Question 1096063: Sales $8,000,000
Operating costs $4,400,000
(excluding depreciation &
amortization)
EBITDA $3,600,000
Depreciation &Amortization 800,000
EBIT $2, 800,000
Interest 600,000
EBT $2,200,000
Taxes(40%) 880,000
Net Income $1,320,000
Question:
The CEO would like to see higher sales and a forecasted
net income of $2,500,000.
Assume that operating costs (excluding depreciation and
amortization are 55% of sales, and depreciation and
amortization and interest expenses will increase by 10% .
The tax rate, which is 40% will remain the same. What
level of sales would generate $2,500,000 in net income?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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 Add 0.924 to both sides
0.27x = 3.424
0.27x/0.27 = 3.424/0.27 divide both sides by 0.27
x = 12.68148148148 use a calculator for this step (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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