Question

Break-Even Sales Under Present and Proposed Conditions

Darby Company, operating at full capacity, sold 121,500 units at a price of $117 per unit during the current year. Its income statement for the current year is as follows:

Sales			$14,215,500
Cost of goods sold			7,020,000
Gross profit			$7,195,500
Expenses:
Selling expenses	$3,510,000
Administrative expenses	3,510,000
Total expenses			7,020,000
Income from operations			$175,500

The division of costs between fixed and variable is as follows:

	Variable		Fixed
Cost of goods sold	70%		30%
Selling expenses	75%		25%
Administrative expenses	50%		50%

Management is considering a plant expansion program that will permit an increase of $1,287,000 in yearly sales. The expansion will increase fixed costs by $128,700, but will not affect the relationship between sales and variable costs.

5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $175,500 of income from operations that was earned in the current year. Enter the final answers rounded to the nearest whole number.
units

6. Determine the maximum income from operations possible with the expanded plant. Enter the final answer rounded to the nearest dollar.
$

7. If the proposal is accepted and sales remain at the current level, what will the income or loss from operations be for the following year? Enter the final answer rounded to the nearest dollar.
$ Income

Answer 1

Formula sheet

A	B	C	D	E	F	G	H
2
3		5)
4			Variable	Fixed
5		Cost of goods sold	0.7	0.3
6		Selling expenses	0.75	0.25
7		Administrative expenses	0.5	0.5
8
9			Total Cost	Variable Cost	Fixed Cost
10		Sales	14215500
11		Cost of goods sold	7020000	=$D11*D5	=$D11*E5
12		Gross profit	=D10-D11
13		Expenses:
14		Selling expenses	3510000	=$D14*D6	=$D14*E6
15		Administrative expenses	3510000	=$D15*D7	=$D15*E7
16		Total expenses	=D14+D15
17		Income from operations	=D12-D16
18
19
20		Sale	=D10
21		Variable Cost	=SUM(E11:E15)
22		Contribution margin	=D20-D21
23		Fixed Cost	=SUM(F11:F15)
24		Operating income	=D22-D23
25
26		Number of units sold in current year	121500
27
28		Sales Price	=D20/D26
29		Contribution margin per unit	=D22/D26
30
31		Calculation of number of units for target profit:
32
33		Required sales in units for a target profit is given by following formula:
34
35
36
37
38		New Fixed cost	128700
39		Contribution margin per unit	=D29
40		Fixed Cost	=D23+D38
41		Target Profit	=D24
42
43		Required Units to be sold	=(Fixed Costs + Target Profit) / Contribution margin per unit
44			=(D40+D41)/D39	=(D40+D41)/D39
45
46		Hence required units to be sold is	=ROUND(D44,0)
47
48		6)
49
50		Increase in Sales	1287000
51		Increase in Fixed cost	128700
52
53		Income statement can be prepared as below:
54
55		Sale	=D20+D50	=D20+D50
56		Variable Cost	=D55*(D21/D20)	=D55*(D21/D20)
57		Contribution margin	=D55-D56
58		Fixed Cost	=D23+D51	=D23+D51
59		Operating income	=D57-D58
60
61		Hence, maximum income from operations possible is	=D59
62
63		7)
64
65		Sale	=D20
66		Variable Cost	=D21
67		Contribution margin	=D65-D66
68		Fixed Cost	=D23+D51	=D23+D51
69		Operating income	=D67-D68
70
71		Hence income from operation if sales remains constant is	=D69
72