Answer:
(A) 1,200 Margin of Safety_{units}
(B) 330,000 Margin of Safety_{usd}
(C) Margin of Safety 40% of Sales
Explanation:
(A)
[tex]Sales \: Revenue - Variable \: Cost = Contribution \: Margin[/tex]
275 - 150 = 125 CM per unit
[tex]\frac{Fixed\:Cost}{Contribution \:Margin} = Break\: Even\: Point_{units}[/tex]
[tex]\frac{225,000}{125} = 1,800 = Break\: Even\: Point_{units}[/tex]
[tex]{units \: sold- BEP_{units} = margin \: of \: safety_{units}[/tex]
3,000 - 1,800 = 1,200 Margin of Safety_{units}
HOW? we Calculate the contribution per unit. Then the BEP in units and with that the margin of safety in units.
(B)
[tex]\frac{Contribution Margin}{Sales Revenue} = $Contribution Margin Ratio[/tex]
125/275 = 0.45454545 = 5/11 CM ratio
[tex]\frac{Fixed\:Cost}{Contribution \:Margin \:Ratio} = Break\: Even\: Point_{dollars}[/tex]
225,000/(5/11) = 495,000 BEP USD
[tex]{current \:sales - BEP_{USD} = margin \: of \: safety[/tex]
825,000-495,000 = 330,000 Margin of Safety_{usd}
HOW? we Calculate the contribution ratio by dividing CM over sales. Then the BEP in dollars and with that the margin of safety in dollars.
Important: When posible to avoid rounding errors express as fraction iof posible
(C)
[tex]\frac{current \:sales - BEP_{USD}}{current \:sales} \times 100 = margin \: of \: safety[/tex]
[tex]\frac{330,000}{825,000} \times 100 = margin \: of \: safety[/tex]
Margin of Safety 40%
275-150 = 125
225000/125
= 1800
3000-1800
= 1200
125/175 = 0.4545
225000/0.4545
= $495,049
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