how do you solve for the quantity break even when you are not given the price bu

Question

how do you solve for the quantity break even when you are not given the price but are given the variable cost and the fixed cost of the problem

QUIZ+6-F17.docx[Compatibility Mode). Word DESIGN PAGE LAYOUT REFERENCES MAILINGS REVIEW HOME INSERT VIEW Mason S 12 Font ParagraphrStyles The Dimmy Company has identified two methods of producing playing cards. One method involves using a machine having a fixed cost of $22,000 and variable costs of S1.10 per deck. The other method would use a less expensive machine having a fixed cost of S5,500, but it would require variable costs of S2.50 per deck. If the selling price per deck will be the same under each method, at what level of output would the two methods produce the same net operating income (EBIT)? Using information from problem 3, what must be quantity break even unit for each method? Using information from problem 5, if the quantity sold is larger than quantity break-even unit, which method will have larger increase in EBIT and why? What if the quantity sold is smaller than quantity break-even unit, which method will have a larger decrease in EBIT and why? ER ENGLISH (UNITED STATES, : 15 i OF1 210 woRDS 12:14 AM 1/28/2017 .

Explanation / Answer

The Dimmy Co. has identified 2 methods of producing cards .

now , we are caluculating the Quantity berak even and selling price per unit .

so that quantity break even =x ,   selling price per unit = y

1st method :

fixed cost = $22,000

Variable cost =$1.10 per deck

Quantity break even = fixed cost / (selling price per unit - variable cost per unit)

x = $22,000/(y-$1.10)

x(y-$1.10) = $22,000

xy-$1.10 x=$22,000 ---------eqaution 1

2nd method :

fixed cost = $5,500

Variable cost =$2.50 per deck

Quantity break even = fixed cost / (selling price per unit - variable cost per unit)

x = $5,500/(y-$2.50)

x(y-$2.50) = $5,500

xy-$2.50 x=$5,500 ---------eqaution 2

Solve (eqaution 1 - eqaution 2) :

xy - $1.10 x = $22,000

xy - $2.50 x = $5,500

- + -   

0+$1.40x = $16,500

x=16500/1.40

x=11,786 decks i.e., quantity break even =11,786 decks

Substitute X value in equation-1 :

xy - $1.10 x = $22,000

(11,786)y - $1.10 (11,786) = $22,000

11,786y - $12,965 =$22,000

11,786y=$34,965

y= $2.97 per deck i.e., selling price per unit = $2.97 per deck

1st method ($) 2nd method($)

Sales   (11,786*2.97) 35,004 35,004

Less: Variable cost (11,786*1.10)= 12,965 (11,786*2.50) = 29,465

Contribution 22,039 5,539

Less :Fixed cost 22,000 5,500

EBIT 39 39

2. Quantity break even for each method is 11,786 decks.

3. If the quantity sold is larger than Break even unit then 1st method produce larger EBIT than 2nd method because the increase in quantity will increase in variable cost where fixed cost is same so variable cost is less in 1st method than 2nd method.

1st method ($) 2nd method($)

Sales   (20,000*2.97) 59,400 59,400

Less: Variable cost (20,000*1.10)= 22,000    (20,000*2.50) = 50,000

Contribution 37,400 9,400

Less :Fixed cost    22,000       5,500

  EBIT    15,400    3,900

3. If the quantity sold is smaller than Break even unit then 1st method produce smaller EBIT than 2nd method because the decrease in quantity will decrease in variable cost but fixed cost is same so fixed cost is high in 1st method than 2nd method.

For example output is 10,000 decks

1st method ($) 2nd method($)

Sales   (10,000*2.97) 29,700 29,700

Less: Variable cost (10,000*1.10)= 11,000    (10,000*2.50) = 25,000

Contribution 18,700 4,700

Less :Fixed cost    22,000       5,500

  EBIT    3,300     800

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