\ =\left(\$46.4\times 20,500\text{ units}\right)+\left(\$51.4\times 20,500\text{ units}\right)\\ =\$951,200+\$1,053,700\\ =\$2,004,900\end{array}$

Hence, the amount of variable cost is $2,004,900.

2. First, calculate the fixed selling and administrative expenses in order to calculate direct fixed expenses:

$\begin{array}{c}\text{Fixed selling and administrative expenses}=\text{Selling and administrative expenses}-\\ \left(\begin{array}{l}\text{Variable selling expenses}\\ \times \text{Number of units}\end{array}\right)\\ =\$1,100,000-\left(\$5\times 20,500\text{ units}\right)\\ =\$1,100,000-\$102,500\\ =\$997,500\end{array}$

Hence, the amount of fixed selling and administrative expense is $997,500.

Calculate direct fixed selling and administrative expenses:

$\begin{array}{c}\text{Direct fixed selling and administrative expenses}=\left(\begin{array}{l}\text{Fixed selling and }\\ \text{administrative expenses}\times \\ \text{Non-allocated expenses}\end{array}\right)\\ =\$997,500\times \left(100\%-30\%\right)\\ =\$997,500\times 70\%\\ =\$698,250\end{array}$

Hence, the direct fixed selling and administrative expense is $698,250.

Calculate the number of units sold:

Let the number of units sold be x. The division sells 50% of its output to another division for $83 per unit. If the division shut down the part would be purchased externally at $100 per unit. Therefore, the equation is given below:

$\begin{array}{c}\left(50\%\times 83x\right)+\left(50\%\times 100x\right)=\$3,751,500\\ 50\%\times \left(83x+100x\right)=\$3,751,500\\ 183x=\frac{\$3,751,500}{50\%}\end{array}$

                                     $\begin{array}{c}183x=\$7,503,000\\ x=41,000\text{units}\end{array}$

Hence, the number of units is 41,000 units.

Calculate direct fixed overhead:

$\begin{array}{c}\text{Direct fixed overheads}=\text{Number of units sold}\times \text{Fixed overhead assigned}\\ =41,000\text{ units}\times \$20\\ =\$820,000\end{array}$

Hence, the direct fixed overhead is $820,000.

Now, calculate the amount of total direct fixed expenses:

$\begin{array}{c}\text{Total direct fixed expenses}=\left(\begin{array}{l}\text{Direct fixed selling and administrative expenses}\\ \text{+Direct fixed overheads}\end{array}\right)\\ =\$698,250+\$820,000\\ =\$1,518,250\end{array}$

Hence, the amount of total direct fixed expense is $1,518,250.

3. Calculation of common fixed expense:

$\begin{array}{c}\text{Common fixed expense}=\left(\begin{array}{c}\text{Fixed selling and administrative expenses}\\ \times \text{Allocated expense percentage}\end{array}\right)\\ =\$997,500\times 0.30\\ =\$299,250\end{array}$

Hence, the amount of common fixed expense is $299,250.

To determine

Describe whether the president should shut down the division. Also, determine the effect of profit, if the division is closed.

Explanation of Solution

The following table represents the appropriate decision regarding the division:

Costs	Alternatives
	Keep ($)	Drop ($)
Sales	3,751,500
Variable cost4	(2,004,900)	(2,050,000)
Direct fixed expenses	(1,518,250)
Annuity		100,000
Total	228,350	(1,950,000)

Table (2)

The relevant benefit to keep the division is $228,350 whereas, if the company drops the division, then the relevant benefit will be ($1,950,000). Therefore, the company should keep the division.

Working Note:

4. Calculation of variable cost if the company drops the division:

$\begin{array}{c}\text{Variable cost}=\text{Number of units}\times \text{Cost of part if it was purchased externally}\\ =20,500\text{ units}\times \$100\\ =\$2,050,000\end{array}$

Hence, the amount of variable cost if the company drops the division is $2,050,000.