In: Accounting
CVP Analysis and Special Decisions
Sweet Grove Citrus Company buys a variety of citrus fruit from
growers and then processes the fruit into a product line of fresh
fruit, juices, and fruit flavorings. The most recent year's sales
revenue was $4,200,000. Variable costs were 60 percent of sales and
fixed costs totaled $1,500,000. Sweet Grove is evaluating two
alternatives designed to enhance profitability.
Round your answers to the nearest whole number.
(a) What is the current break-even point in sales dollars?
(b) Assuming an income tax rate of 37 percent, what dollar sales volume is currently required to obtain an after-tax profit of $300,000?
(c) In the absence of income taxes, at what sales volume will both alternatives (automation and outsourcing) provide the same profit?
Answer:
(a). Current break even point in sales dollars = $3,750,000
Calculation:
Break even point in sales dollars = Fixed cost / Contribution margin ratio
Fixed cost = $1,500,000
Calculation of contribution margin ratio:
Sales | $4,200,000 |
Less:Variable cost (Sales * 60% = $4,200,000 * 60%) |
($2,520,000) |
Contribution margin | $1,680,000 |
Contribution margin ratio = Contribution margin / Sales |
$1,680,000 / $4,200,000 = 0.4 or 40% |
or, Contribution margin ratio = 100 - variable cost ratio = 100 - 60 = 40%
Break even point in sales dollars = $1,500,000 / 0.4 = $3,750,000
(b) Dollar sales volume currently required to obtain after tax profit = $4,940,475
Calculation:
After tax profit = $300,000
Income tax rate = 37%
So, the profit before tax = $300,000 / (100% - 37%) = $300,000 / 63%
= $300,000 / 0.63 = $476,190.47 rounded to $476,190
Dollar sales volume required to obtain after tax profit of $300,00
= (fixed cost + Target profit before tax) / Contribution margin ratio
Fixed cost = $1,500,000
Target profit before tax = $476,190
Contribution margin ratio = 0.4
So, required dollar sales volume to earn an after tax profit of $300,000
= ($1,500,000 + $476,190) / 0.4 = $1,976,190 / 0.4 = $4,940,475
(c) The sales volume that both alternatives give same profit in the absence of income taxes
= $7,272,727
Calculation:
First, let's calculate the total fixed costs and contribution margin ratio for each alternative:
Automation | Outsourcing | ||
Fixed costs ($4,00,000 + $1,500,000) |
$1,900,000 |
Fixed costs ($1,500,000 - $4,00,000) |
$1,100,000 |
Variable cost ratio | 54% | Variable cost ratio | 65% |
Contribution margin ratio (100% - variable cost ratio = 100% - 54%) |
46% or 0.46 |
Contribution margin ratio (100% - 65%) |
35% or 0.35 |
PROFIT = (SALES * CONTRIBUTION MARGIN RATIO) - FIXED COST
Let the sales be "x".
Profit from automation = Profit from outsourcing
0.46x - $1,900,000 = 0.35x - $1,100,000
0.46 - 0.35 = -$1,100,000 + $1,900,000
0.11x = $8,00,000
x = $8,00,000 / 0.11 = $7,272,727.27 rounded to $7,272,727
So, at the level of $7,272,727 sales , the profit from both alernatives will be equal.