required information\nuse the following information for the exercises below. (algo)\nthe following…

required information\nuse the following information for the exercises below. (algo)\nthe following information applies to the questions displayed below.\nhudson company reports the following contribution margin income statement.\nhudson company\ncontribution margin income statement\nfor year ended december 31\nsales (10,100 units at $300 each) $ 3,030,000\nvariable costs (10,100 units at $240 each) 2,424,000\ncontribution margin 606,000\nfixed costs 468,000\nincome $ 138,000\nexercise 18 - 12 (algo) target income and margin of safety lo c2\nquestion\n1. assume hudson has a target income of $167,000. what amount of sales (in dollars) is needed to produce this target income?\n2. if hudson achieves its target income, what is its margin of safety (in percent)?\nnotes: round your answer to 1 decimal place.

required information\nuse the following information for the exercises below. (algo)\nthe following information applies to the questions displayed below.\nhudson company reports the following contribution margin income statement.\nhudson company\ncontribution margin income statement\nfor year ended december 31\nsales (10,100 units at $300 each) $ 3,030,000\nvariable costs (10,100 units at $240 each) 2,424,000\ncontribution margin 606,000\nfixed costs 468,000\nincome $ 138,000\nexercise 18 - 12 (algo) target income and margin of safety lo c2\nquestion\n1. assume hudson has a target income of $167,000. what amount of sales (in dollars) is needed to produce this target income?\n2. if hudson achieves its target income, what is its margin of safety (in percent)?\nnotes: round your answer to 1 decimal place.

Answer

Explanation:

Step1: Calculate contribution - margin ratio

Contribution - margin per unit = Selling price per unit - Variable cost per unit = $300 - $240=$60. Contribution - margin ratio = $\frac{\text{Contribution - margin per unit}}{\text{Selling price per unit}}=\frac{60}{300}=0.2$.

Step2: Calculate required sales for target income

The formula for required sales to reach target income is $\text{Required sales}=\frac{\text{Fixed costs}+\text{Target income}}{\text{Contribution - margin ratio}}$. Fixed costs = $468,000$, target income = $167,000$. Required sales=$\frac{468000 + 167000}{0.2}=\frac{635000}{0.2}=3175000$.

Step3: Calculate break - even sales

Break - even sales = $\frac{\text{Fixed costs}}{\text{Contribution - margin ratio}}=\frac{468000}{0.2}=2340000$.

Step4: Calculate margin of safety percentage

Margin of safety = $\frac{\text{Actual (or budgeted) sales}-\text{Break - even sales}}{\text{Actual (or budgeted) sales}}\times100%$. Actual sales = $3030000$ (from the income statement), break - even sales = $2340000$. Margin of safety percentage=$\frac{3030000 - 2340000}{3030000}\times100%\approx22.8%$.

Answer:

  1. $3,175,000
  2. $22.8%$