Question

Phoenix-based CompTronics manufactures audio speakers for desktop computers. The following data relate to the period just ended when the company produced and sold 44,000 speaker sets: Sales $ 3,608,000 Variable costs 902,000 Fixed costs 2,250,000 Management is considering relocating its manufacturing facilities to northern Mexico to reduce costs. Variable costs are expected to average $18.00 per set; annual fixed costs are anticipated to be $1,988,000. (In the following requirements, ignore income taxes.) Required:

1. Calculate the company’s current income and determine the level of dollar sales needed to double that figure, assuming that manufacturing operations remain in the United States. (Do not round intermediate calculations and round your final answers to nearest whole dollar.)

2. Determine the break-even point in speaker sets if operations are shifted to Mexico. (Do not round intermediate calculations and round your final answer up to nearest whole number.)

3. Assume that management desires to achieve the Mexican break-even point; however, operations will remain in the United States.

a. If variable costs remain constant, by how much must fixed costs change? (Round your final answer to nearest whole dollar.)

b. If fixed costs remain constant, by how much must unit variable cost change? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

Working:

Sale price per unit = 3608000/44000 = $ 82

Variable cost per unit = 902000/44000 = $ 20.5

(1) Current income = Sales - Variable cost - Fixed cost

= 3608000 - 902000 - 2250000

= $ 456,000

Contribution per unit = Sale price per unit - Variable cost per unit

= 82 - 20.5

= $ 61.5

Desired profit = 2 x current income

= 2 x 456000

= $ 912,000

units to be sold to achieve that desired profit = ( Fixed cost + Desired profit)/ Contribution per unit

= (2250000 + 912000)/ 61.5

= 51414.63 i.e 51415 units approximately

Level of dollar sales needed to double the current income= units to be sold to achieve desired profit x sale price per unit

= 51415 x 82

= $ 4,216,030

(2) If operations are shifted to mexico

Sale price per unit = $ 82

Variable cost per unit = $ 18

Contribution per unit = Sale price per unit - Variable cost per unit = 82 - 18 = $ 64

Fixed cost = $ 1,988,000

Break even point = Fixed cost/ Contribution per unit

= 1988000/64

= 31062.5 i.e 31063 approximately  

(3) Management wants to achieve Mexican break even point while staying in US

(a) variable costs remain constant, by how much must fixed costs change:

Lets take fixed cost as X

Break even point of Mexico = Fixed cost / Contribution per unit

31063 = X / 64

X = 31063 x 64

Therefore X i.e fixed cost = $ 1,988,032

Current fixed cost = $ 2250000

Change in fixed cost (i.e reduction in fixed cost = Current fixed cost - Fixed cost at Mexican break even point at US

= 2250000 - 1988032

=$ 261,968

(b) If fixed costs remain constant, by how much must unit variable cost change

Let X be the required variable cost per unit

Break even point of Mexico = Fixed cost / Contribution per unit

31063 = 2250000/ (82 - X)

(82 - X) = 2250000/31063

(82 - X) = 72.43

X = 82 - 72.43

Therefore X (i.e Variable cost per unit) = $ 9.57

Current Variable cost = $ 20.5

Change in variable cost per unit(i.e required reduction) = 20.5 - 9.57 = $10.93 per unit