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 $91 per unit, and variable expenses are $61 per unit. Fixed expenses are $836,400 per year. The present annual sales volume (at the $91 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) Present yearly net operating income or loss = Sales - Variable costs - Fixed costs

Sales for the year = Annual Sales volume*Sale price per unit

= 25,200*$91 = $2,293,200

Variable costs = Annual Sales volume*Variable cost per unit

= 25,200*$61 = $1,537,200

Fixed costs = $836,400 per year

Present yearly net operating loss = $2,293,200 - $1,537,200 - $836,400 = ($80,400)

2) Break even units = Fixed cost/Contribution per unit

Contribution per unit = Sale price per unit - Variable cost per unit

= $91 - $61 = $30 per unit

Break even units = $836,400/$30 = 27,880 units

Break even point in dollars = Break even units*Sale price per unit

= 27,880 units*$91 per unit = $2,537,080

3) We need to analyze the every situation to find the maximum profit in this case which is shown as follows:- (Amount in $)

Sale Price (a)	Units Sold (b)	Variable cost (c)	Contribution (d = a-c)	Total contribution (e = d*b)	Fixed cost (f)	Annual Profit/(loss) (g = e-f)
91	25,200	61	30	756,000	836,400	(80,400)
89	30,200	61	28	845,600	836,400	9,200
87	35,200	61	26	915,200	836,400	78,800
85	40,200	61	24	964,800	836,400	128,400
83	45,200	61	22	994,400	836,400	158,000
81	50,200	61	20	1,004,000	836,400	167,600
79	55,200	61	18	993,600	836,400	157,200
77	60,200	61	16	963,200	836,400	126,800

As we can see in the above table that annual profit is maximum when units sold are 50,200 and Sale price is $81 per unit resulting in annual profit of $167,600.

4) Break even units = Fixed cost/Contribution per unit

Contribution per unit = Sale price per unit - Variable cost per unit

= $81 - $61 = $20 per unit

Break even units = $836,400/$20 = 41,820 units

Break even point in dollars = Break even units*Sale price per unit

= 41,820 units*$81 per unit = $3,387,420