forrester company is considering buying new equipment that would increase monthly fixed costs from $290,000…

forrester company is considering buying new equipment that would increase monthly fixed costs from $290,000 to $320,000 and would decrease the current variable costs of $70 by $10 per unit. the selling price of $120 is not expected to change. forresters current break - even sales are $570,000 and current break - even units are 7,500. if forrester purchases this new equipment, the revised contribution margin ratio would be:

forrester company is considering buying new equipment that would increase monthly fixed costs from $290,000 to $320,000 and would decrease the current variable costs of $70 by $10 per unit. the selling price of $120 is not expected to change. forresters current break - even sales are $570,000 and current break - even units are 7,500. if forrester purchases this new equipment, the revised contribution margin ratio would be:

Answer

Explanation:

Step1: Calculate current variable cost per unit

Current break - even sales = $570,000, current break - even units = 7,500. Selling price per unit (P=\frac{570000}{7500} = 76) (This step is wrong in the original logic, we should use the formula for break - even: (BEP=\frac{FC}{CM}), and also (CM = P - VC). But we can also calculate variable cost per unit from another way. Since (BEP) (in units) (=\frac{FC}{P - VC}), (7500=\frac{290000}{120 - VC}), then (120 - VC=\frac{290000}{7500}\approx38.67), (VC = 120- 38.67 = 81.33) (This is wrong approach. The correct way: Current break - even (in units) (=\frac{FC}{P - VC}), so (7500=\frac{290000}{120 - VC}), (120 - VC=\frac{290000}{7500}), (VC = 120-\frac{290000}{7500}\approx120 - 38.67=81.33) (error - prone). The right formula: Contribution margin per unit (CM=P - VC). At break - even, (FC = CM\times Q). So (CM=\frac{FC}{Q}=\frac{290000}{7500}\approx38.67), (VC = P - CM=120 - 38.67 = 81.33). New (VC=81.33 - 10=71.33) Contribution margin per unit (CM_{new}=120 - 71.33 = 48.67) Contribution margin ratio (CMR=\frac{CM_{new}}{P})

Another way: Original variable cost per unit: Since break - even (in units) (Q=\frac{FC}{P - VC}), (7500=\frac{290000}{120 - VC}), (120 - VC=\frac{290000}{7500}), (VC = 120-\frac{290000}{7500}) New variable cost per unit (VC_{new}=VC - 10) Contribution margin per unit (CM = 120-(VC - 10)=130 - VC) Contribution margin ratio (CMR=\frac{130 - VC}{120})

The formula for contribution margin ratio (CMR=\frac{P-(VC - 10)}{P}) We know that originally (FC = 290000), (Q = 7500), (P = 120) Originally (CM=P - VC), (FC=CM\times Q), so (VC=P-\frac{FC}{Q}=120-\frac{290000}{7500}) New (VC=VC - 10) (CMR=\frac{120-(120-\frac{290000}{7500}-10)}{120}=\frac{10+\frac{290000}{7500}}{120}) (complex). The simple formula: Contribution margin ratio (CMR=\frac{P - VC_{new}}{P}) (VC_{new}=(120\times7500 - 290000)\div7500-10) (120\times7500=900000), (900000 - 290000 = 610000), (VC=\frac{610000}{7500}\approx81.33), (VC_{new}=81.33 - 10 = 71.33) (CMR=\frac{120 - 71.33}{120}=\frac{48.67}{120}\approx0.4056\approx40%)

Answer:

40%