Question

A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A and B, have been identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $36,000 for A and $31,000 for B; variable costs per unit would be $8 for A and $11 for B; and revenue per unit would be $16.

    

a.	Determine each alternative’s break-even point in units. (Round your answer to the nearest whole amount.)

    

QBEP,A	units
QBEP,B	units

   

b.	At what volume of output would the two alternatives yield the same profit? (Round your answer to the nearest whole amount.)

    

Profit

units

   

c.	If expected annual demand is 11,000 units, which alternative would yield the higher profit?

    

Higher profit

(Click to select)BA

Answer 1

a	The break even quantity for Machine A
Qbep	FC /Contribution Per unit
	$36000/($16-$8)
	4500 units
	The break even quantity for Machine B
Qbep	FC /Contribution Per unit
	$31000/($16-$11)
	6200 units
b	The contribution per unit
	Contribution per unit	=	SP per unit-VC per unit
	Therefore the qty when the profit of both the machines will be the same would be
	Q(R-Va)-Fca =	Q(R-Vb)-Fcb
	Q=	(Fca-Fcb)/(R-Va)-(R-Vb)
	Where
	Fcx	Fixed Cost for Machine X
	Vx	Variable cost for Machine x
	R	Revenue per unit
	Q=	$36000-$31000/($16-$8)-($16-$11)
		$5000/$8-$5
		$5000/$3
		1667
	The volume at which the profits would be the same using either machine would be 1667 units
c	If the expected volume is 11000 units then the profit by each machine would be
	Profit	=	Qty * Contribution -F.C
	Profit Machine A	=	11000*$8-$36000
		=	$88000-$36000
		=	$52,000
	Profit Machine B	=	Qty * Contribution -F.C
		=	11000*$5-$31000
		=	$55000-$31000
		=	$24,000
	Hence when the expected annual demand is 11000 units alternative A would yield higher profit.