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CVP Analysis and Special Decisions Sweet Grove Citrus Company buys a variety of citrus fruit from...

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.

  • One staff member has proposed that Sweet Grove purchase more automated processing equipment. This strategy would increase fixed costs by $400,000 but decrease variable costs to 54 percent of sales.
  • Another staff member has suggested that Sweet Grove rely more on outsourcing for fruit processing. This would reduce fixed costs by $400,000 but increase variable costs to 65 percent of sales.

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?

Solutions

Expert Solution

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.


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