Cost-Volume-Profit Relationships connect Al appli PROBLEM 5-19 Break-Even Analys

ID: 2563763 • Letter: C

Question

Cost-Volume-Profit Relationships connect Al appli PROBLEM 5-19 Break-Even Analysis: Pricing ILo5-1. Los-4, LOS-51 cable problems are available with McGraw-Hill's Connect Accounting a introduced a new product last year for which it is trying to find an optimal sell- that the company can increase sales by 5,000 units for each he selling price. The company's present selling price is $70 per unit, and variable e are Si0 per unit. Fixed expenses are s540,000 per year. The present annual sales volume S2 Cat the S70 selling price) is 15,000 units. Required: I. What is the present yearly net operating income or loss? 2. What is the present break-even point in unit sales and in dollar sales? 3. Assuming that the marketing studies are correct, what is the maximum annual profit that the company can earn? At how many units and at what selling price per unit would the company generate this profit?

Explanation / Answer

Minden Company

Contribution margin income statement

Unit price

Total

Sales 15,000 units

$70

$1,050,000

Less: Variable costs

$40

$600,000

Contribution margin

$30

$450,000

Fixed Expenses

$540,000

Net operating loss

($90,000)

Break-even point in unit sales –

= fixed cost/contribution margin per unit

Fixed cost = $540,000

Contribution margin per unit = $30

Unit sales break-even point = $540,000/$30 = 18,000 units

Break-even point in sales dollars –

= fixed cost/contribution margin ratio

Contribution margin ratio = (Contribution margin/ sales price) x 100 = 42.9%

Break-even point in dollar sales = $540,000/42.9% = $1,260,000

Assume the multiple of units increased is n

Hence total desired units = 15,000 + (5,000 x n)

Sales revenue = number of units x ($70 – ( n x2))

Cost = (number of units x $40) + $540,000

Assuming n = 2,

Total desired units = 25,000 units

Sales revenue = 25,000 x $66 = $1,650,000

Cost = (25,000 x$40) + $540,000 = $1,540,000

Profit /(loss) = revenue – total cost

= $1,650,000 – 640,000 = $110,000

Assuming n = 3

Units = 15,000 + (5,000 x 3) = 30,000

Revenue = 30,000 x 64 =$1,920,000

Costs = 30,000 x $40 + 540,000 = $1,740,000

Profit = 1,920,000 – $1,740,000 = $180,000

Assuming n = 4

Units = 35,000

Revenue = 35,000 x $62 = $2,170,000

Cost = 35,000 x $40 + 540,000 = $1,940,000

Profit = $230,000

Assuming n = 5

Units = 40,000

Revenue = 40,000 x$60 = $2,400,000

Costs = 40,000 x $40 + $540,000 = $2,140,000

Profit = $2,400,000 - $2,140,000 = $260,000

Assuming n = 6

Units = 45,000

Revenue = 45,000 x $58 = $2,610,000

Costs = 45,000 x $40 + $540,000 = $2,340,000

Profit = $2,610,000 - $2,340,000 = $270,000

Assuming n = 7

Units = 50,000

Revenue = 50,000 x $56 = $280,000

Costs = 50,000 x $40 + 540,000 = $2,540,000

Profit = $260,000

Since profits are decreasing at this level, and the maximum profit of $270,000 is at 45,000 units and selling price of $58, the desired level of activity is 45,000 units at a selling price of $58 per unit.