Question 537666: how many widgets must little business inc. make and sell before they start making a profit? Given: total fixed costs are $10,000.00, widgets are sold for $7.50 and the cost to make "ten" widgets is $25.00.
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! There are a couple of ways to solve this problem. The easist requires logic and intuition but not much else: there will be a head slapping moment when I explain this. First let's make sure we know what the question is asking: how many units need to be sold before the business is profitable? We are asked for the quantity of units at the breakeven point where total costs (normally abbreviated TC) = the total revenues (normally abbreviated TR).
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Total costs (TC) are comprised of fixed costs (FC) + variable costs (VC). Ignore the fixed costs for a moment (we'll get back to them) and consider the variable costs only.
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Given:
The cost to produce 10 widgets = $25, therefore, divide by 10 to find the VC per widget = $2.50 (at the unit level, this is often called the Marginal Cost (MC), the cost to produce one more unit.)
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Revenue for each widget: $7.50 (like Marginal Cost, this is often called Marginal Revenue (MR), the revenue derived from selling one more unit.)
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We care about the relationship between these two numbers. The Contribution (towards profits) is the difference between Little Business, Inc.'s (LBI) MR per widget and the MC per widget is:
MR = $7.50
MC = $2.50
Contribution = MR - MC
= 7.50 - 2.50
= 5.00 per widget sold
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Now, to get to the breakeven point, LBI must make enough revenue to cover all costs. At that point, with the next widget sale, they are then making a profit.
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Let FC = fixed costs
Let Qb = quantity of widgets sold at breakeven
Let P = Price per widget
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Given:
FC = 10,000
Calculated:
Contribution = 5.00
Need to find:
Qb
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Short answer to the problem:
Divide FC by contribution per unit to determine Qb:
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10,000/5.00 = 2,000 units sold for breakeven
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check your work:
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VC = MC * Qb
VC = 2.50 * 2,000
VC = 5,000
FC = 10,000 (given)
TC = FC + VC
TC = 10,000 + 5,000
TC = 15,000
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TR = P * Qb
TR = 7.50 * 2,000
TR = 15,000
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Breakeven occurs where TC = TR
TR = 15,000
TC = 15,000
TC = TR checks
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cheers,
Lee
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