A firm produces three products in a repetitive process facility. Product A sells for $60; its variable costs are $20. Product B sells for $200; its variable costs are $80. Product C sells for $25; its variable costs are $15. The firm has annual fixed costs of $320,000. Last year, the firm sold 1000 units of A, 2000 units of B, and 10,000 units of C. Calculate the break-even point of the firm. The firm has some idle capacity at these volumes, and chooses to cut the selling price of A from $60 to $45, believing that its sales volume will rise from 1000 units to 2500 units. What is the revised break-even point?

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sumielizabath george · Accepted Answer

Final Answer :  Calculations for the original version of this problem are:  Selling   Variable   Percent of   Weighted   Product   price P   cost V  V / P 1 − V / P  Sales   sales   contrib  A $ 60 $ 20 . 333 . 667 $ 60 , 000 . 0845 . 0564 B $ 200 $ 80 400 . 600 $ 400 , 000 . 5634 . 3380 C $ 25 $ 15 . 600 400 $ 250 , 000 . 3521 1408 $ 710 , 000 1.0000 0.5352 \begin{array}{|l|r|r|r|r|r|r|r|}\hline & 	ext { Selling }  &  	ext { Variable } & & & &  	ext { Percent of }  & 	ext { Weighted }\	ext { Product } & 	ext { price P }  &  	ext { cost V }  & \mathrm{V} / \mathrm{P}  &  1-\mathrm{V} / \mathrm{P}  &  	ext { Sales } & 	ext { sales } & 	ext { contrib }\\hline \mathrm{A}  &  \$ 60  &  \$ 20  &  .333  &  .667  &  \$ 60,000  &  .0845  &  .0564 \\hline \mathrm{B}  &  \$ 200  &  \$ 80  &  400  &  .600  &  \$ 400,000  &  .5634  &  .3380 \\hline \mathrm{C}  &  \$ 25  &  \$ 15  &  .600  &  400  &  \$ 250,000  &  .3521  &  1408 \\hline  &   &   &   & &  \$ 710,000  &  1.0000  &  0.5352 \\hline\end{array}  Product  A B C ​  Selling   price P  $60 $200 $25 ​  Variable   cost V  $20 $80 $15 ​ V / P .333 400 .600 ​ 1 − V / P .667 .600 400 ​  Sales  $60 , 000 $400 , 000 $250 , 000 $710 , 000 ​  Percent of   sales  .0845 .5634 .3521 1.0000 ​  Weighted   contrib  .0564 .3380 1408 0.5352 ​ ​   The original break-even for this firm was $320,000 / .5352 = $597,907. This is a calculator-based result; Excel reports $597,895.When the price of A is reduced, the revised calculations are:  Selling   Variable   Percent of   Weighted   Product   price P   cost V  V / P 1 − V / P  Sales   sales   contrib  A $ 45 $ 20 444 556 $ 112 , 500 . 1475 . 0820 B $ 200 $ 80 400 . 600 $ 400 , 000 . 5246 . 3149 C $ 25 $ 15 . 600 400 $ 250 , 000 . 3279 131 $ 762 , 500 1.0000 0.5280 \begin{array}{|l|r|r|r|r|r|r|r|}\hline & 	ext { Selling }  &  	ext { Variable } & & & &  	ext { Percent of }  & 	ext { Weighted }\	ext { Product } & 	ext { price P }  &  	ext { cost V }  & \mathrm{V} / \mathrm{P}  &  1-\mathrm{V} / \mathrm{P}  &  	ext { Sales } & 	ext { sales } & 	ext { contrib }\\hline \mathrm{A}  &  \$ 45  &  \$ 20  &  444  &  556  &  \$ 112,500  &  .1475  &  .0820 \\hline \mathrm{B}  &  \$ 200  &  \$ 80  &  400  &  .600  &  \$ 400,000  &  .5246  &  .3149 \\hline \mathrm{C}  &  \$ 25  &  \$ 15  &  .600  &  400  &  \$ 250,000  &  .3279  &  131 \\hline  &   &   &   &   &  \$ 762,500  &  1.0000  &  0.5280 \\hline\end{array}  Product  A B C ​  Selling   price P  $45 $200 $25 ​  Variable   cost V  $20 $80 $15 ​ V / P 444 400 .600 ​ 1 − V / P 556 .600 400 ​  Sales  $112 , 500 $400 , 000 $250 , 000 $762 , 500 ​  Percent of   sales  .1475 .5246 .3279 1.0000 ​  Weighted   contrib  .0820 .3149 131 0.5280 ​ ​   The firm's breakeven point has increased to $320,000 / .5280 = $606,061. (Calculator-based; Excel reports $606,211).

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