Please help Astro Co. sold 20,000 units of its only product and incurred a $50,0
ID: 2565491 • Letter: P
Question
Please help
Astro Co. sold 20,000 units of its only product and incurred a $50,000 loss (ignoring taxes) for the current year as shown here. During a planning session for year 2014's activities, the production manager notes that variable costs can be reduced 50% by installing a machine that automates several operations. To ob- tain these savings, the company must increase its annual fixed costs by $200,000. The maximum output capacity of the company is 40,000 units per year Problem 18-4A Break-even analysis; income targeting and forecasting c2 P2 A ASTRO COMPANY Contribution Margin Income Statement For Year Ended December 31,2013 800,000 200,000 250,000 (50,000) Net loss Required 1. Compute the break-even point in dollar sales for year 2013 2. Compute the predicted break-even point in dollar sales for year 2014 assuming the machine is in- stalled and there is no change in the unit sales price 3. Prepare a forecasted contribution margin income statement for 2014 that shows the expected results Check (3) Net income, $150,000 with the machine installed. Assume that the unit sales price and the number of units sold will not change, and no income taxes will be due 4. Compute the sales level required in both dollars and units to earn $140,000 of after-tax income in 2014 (4) Required sales, with the machine installed and no change in the unit sales price. Assume that the income tax rate is $1,083,333 or 21,667 units 30%. (Hint: Use the procedures in Exhibits 18.22 and 18.23.) (Round answers to whole dollars or units.) 5. Prepare a forecasted contribution margin income statement that shows the results at the sales level computed in part 4, Assume an income tax rate of 30%Explanation / Answer
Astro Company
Break-even point in dollar sales = fixed cost/contribution margin ratio
Fixed cost = $250,000
Contribution margin ratio = (contribution margin/sales) x 100
Contribution margin = $200,000
Sales = $1,000,000
Contribution margin ratio = (200,000/1,000,000) x 100 = 20%
Break-even point in dollar sales = $250,000/20% = $1,250,000
With machine installed, the fixed cost would increase by $200,000
Hence total fixed cost = 250,000 + 200,000 = $450,000
The variable cost would reduce by 50%
Original variable cost per unit = $800,000/20,000 units = $40 per unit
New variable cost = $20 per unit (40 – 50% of 40)
Sales price per unit would remain constant at $1,000,000/20,000 units = $50 per unit
Hence the new contribution margin = sales price – variable cost per unit
= $50 - $20 = $30 per unit
New CM ratio = ($30/$50) x100 = 60%
Predicted Break-even point in dollar sales = $450,000/60% = $750,000
Contribution Margin Income Statement for Year 2014
unit price
Total
Sales 20,000 units
$50
$1,000,000
Variable cost
$20
$400,000
Contribution Margin
$30
$600,000
Fixed cost
$450,000
Net Income
$150,000
After tax income = $140,000
Tax rate = 30%
Before tax income = $140,000/70% = $200,000
Fixed cost = $450,000 (with machine installed)
Contribution margin = $30 per unit (assumed reduction in variable cost by 50% and constant sales price)
Desired units = (fixed cost + target net income)/ contribution margin
= ($450,000 + $200,000)/$30
= $650,000/$30 = 21,667 units
Desired sales in dollars = 21,667 x $50 = $1,083,333
Contribution Margin Income Statement for Year 2014
unit price
Total
Sales 21,667 units
$50
$1,083,333
Variable cost
$20
$433,333
Contribution Margin
$30
$650,000
Fixed cost
$450,000
Net Income
$200,000
Tax at 30%
$60,000
Net Income after Tax
$140,000
Contribution Margin Income Statement for Year 2014
unit price
Total
Sales 20,000 units
$50
$1,000,000
Variable cost
$20
$400,000
Contribution Margin
$30
$600,000
Fixed cost
$450,000
Net Income
$150,000