Answer:
(A) 1,200 Margin of Safety_{units}
(B) 330,000 Margin of Safety_{usd}
(C) Margin of Safety 40% of Sales
Explanation:
(A)
![Sales \: Revenue - Variable \: Cost = Contribution \: Margin](https://tex.z-dn.net/?f=Sales%20%5C%3A%20Revenue%20-%20Variable%20%5C%3A%20Cost%20%3D%20Contribution%20%5C%3A%20Margin)
275 - 150 = <u>125 CM per unit</u>
![\frac{Fixed\:Cost}{Contribution \:Margin} = Break\: Even\: Point_{units}](https://tex.z-dn.net/?f=%5Cfrac%7BFixed%5C%3ACost%7D%7BContribution%20%5C%3AMargin%7D%20%3D%20Break%5C%3A%20Even%5C%3A%20Point_%7Bunits%7D)
![\frac{225,000}{125} = 1,800 = Break\: Even\: Point_{units}](https://tex.z-dn.net/?f=%5Cfrac%7B225%2C000%7D%7B125%7D%20%3D%201%2C800%20%3D%20Break%5C%3A%20Even%5C%3A%20Point_%7Bunits%7D)
![{units \: sold- BEP_{units} = margin \: of \: safety_{units}](https://tex.z-dn.net/?f=%7Bunits%20%5C%3A%20sold-%20BEP_%7Bunits%7D%20%3D%20margin%20%5C%3A%20of%20%5C%3A%20safety_%7Bunits%7D)
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)
![\frac{Contribution Margin}{Sales Revenue} = $Contribution Margin Ratio](https://tex.z-dn.net/?f=%5Cfrac%7BContribution%20Margin%7D%7BSales%20Revenue%7D%20%3D%20%24Contribution%20Margin%20Ratio)
125/275 = 0.45454545 = <u>5/11 CM ratio</u>
![\frac{Fixed\:Cost}{Contribution \:Margin \:Ratio} = Break\: Even\: Point_{dollars}](https://tex.z-dn.net/?f=%5Cfrac%7BFixed%5C%3ACost%7D%7BContribution%20%5C%3AMargin%20%5C%3ARatio%7D%20%3D%20Break%5C%3A%20Even%5C%3A%20Point_%7Bdollars%7D)
225,000/(5/11) = 495,000 BEP USD
![{current \:sales - BEP_{USD} = margin \: of \: safety](https://tex.z-dn.net/?f=%7Bcurrent%20%5C%3Asales%20-%20BEP_%7BUSD%7D%20%3D%20margin%20%5C%3A%20of%20%5C%3A%20safety)
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.
<em><u>Important:</u></em> When posible to avoid rounding errors express as fraction iof posible
(C)
![\frac{current \:sales - BEP_{USD}}{current \:sales} \times 100 = margin \: of \: safety](https://tex.z-dn.net/?f=%5Cfrac%7Bcurrent%20%5C%3Asales%20-%20BEP_%7BUSD%7D%7D%7Bcurrent%20%5C%3Asales%7D%20%5Ctimes%20100%20%3D%20margin%20%5C%3A%20of%20%5C%3A%20safety)
![\frac{330,000}{825,000} \times 100 = margin \: of \: safety](https://tex.z-dn.net/?f=%5Cfrac%7B330%2C000%7D%7B825%2C000%7D%20%5Ctimes%20100%20%3D%20margin%20%5C%3A%20of%20%5C%3A%20safety)
Margin of Safety 40%