Question

Lindon Company is the exclusive distributor for an automotive product that sells for $44.00 per unit and has a CM ratio of 30%. The company’s fixed expenses are $283,800 per year. The company plans to sell 25,100 units this year. Required: 1. What are the variable expenses per unit? (Round your "per unit" answer to 2 decimal places.) 2. What is the break-even point in unit sales and in dollar sales? 3. What amount of unit sales and dollar sales is required to attain a target profit of $151,800 per year? 4. Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $4.40 per unit. What is the company’s new break-even point in unit sales and in dollar sales? What dollar sales is required to attain a target profit of $151,800?

Answer 1

Answer:

1. $30,80

2. 21,500 units and $946,000

3. 33,000 units and $1,452,000

4. 16,125 units and $709,500 , $1,089,000

Explanation:

The variable expenses per unit

First determine the variable expenses ratio

Variable expenses ratio = 1 - CM ratio

                                        = 1-0.30

                                        = 0.70

Variable expenses per unit = $44.00 ×0.70

                                             = $30,80

Break-even point in unit sales and in dollar sales

break-even point in unit sales  = Fixed Costs / Contribution per Unit

                                                   = $283,800/ ($44.00×30%)

                                                   = $283,800/$13.20

                                                   = 21,500

break-even point in in dollar sales = Fixed Costs / Contribution Margin Ratio

                                                         = $283,800/0.30

                                                         = $946,000

Amount of unit sales and dollar sales is required to attain a target profit of $151,800 per year

Target Sales (Unit Sales) = Fixed Costs + Target Profit / Contribution per Unit

                                          = ($283,800 + $151,800) / $13.20

                                          = 33,000

Target Sales (Dollar Sales) = Fixed Costs + Target Profit / Contribution Margin Ratio

                                           = ($283,800 + $151,800) / 0.30

                                           = $1,452,000

the company’s new break-even point in unit sales and in dollar sales

break-even point in unit sales  = Fixed Costs / Contribution per Unit

                                                   = $283,800/ ($44.00-$30,80+$4.40)

                                                   = $283,800/$17,60

                                                   = 16,125

break-even point in in dollar sales = Fixed Costs / Contribution Margin Ratio

                                                         = $283,800/($17,60/$44.00)

                                                         = $283,800/0.40

                                                         = $709,500

dollar sales is required to attain a target profit of $151,800

Target Sales (Dollar Sales) = Fixed Costs + Target Profit / Contribution Margin Ratio

                                           = ($283,800 + $151,800) / 0.40

                                           = $1,089,000

Answer 2

Answer:

current scenario

Variable cost: $30.80

BEP in dollar $946.000‬

Sales to profit of 151,800:   $   1,452,000

if variable cost decrease by $4.40

BEP $709,500

to profit: $1,089,000

Explanation:

the Contribution margin ratio is what is left fro mthe sales price after paying the variable cost:

$Sales \: Revenue - Variable \: Cost = Contribution \: Margin$

$\frac{Contribution \: Margin}{Sales \: Revenue} = Contribution \: Margin \: Ratio$

( 44 - variable cost ) / 44 = 0.3

44 - 0.3 x 44 = variable cost = 30,80

The break even point is the sales volume at which the operating income is zero:

$\frac{Fixed\:Cost}{Contribution \:Margin \:Ratio} = Break\: Even\: Point_{dollars}$

283,800 / 0.3 = 946.000‬

A profit of 151,800 is achieve when selling above enought to make that 30%

151,800 / 0.3   =   506.000‬   + 946,000 = 1,452,000

other way would be:

( 283,800 + 151,800 ) / 0.3 = 1,452,000

if variable expense decrease by 4.4 then:

(44 - 30.8 + 4.4) / 44 = 0.4

we recalculate:

283,800 / 0.4 = 709,500

to profit

( 283,800 + 151,800 ) / 0.4 = 1,089,000