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 $832,200 per year. The present annual sales volume (at the $91 selling price) is 25,900 units.

Required:

1. What is the present yearly 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-a. 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

Solution

1. Current sales= 25900*91=2356900

Variable cost= 25900*61=1579900

Fixed cost= 832200

Operating income = Sales- Variable cost- fixed cost

= 2356900-1579900-832200= -55200 (Loss)

2. Sales price /unit= 91

Variable cost per unit= 61

Contribution per unit= 91-61

=30

Break even point in unit sales = Fixed cost/Contribution=832200/30

=27740

Break even in dollar sales = Break even point in unit sales * selling price=27740*91

=2524340

3. The calculation for maximum profit is given below

Units sold (a)	Unit selling price (b)	Unit Var cost (c)	Unit contribution d=b-c	Total contibution tc=a*d	Fixed cost (fc)	Net income        = tc-fc	Break even pt = fc/d
25900	91	61	30	777000	832200	-55200	27740
30900	89	61	28	865200	832200	33000	29721
35900	87	61	26	933400	832200	101200	32008
40900	85	61	24	981600	832200	149400	34675
45900	83	61	22	1009800	832200	177600	37827
50900	81	61	20	1018000	832200	185800	41610
55900	79	61	18	1006200	832200	174000	46233
60900	77	61	16	974400	832200	142200	52013
65900	75	61	14	922600	832200	90400	59443
70900	73	61	12	850800	832200	18600	69350
75900	71	61	10	759000	832200	-73200	83220
80900	69	61	8	647200	832200	-185000	104025
85900	67	61	6	515400	832200	-316800	138700
90900	65	61	4	363600	832200	-468600	208050
95900	63	61	2	191800	832200	-640400	416100
100900	61	61	0	0	832200	-832200	#DIV/0!

Thus maximum profit can be 185800 at a sleeping price of 81 and 50900 units

4. As seen in the above table the break-even point will be 41610 units

and the dollar sales will be = Break-even point* selling price

=41610*81

=3370410

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