Question 1096063
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Sales = x million dollars


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Operating Costs = 55% of sales 


Operating Costs = 55% of x 


Operating Costs = (55/100)*x 


Operating Costs = 0.55*x (in millions of dollars)


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EBITDA = (Sales) - (Operating Costs) 


EBITDA = x - 0.55x 


EBITDA = 1x-0.55x 


EBITDA = (1-0.55)x


EBITDA = 0.45x (in millions of dollars)


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DA = Depreciation & Amortization


DA = (old DA) + 10% of (old DA)


DA = (0.8 million) + 10% of (0.8 million)


DA = (0.8 million) + 0.10*(0.8 million)


DA = (0.8 + 0.10*0.8) million


DA = 0.88 million


Note: 0.88 million = 880 thousand = 880,000


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EBIT = (EBITDA) - (DA)


EBIT = 0.45x - 0.88


EBIT amount is in millions of dollars


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Interest = (old interest) + (10% of old interest)


Interest = (0.6 million) + (0.10*(6 million))


Interest = (0.6 + 0.10*0.6) million


Interest = 0.66 million


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EBT = (EBIT) - (Interest)


EBT = (0.45x - 0.88) - (0.66)


EBT = 0.45x - 0.88 - 0.66 


EBT = 0.45x - 1.54 


EBT (earnings before taxes) is in millions of dollars.


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Taxes = 40% of EBT


Taxes = 40% of (0.45x - 1.54)


Taxes = 0.40*(0.45x - 1.54)


Taxes = 0.40*(0.45x) + 0.40*(-1.54)


Taxes = 0.18x - 0.616


Tax amount is in millions of dollars


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Net Income = (EBT) - (Taxes)


Net Income = (0.45x - 1.54) - (0.18x - 0.616)


Net Income = 0.45x - 1.54 - 0.18x + 0.616


Net Income = (0.45x - 0.18x) + (-1.54 + 0.616)


Net Income = 0.27x - 0.924


Net Income amount is in millions of dollars


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In the previous section above, the Net Income expression is 0.27x - 0.924 which represents the amount in millions of dollars. 
The desired Net Income amount we want is 2.5 million.
Set the expression 0.27x - 0.396 equal to 2.5 and solve for x.


0.27x - 0.924 = 2.5


0.27x - 0.924 + 0.924 = 2.5 + 0.924 <font color=blue>Add 0.924 to both sides</font>


0.27x = 3.424


0.27x/0.27 = 3.424/0.27 <font color=blue>divide both sides by 0.27</font>


x = 12.68148148148 <font color=blue>use a calculator for this step</font> (this value is approximate)


If you round up to 2 decimal places, then you get x = 12.69 which indicates the desired level of sales must be approximately 12.69 million (12,690,000) dollars.


Note 1: the more accurate sales value is 12,681,481.48 dollars. Though its helpful to round to the nearest ten thousand at least to simplify things.


Note 2: We round up to ensure that we meet or surpass the sales target. If we rounded to 12.68 million instead of 12.69 million, then we'd come short of our net income goal. 


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Final Answer: 


The desired level of sales is roughly 12.69 million dollars ($12,690,000) to generate a net income of $2.5 million or larger. 


If you need the more accurate sales figure, then it would be roughly $12,681,481.48


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Check:


Sales = $12,681,481.48
Operating Costs = 0.55*x = 0.55*12681481.48 = 6,974,814.814 = 6,974,814.81
EBITDA = (Sales) - (Operating Costs) = (12,681,481.48) - (6,974,814.81) = 5,706,666.67
DA = 880,000
EBIT = (EBITDA) - (DA) = (5,706,666.67) - (880,000) = 4,826,666.67
Interest = 660,000
EBT = EBIT - Interest = 4,826,666.67 - 660,000 = 4,166,666.67
Taxes = 40% of EBT = 0.4*(4,166,666.67) = 1,666,666.668 = 1,666,666.67
Net Income = EBT - Taxes = 4,166,666.67 - 1,666,666.67 = 2,500,000


So that checks out

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