Question

Lin Corporation has a single product whose selling price is $136 per unit and whose variable expense is $68 per unit. The company's monthly fixed expense is $32,400. Required: 1. Calculate the unit sales needed to attain a target profit of $5,000. (Do not round intermediate calculations.) 2. Calculate the dollar sales needed to attain a target profit of $8,400. (Round your intermediate calculations to the nearest whole number.) 1. Units sales to attain target profit 2. Dollar sales to attain target profit

Answer 1

1)

Calculation for unit sales to attain target profit of $ 5,000

= [Fixed costs + target profit ] / [selling price per unit - variable costs per unit ]

=[ $ 32,400 + $ 5,000] / [$ 136 - $ 68] = 550 units

Calculation for unit sales to attain target profit of $ 8,400

= [ $ 32,400 + $ 8,400] / [ $ 136 - $ 68] = 600 units

2) ( 5 - 8)

Calculation for margin of safety :

= Actual sales - BEP sales

Actual sales = 950 units

BEP sales = $ 8,000 / [ $ 27 - $ 17] = 800 units.

Margin of safety = 950 units - 800 units = 150 units

Margin of safety in dollars = 150 units X 27 = $ 4,050

Margin of safety percentage = [margin of safety / Actual sales ] X 100 % = [$ 4,050/ {$ 27 X 950}] X 100 % = 15.79%

3) ( 5 - 14)

CM ratio = [{sales - variable cost } / sales ]

30/ 100 = [{ 27,200 X $ 50} - variable cost] / { 27,200 X 50}

3/ 10 = { $1,360,000 - variable costs} /$ 1,360,000

$ 1,360,000 X 3 = $ 1,360,000 X 10 - variable cost X 10

Variable cost = {$ 1,360,000 X 7} / 10 = $ 952,000

(A) Variable cost per unit = $ 952,000 / 27,200 = $ 35

Break even point sales = fixed cost /{ sales price per unit- variable cost per unit }

(B) Break even point sales = $ 345,000 /[ $ 50 - $ 35] = 23,000 units

(C) Break even point sales in dollar = fixed cost / CM ratio

= $ 345,000 / 30% = $ 1,150,000

(D) Unit sales to attain $ 195,000 as profit : [ Fixed cost + target profit ] / [ selling price per unit - variables cost per unit ]

= [ $ 345,000 + $ 195,000 ] / [ $ 50 - $ 35 ] = 36,000 units

(E) Dollar sales to attain $ 195,000 as profit = 36,000 X $ 50 = $ 1,800,000

(F) New variable cost per unit = $ 35 - $5 = $ 30

Selling price per unit = $ 50

Contribution per unit = $ 50 - $ 30 = $20

New Break even point sales ( units) = fixed costs / contributions per unit

New Break even point sales ( units) = $ 345,000 / $ 20 = 17,250 units

(G) New break even point sales ( dollars ) = fixed cost / CM ratio

CM ratio = [contributions / sales ] X 100%

=[$ 20/ $ 50] X 100 % = 40%

=$ 345,000 / 40% = $ 862,500

(H) to attain $ 195,000 as profit dollars sales needed :

[ Fixed cost + profit] / [ selling price per unit - variable costs per unit ]

= [ $ 345,000 + $ 195,000 ] / [ $ 50 - $ 30] = 27,000 units

Sales in dollar = 27,000 X $ 50 = $ 1,350,000