Question

Minden Company introduced a new product last year for which it is trying to find an optimal selling price. Marketing studies suggest that the company can increase sales by 5,000 units for each $2 reduction in the selling price. The company’s present selling price is $98 per unit, and variable expenses are $68 per unit. Fixed expenses are $832,800 per year. The present annual sales volume (at the $98 selling price) is 25,200 units.

Required:

1. What is the present yearly net operating income or loss?

2. What is the present break-even point in unit sales and in dollar sales?

3. Assuming that the marketing studies are correct, what is the maximum annual profit that the company can earn? At how many units and at what selling price per unit would the company generate this profit?

4. What would be the break-even point in unit sales and in dollar sales using the selling price you determined in (3) above (e.g., the selling price at the level of maximum profits)?

Answer 1

(1) -- What is the present yearly net operating income or loss?

Answer -

	Particulars	Explanation	Amount ($)
I.	Sales	25200 units * $98	2469600
II.	Variable expenses	25200 units * $68	1713600
III.	Contribution margin	I - II	756000
IV.	Fixed expenses	Given in question	832800
Net operating loss		III - IV	(76800)

.

(2) -- What is the present break-even point in unit sales and in dollar sales?

Answer -

	Particulars	Explanation
I.	Break-even point in unit sales	Fixed expenses / Unit contribution margin = $832800 / ($98 - $68)	27760 units
II.	Break-even point in dollar sales	Break-even point in unit * Selling price = 27760 units * $98	$2720480

.

(3) -- Assuming that the marketing studies are correct, what is the maximum annual profit that the company can earn? At how many units and at what selling price per unit would the company generate this profit?

Answer -

	Particulars	Explanation
I.	Maximum profit	Refer working note - (1)	$171200
II.	Number of units	Refer working note - (1)	50200 units
III.	Selling price per unit	Refer working note - (1)	$88

# Working note - (1) -

Unit Selling Price ($)	Unit Variable Expense ($)	Unit Contribution Margin ($)	Volume (Units)	Total Contribution Margin ($)	Fixed Expenses ($)	Net Operating Income (Loss) ($)
98 [Given in question]	68 [Given in question]	30 [98 - 68]	25200 [Given in question]	756000 [25200 * $30]	832800 [Given in question]	(76800) [756000 - 832800]
96 [98 - 2]	68 [Given in question]	28 [96 - 68]	30200 [25200 + 5000]	845600 [30200 * $28]	832800 [Given in question]	12800 [845600 - 832800]
94 [96 - 2]	68 [Given in question]	26 [94 - 68]	35200 [30200 + 5000]	915200 [35200 * $26]	832800 [Given in question]	82400 [915200 - 832800]
92 [94 - 2]	68 [Given in question]	24 [92 - 68]	40200 [35200 + 5000]	964800 [40200 * $24]	832800 [Given in question]	132000 [964800 - 832800]
90 [92 - 2]	68 [Given in question]	22 [90 - 68]	45200 [40200 + 5000]	994400 [45200 * $22]	832800 [Given in question]	161600 [994400 - 832800]
88 [90 - 2]	68 [Given in question]	20 [88 - 68]	50200 [45200 + 5000]	1004000 [50200 * $20]	832800 [Given in question]	171200 [1004000 - 832800]
86 [88 - 2]	68 [Given in question]	18 [86 - 68]	55200 [50200 + 5000]	993600 [55200 * $18]	832800 [Given in question]	160800 [993600 - 832800]

The maximum profit is $171200. This level of profit can be earned by selling 50200 units at a price of $88 per unit.

.

(4) -- What would be the break-even point in unit sales and in dollar sales using the selling price you determined in (3) above (e.g., the selling price at the level of maximum profits)?

Answer -

	Particulars	Explanation
I.	Break-even point in unit sales	Fixed expenses / Unit contribution margin = $832800 / ($88 - $68)	41640 units
II.	Break-even point in dollar sales	Break-even point in unit * Selling price = 41640 units * $88	$3664320