Question 19.IP.1: Wyatt Inc. expects to maintain the same inventories at the e...

Wyatt Inc. expects to maintain the same inventories at the end of the year as at the beginning of the year. The estimated fixed costs for the year are $288,000, and the estimated variable costs per unit are $14. It is expected that 60,000 units will be sold at a price of $20 per unit. Maximum sales within the relevant range are 70,000 units.
Instructions
1. What is (a) the contribution margin ratio and (b) the unit contribution margin?
2. Determine the break-even point in units.
3. Construct a cost-volume-profit chart, indicating the break-even point.
4. Construct a profit-volume chart, indicating the break-even point.
5. What is the margin of safety?

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1.   a.   Contribution Margin Ratio = \frac{Sales  –  Variable  Costs}{Sales}

Contribution Margin Ratio = \frac{(60,000  units  ×  \$20)  –  (60,000  units  ×  \$14)}{(60,000  units  ×  \$20)} 

Contribution Margin Ratio = \frac{\$1,200,000  –  \$840,000}{ \$1,200,000} = \frac{\$360,000}{ \$1,200,000}

Contribution Margin Ratio = 30%

     b.  Unit Contribution Margin = Unit Selling Price – Unit Variable Costs

Unit Contribution Margin = $20 – $14 = $6

2.  Break-Even Sales (units) = \frac{Fixed  Costs}{Unit  Contribution  Margin}

      Break-Even Sales (units) = \frac{\$ 288,000}{\$6} = 48,000 units 

5. Margin of safety:

Expected sales (60,000 units × $20)          $1,200,000

Break-even point (48,000 units × $20)          960,000

Margin of safety                                               \underline{\underline{\$ \ 240,000}}

or

Margin of Safety (units) = \frac{ Margin  of  Safety  (dollars)}{ Unit  Selling  Price}

or

12,000 units ($240,000/$20)

or

Margin of Safety = \frac{ Sales  –  Sales  at  Break-Even  Point}{Sales}

Margin of Safety = \frac{\$ 240,000}{\$ 1,200,000} = 20% 

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