document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096063>Question 1096063</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sales $8,000,000<BR>\n" );
document.write( "Operating costs $4,400,000<BR>\n" );
document.write( "(excluding depreciation &<BR>\n" );
document.write( "amortization)<BR>\n" );
document.write( "EBITDA $3,600,000<BR>\n" );
document.write( "Depreciation &Amortization 800,000<BR>\n" );
document.write( "EBIT $2, 800,000<BR>\n" );
document.write( "Interest 600,000<BR>\n" );
document.write( "EBT $2,200,000<BR>\n" );
document.write( "Taxes(40%) 880,000<BR>\n" );
document.write( "Net Income $1,320,000<BR>\n" );
document.write( "Question:<BR>\n" );
document.write( "The CEO would like to see higher sales and a forecasted<BR>\n" );
document.write( "net income of $2,500,000.<BR>\n" );
document.write( "Assume that operating costs (excluding depreciation and<BR>\n" );
document.write( "amortization are 55% of sales, and depreciation and<BR>\n" );
document.write( "amortization and interest expenses will increase by 10% .<BR>\n" );
document.write( "The tax rate, which is 40% will remain the same. What<BR>\n" );
document.write( "level of sales would generate $2,500,000 in net income? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710534 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=710534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">\r<BR>\n" );
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document.write( "Sales = x million dollars\r<BR>\n" );
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document.write( "Operating Costs = 55% of sales \r<BR>\n" );
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document.write( "Operating Costs = 55% of x \r<BR>\n" );
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document.write( "Operating Costs = (55/100)*x \r<BR>\n" );
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document.write( "Operating Costs = 0.55*x (in millions of dollars)\r<BR>\n" );
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document.write( "EBITDA = (Sales) - (Operating Costs) \r<BR>\n" );
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document.write( "EBITDA = x - 0.55x \r<BR>\n" );
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document.write( "EBITDA = 1x-0.55x \r<BR>\n" );
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document.write( "EBITDA = (1-0.55)x\r<BR>\n" );
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document.write( "EBITDA = 0.45x (in millions of dollars)\r<BR>\n" );
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document.write( "DA = Depreciation & Amortization\r<BR>\n" );
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document.write( "DA = (old DA) + 10% of (old DA)\r<BR>\n" );
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document.write( "DA = (0.8 million) + 10% of (0.8 million)\r<BR>\n" );
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document.write( "DA = (0.8 million) + 0.10*(0.8 million)\r<BR>\n" );
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document.write( "DA = (0.8 + 0.10*0.8) million\r<BR>\n" );
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document.write( "DA = 0.88 million\r<BR>\n" );
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document.write( "Note: 0.88 million = 880 thousand = 880,000\r<BR>\n" );
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document.write( "EBIT = (EBITDA) - (DA)\r<BR>\n" );
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document.write( "EBIT = 0.45x - 0.88\r<BR>\n" );
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document.write( "EBIT amount is in millions of dollars\r<BR>\n" );
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document.write( "Interest = (old interest) + (10% of old interest)\r<BR>\n" );
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document.write( "Interest = (0.6 million) + (0.10*(6 million))\r<BR>\n" );
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document.write( "Interest = (0.6 + 0.10*0.6) million\r<BR>\n" );
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document.write( "Interest = 0.66 million\r<BR>\n" );
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document.write( "EBT = (EBIT) - (Interest)\r<BR>\n" );
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document.write( "EBT = (0.45x - 0.88) - (0.66)\r<BR>\n" );
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document.write( "EBT = 0.45x - 0.88 - 0.66 \r<BR>\n" );
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document.write( "EBT = 0.45x - 1.54 \r<BR>\n" );
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document.write( "EBT (earnings before taxes) is in millions of dollars.\r<BR>\n" );
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document.write( "Taxes = 40% of EBT\r<BR>\n" );
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document.write( "Taxes = 40% of (0.45x - 1.54)\r<BR>\n" );
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document.write( "Taxes = 0.40*(0.45x - 1.54)\r<BR>\n" );
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document.write( "Taxes = 0.40*(0.45x) + 0.40*(-1.54)\r<BR>\n" );
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document.write( "Taxes = 0.18x - 0.616\r<BR>\n" );
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document.write( "Tax amount is in millions of dollars\r<BR>\n" );
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document.write( "Net Income = (EBT) - (Taxes)\r<BR>\n" );
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document.write( "Net Income = (0.45x - 1.54) - (0.18x - 0.616)\r<BR>\n" );
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document.write( "Net Income = 0.45x - 1.54 - 0.18x + 0.616\r<BR>\n" );
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document.write( "Net Income = (0.45x - 0.18x) + (-1.54 + 0.616)\r<BR>\n" );
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document.write( "Net Income = 0.27x - 0.924\r<BR>\n" );
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document.write( "Net Income amount is in millions of dollars\r<BR>\n" );
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document.write( "In the previous section above, the Net Income expression is 0.27x - 0.924 which represents the amount in millions of dollars. <BR>\n" );
document.write( "The desired Net Income amount we want is 2.5 million.<BR>\n" );
document.write( "Set the expression 0.27x - 0.396 equal to 2.5 and solve for x.\r<BR>\n" );
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document.write( "0.27x - 0.924 = 2.5\r<BR>\n" );
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document.write( "0.27x - 0.924 + 0.924 = 2.5 + 0.924 <font color=blue>Add 0.924 to both sides</font>\r<BR>\n" );
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document.write( "0.27x = 3.424\r<BR>\n" );
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document.write( "0.27x/0.27 = 3.424/0.27 <font color=blue>divide both sides by 0.27</font>\r<BR>\n" );
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document.write( "x = 12.68148148148 <font color=blue>use a calculator for this step</font> (this value is approximate)\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "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. \r<BR>\n" );
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document.write( "Final Answer: \r<BR>\n" );
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document.write( "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. \r<BR>\n" );
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document.write( "If you need the more accurate sales figure, then it would be roughly $12,681,481.48\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Sales = $12,681,481.48<BR>\n" );
document.write( "Operating Costs = 0.55*x = 0.55*12681481.48 = 6,974,814.814 = 6,974,814.81<BR>\n" );
document.write( "EBITDA = (Sales) - (Operating Costs) = (12,681,481.48) - (6,974,814.81) = 5,706,666.67<BR>\n" );
document.write( "DA = 880,000<BR>\n" );
document.write( "EBIT = (EBITDA) - (DA) = (5,706,666.67) - (880,000) = 4,826,666.67<BR>\n" );
document.write( "Interest = 660,000<BR>\n" );
document.write( "EBT = EBIT - Interest = 4,826,666.67 - 660,000 = 4,166,666.67<BR>\n" );
document.write( "Taxes = 40% of EBT = 0.4*(4,166,666.67) = 1,666,666.668 = 1,666,666.67<BR>\n" );
document.write( "Net Income = EBT - Taxes = 4,166,666.67 - 1,666,666.67 = 2,500,000\r<BR>\n" );
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document.write( "So that checks out\r<BR>\n" );
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