In 2016, Raleigh sold 1,000 units at $500 each, and earned net income of $40,000. Variable expenses were $300 per unit, and fixed expenses were $160,000. The same selling price is expected for 2017. Raleigh's variable cost per unit will rise by 10% in 2017 due to increasing material costs, so they are tentatively planning to cut fixed costs by $10,000. How many units must Raleigh sell in 2017 to maintain the same income level as 2016?

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aquialaska aquialaska · Answer 1 · 2020-05-09T03:48:03+02:00

The number of units that must Raleigh sell in 2017 to maintain the same income level as 2016 is 1,118 units.

For the Year 2016

Number of Units Sold = 1,000 units

Unit selling price = $500 per unit

Total Sales = $500 × 1,000 = $500,000

Variable Costs = $300 × 1,000

= $300,000

Contribution = $500,000 - $300,000

= $200,000

Fixed Costs = $160,000

Net Income = $200,000 - $160,000

= $40,000

For the Year 2017

Unit Selling Price = $500 per unit

Unit Variable Cost = $300 × 1.10

= $330 per unit

Contribution per unit = $500 - $330 = $170 per unit

Fixed Cost = $160,000 - $10,000 = $150,000

Now, to maintain the same income of $ 40,000 the Company have a total contribution

$150,000 + $40,000

= $190,000

Number of units to be sold = Total contribution ÷ Contribution per unit

= $190,000 ÷ $170

= 1,117.64

or

1,118 units.

Hence, The number of units that must Raleigh sell in 2017 to maintain the same income level as 2016 is 1,118 units.

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