Sultan Corporation operated at its normal capacity during the current year, prod

Question

Sultan Corporation operated at its normal capacity during the current year, producing 64,000 units of its single product. Sales totalled 54,000 units at an average price of $25 per unit. Variable cost of goods sold amounted to $10 per unit, and sales commissions were paid out at $3 per unit sold. Fixed product costs, incurred uniformly throughout the year, amounted to $196,000 and fixed period costs, incurred uniformly, amounted to $22,000 per quarter.

Required:

1. What is Sultan’s break-even point in sales dollars for the current year? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

2. If Sultan’s fixed product costs unexpectedly increase by 20%, what is the new unit selling price that would yield the same break-even sales as before the cost increase? (Do not round intermediate calculations and round your answer to 2 decimal places.)

Explanation / Answer

Answer 1

Contribution per unit = Selling price - Variable Cost =  $25 - $10 - $3 = $12 per unit

Total Fixed cost for the year = $196,000 + ( $22,000 * 4) = $284,000

Break even point in sales units = Total Fixed cost / Contribution per unit = $284,000 / $12 = 23,667 units

Break-even point in sales dollars = Break even point in sales units * Seling price per unit = $591,675

Answer 2

Revised Fixed Cost for the year = $196,000 + ($22,000 * 4 *120 %) = $301,600

Now , let the revised unit selling price = $x

thus, revised Contribution per unit = $x - $10 - $3 = $x - $13

Revised , Break even point in sales units = $301,600 / $x - $13

Therefore revised Break-even point in sales dollars = ( $301,600 / $x - $13) * $x

But as per qustion the Break-even point in sales dollars to remain same ie $591,675

Thus , we can form the following equation :

( $301,600 / $x - $13) * $x = $591,675

or , 301,600 x =  591,675 ( x - 13)

or 29,0075 x = 7,691,775 ;

x =  7,691,775 / 29,0075 = $26.52

Answer : The required new unit selling price is $26.52

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