The Price Company will produce 55,000 widgets next year. Variable costs will equal 40 percent of sales, while fixed costs will total $110,000. At what price must each widget be sold for the company to achieve an EBIT of $95,000?
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A. B. C. D. E.E
EBIT = PQ - VQ - FC -
$95,000 = P(55,000) - (0.4)P(55,000) - $110,000
$205,000 = (0.6)(55,000)P
$205,000 = 33,000P
P = $6.21.
To determine the price at which each widget must be sold for The Price Company to achieve an EBIT (Earnings Before Interest and Taxes) of $95,000, we need to calculate the total costs and then add the desired profit to arrive at the target sales revenue.
Let's break down the information given:
Variable costs: 40% of sales Fixed costs: $110,000 EBIT (desired profit): $95,000
First, we need to calculate the total costs. The variable costs are given as 40% of sales. Therefore, the variable costs can be calculated as follows:
Variable costs = 40% of sales = 0.40 * sales
Next, we need to calculate the total costs by adding the variable costs and fixed costs:
Total costs = Variable costs + Fixed costs
Since we don't know the sales yet, we will express the total costs as a percentage of sales:
Total costs as a percentage of sales = Total costs / Sales
Now, let's rearrange the equation to solve for sales:
Sales = Total costs / (1 - Total costs as a percentage of sales)
We know that EBIT (Earnings Before Interest and Taxes) is equal to Sales minus Total costs. Therefore, we can write:
EBIT = Sales - Total costs
Now, substitute the expressions for Sales and Total costs:
EBIT = Sales - (Total costs / (1 - Total costs as a percentage of sales))
Since EBIT is given as $95,000, we can rearrange the equation to solve for Sales:
Sales = EBIT + (Total costs / (1 - Total costs as a percentage of sales))
Now, let's plug in the given values:
Fixed costs = $110,000 EBIT (desired profit) = $95,000 Total costs as a percentage of sales = (Variable costs + Fixed costs) / Sales
Given that Variable costs = 40% of sales, we can substitute this into the equation:
Total costs as a percentage of sales = (0.40 * sales + $110,000) / sales
Substituting all the values into the equation, we get:
Sales = $95,000 + (($110,000 + 0.40 * Sales) / (1 - (0.40 * Sales + $110,000) / Sales))
To solve this equation and find the value of Sales, we can use algebraic techniques or solve it numerically. In this case, we'll use a numerical approach to find the approximate value of Sales.
Using the given answer options, we can substitute each price option into the equation and find the corresponding Sales value. We'll select the price option that results in Sales closest to the expected number of widgets (55,000).
Let's substitute each answer option into the equation and calculate the corresponding Sales value:
For option A ($5.37): Sales = $95,000 + (($110,000 + 0.40 * 55,000) / (1 - (0.40 * 55,000 + $110,000) / 55,000))
For option B ($5.00): Sales = $95,000 + (($110,000 + 0.40 * 55,000) / (1 - (0.40 * 55,000 + $110,000) / 55,000))
For option C ($4.45): Sales = $95,000 + (($110,000 + 0.40 * 55,000) / (1 - (0.40 * 55,000 + $110,000) / 55,000))
For option D ($2.00): Sales = $95,000 + (($110,000 + 0