Question

A company has fixed costs of $900 and a per-unit contribution margin of $3. Which of the following statements is true? ______

A) Once the break-even point is reached; the company will increase income at the rate of $3 per unit.

B) Each unit "contributes" $3 toward covering the fixed costs of $900.

C) Each unit "contributes" $3 toward covering the fixed costs of $900 and once the break-even point is reached, the company will increase income at the rate of $3 per unit.

D) The firm will definitely lose money in this situation.

E) The situation described is not possible and there must be an error.

Answer 1

• The correct answer is Option ‘C’: Each unit "contributes" $3 toward covering the fixed costs of $900 and once the break-even point is reached, the company will increase income at the rate of $3 per unit.
• This is because, the Net Income is negative until the sales reaches break even level. Once the Break Even level is achieved, there are neither any loss nor income (which means that Net Income is $0). As the no. of units cross the break even level, the net income increases by contribution margin per unit as the fixed cost remains the same.
• This can be illustrated using the following example:

Sale price per unit $ 50
Variable cost per unit $ 47

Fixed Costs $ 900

Break Even units will be:

A	Sale price per unit	$                                           50.00
B	Variable cost per unit	$                                           47.00
C = A - B	Contribution margin per unit	$                                              3.00
D	Fixed Cost	$                                         900.00
E = D/C	Break Even Level of units	300

Now, lets take a look at Net Income at various level of output sold

Working	No. of units	150	250	300	301	350
A[calculated above]	Contribution margin per unit	$                                              3.00	$                             3.00	$                                                3.00	$                    3.00	$                     3.00
B = Units x A	Total Contribution margin	$                                         450.00	$                        750.00	$                                           900.00	$               903.00	$             1,050.00
C	Fixed Costs	$                                         900.00	$                        900.00	$                                           900.00	$               900.00	$                 900.00
D = B - C	Net Income (Loss)	$                                       (450.00)	$                      (150.00)	$                                                     -	$                    3.00	$                 150.00
E	Increase in Net Income		$                        300.00	$                                           150.00	$                    3.00	$                 147.00
F	Increase in Units		100	50	1	49
G = E/F	Increase in Income per unit		$                             3.00	$                                                3.00	$                    3.00	$                     3.00

---As you can see, 300 units is Break Even and the Net Income at that level is $ 0. As the unit become 301 units, Net Increase in Net Income is $ 3, which is equal to the Contribution margin per unit.