Chapter 3, Problem 49P

a.

To determine

Compute the volume in units and the dollar sales level necessary to maintain the present profit level of Company S; assuming that the maximum price increase is implemented.

Answer to Problem 49P

The target volume is 78,413 and target dollar sales are $5,175,258 at the current level of profit.

Explanation of Solution

Target volume: the level of sales which need to be achieved during a particular period of time is termed as target volume.

Target profit: the amount of profit which needs to be achieved during a particular period of time on a particular level of sales is termed as target profit.

Compute the volume in units and the dollar sales level necessary to maintain the present profit level of Company S; assuming that the maximum price increase is implemented:

$\begin{array}{c}\text{Sales}\text{=}\text{Target}\text{volume}\text{×}\text{Sales}\text{price}\text{(unit)}\\ \text{=}78,413\times \$66\\ =\$5,175,258\end{array}$

Compute the target volume at the current level of profit:

$\begin{array}{c}\text{Target}\text{volume}\text{=}\frac{\text{Fixed}\text{cost}\text{(3)}\text{+}\text{}\text{Desrised}\text{profit}\text{(1)}}{\text{Contribution}\text{margin}\text{(5)}}\\ =\frac{\$1,470,000+\$1,000,000}{\$31.5}\\ =78,413\text{units}\end{array}$

Thus, the target volume is 78,413 and target dollar sales are $5,175,258 at the current level of profit.

Working note 1:

Compute the current level of profit:

$\begin{array}{c}\text{Profit}\text{=}\text{Total}\text{revenue}-\text{Total}\text{costs}\\ \text{=}\text{Sales}\text{(unit)}\times \text{Sales}\text{price}\text{(unit)}-\text{V}a\text{riable}\text{costs}\text{+}\text{Fixed}\text{cost}\\ \text{=}\text{Sales}\text{(unit)}\times \text{Sales}\text{price}\text{(unit)}-[(\text{Sales}\text{(unit)}\text{×}\text{Variable}\text{cost}\text{(unit))+}\text{Fixed}\text{cost]}\\ \text{=}8\text{0,000}\times \text{\$60}-[(80,000\times \$30)+\$1,400,000]\\ =\$1,000,000\end{array}$

Working note 2:

Compute the revised variable cost:

Sales price is expected to increase by not more than 10%.

$\begin{array}{c}\text{Revised}\text{sales}\text{=}\text{Sales}\text{+}\text{}\text{Change}\%\\ =\$60+(\$60\times 10\%)\\ =\$66\end{array}$

Working note 3:

Compute the revised fixed cost:

Fixed cost is expected to increase by 5%.

$\begin{array}{c}\text{Revised}\text{fixed}\text{cost}\text{=}\text{Fixed}\text{cost}\text{+}\text{}\text{Change}\%\\ =\$1,400,000+(\$1,400,000\times 5\%)\\ =\$1,470,000\end{array}$

Compute the revised variable cost:

Total variable cost is $30.

Distribution of variable cost:

Expense	Ratio	Amount
Labor costs	50%	15
Material costs	25%	7.5
Variable overhead costs	25%	7.5
Total variable cost		30

Table: (1)

Variable cost overhead is not given in the question so it is assumed that it is calculated by subtracting the labor costs (50%) and material costs (25%) from the total variable cost (100%).

Working note 4:

Compute the revised variable cost:

Variable cost is raised by the following percentage:

Expense	Amount	Change %	Revised amount
Labor costs	15	15%	17.25
Material costs	7.5	10%	8.25
Variable overhead costs	7.5	20%	9
Total revised variable cost			34.5

Table: (2)

Working note 5:

Compute the contribution margin:

Particulars	Amount
Sales (unit) (2)	$66
Less: Variable cost (unit) (4)	$34.5
Contribution	$31.5

Table: (3)

b.

To determine

Compute the volume of sales and the dollar sales level necessary to provide the 6 per cent increase in profits of Company S; assuming that the maximum price increase is implemented.

Answer to Problem 49P

The necessary volume of sales is 80,318 units and the dollar sales level is $5,300,988 required to provide the 6 per cent increase in profits of Company S; assuming that the maximum price increase is implemented.

Explanation of Solution

Target volume: the level of sales which need to be achieved during a particular period of time is termed as target volume.

Target profit: the amount of profit which needs to be achieved during a particular period of time on a particular level of sales is termed as target profit.

Compute the volume of sales and the dollar sales level necessary to provide the 6 per cent increase in profits of Company S; assuming that the maximum price increase is implemented:

$\begin{array}{c}\text{Sales}\text{=}\text{Target}\text{volume}\text{(6)}\text{×}\text{Sales}\text{price}\text{(unit)}\\ \text{=}80,318\times \$66\\ =\$5,300,988\end{array}$

Working note 6:

Compute the target volume to provide the 6 per cent increase in profit of Company S:

$\begin{array}{c}\text{Target}\text{volume}\text{=}\frac{\text{Fixed}\text{cost}\text{(3)}\text{+}\text{}\text{Desrised}\text{profit}\text{(7)}}{\text{Contribution}\text{margin}\text{(5)}}\\ =\frac{\$1,470,000+\$1,060,000}{\$31.5}\\ =80,318\text{units}\end{array}$

Thus, the target volume is 80,318 and target dollar sales are $5,300,988 at the current level of profit

Working note 7:

Compute the desired profit:

$\begin{array}{c}\text{Desired}\text{profit}\text{=}\text{Present}\text{level}\text{profit}\text{+}\text{Change\%}\\ \text{=}\$1,000,000+(1,000,000\times 6\%)\\ =\$1,060,000\end{array}$

c.

To determine

Compute the price increase required to attain the 6 per cent increase in profit when the volumes of sales were to remain at 80,000 units.

Answer to Problem 49P

The price decrease required to attain the 6 per cent increase in profit when the volumes of sales were to remain at 80,000 units is $6.125 which is 10.2%

Explanation of Solution

Compute the price increase required to attain the 6 per cent increase in profit when the volumes of sales were to remain at 80,000 units:

$\begin{array}{c}\text{Price}\text{increase}\text{=}\text{Current}\text{price}\text{(8)}-\text{Original}\text{price}\\ \text{=}\$66.125-\$60\\ =\$6.125\end{array}$

Thus, the price should be increased by $6.125 to attain a 6% increase in profit.

Working note 8:

Let

Sales price: P

Put the values in the profit equation:

$\begin{array}{c}\text{Profit}\text{=}\text{Total}\text{revenue}-\text{Total}\text{costs}\\ \$1,060,000\text{=}\text{Sales}\text{(unit)}\times \text{Sales}\text{price}\text{(unit)}\\ -[(\text{Sales}\text{(unit)}\text{×}\text{Variable}\text{cost}\text{(unit))+}\text{Fixed}\text{cost]}\\ \text{\$1,060,000}\text{=}8\text{0,000}\times \text{P}-[(80,000\times \$34.5)-\$1,470,000\\ 8\text{0,000}\times \text{P}\text{=}\text{\$1,060,000}+\$1,470,000+(80,000\times \$34.5)\end{array}$

Thus,

$\begin{array}{c}\text{\$5,290,000}\text{=}\text{80,000}\times \text{P}\\ \text{P}\text{=}\frac{\$5,290,000}{80,000}\\ \text{P}\text{=}\$\text{66}\text{.125}\end{array}$