document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149063>Question 1149063</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a basic formula to calculate \"weighted average cost of capital\" which is this \r<BR>\n" );
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document.write( "WACC = E / (E + D) * Ce + D / (E + D) * Cd * (100% - T)\r<BR>\n" );
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document.write( "E is the equity,<BR>\n" );
document.write( "D is the debt,<BR>\n" );
document.write( "Ce is the cost of equity,<BR>\n" );
document.write( "Cd is the cost of debt, and<BR>\n" );
document.write( "T is the corporate tax rate\r<BR>\n" );
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document.write( "Now from this formula i want to drive formulas for the following<BR>\n" );
document.write( "\"cost of equity \", \"equity\", \"cost of debt\", \"debt\" , \"corporate tax rate\"<BR>\n" );
document.write( "How can i drive those formulas? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770507 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=770507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula needs to be modified somewhat to make it accurate.<BR>\n" );
document.write( "it should be:<BR>\n" );
document.write( "WACC = E / (E + D) * Ce + D / (E + D) * Cd * (1 - T).<BR>\n" );
document.write( "E is value of the equity.<BR>\n" );
document.write( "D is the value of the debt.<BR>\n" );
document.write( "Ce is the cost of equity as a rate, not as a percent.<BR>\n" );
document.write( "Cd is the cost of debt as a rate, not as a percent.<BR>\n" );
document.write( "T is the federal tax rate as a rate, not as a percent.<BR>\n" );
document.write( "it''s not 100% - T.<BR>\n" );
document.write( "it's 1 - T.<BR>\n" );
document.write( "once you get the average cost of capital, you multiply it by 100 to get the percent.\r<BR>\n" );
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document.write( "i'll derive the formulas for you and then give you an example that will show you how it works.\r<BR>\n" );
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document.write( "i'll do it on a manually generated worksheet since it's a real pain to have to type the formulas.\r<BR>\n" );
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document.write( "the first worksheet derives the cost of equity.\r<BR>\n" );
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document.write( "the second worksheet derives the equity.\r<BR>\n" );
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document.write( "the third worksheet derives the cost of debt.\r<BR>\n" );
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document.write( "the fourth worksheet derives the debt.\r<BR>\n" );
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document.write( "the fifth worksheet derives the corporate tax rate.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/112005.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the formulas might have been able to be simplified more than i did, but they work and are fairly clear to understand so i left them the way you see them.\r<BR>\n" );
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document.write( "wen you solve for somthing, you have to isolate that something to one side of the equation and place everything else on the other side of the equation.\r<BR>\n" );
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document.write( "you do that by multiplying or dividing both sides of the equation or adding to or subtracting from both sides of the equation.\r<BR>\n" );
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document.write( "note that if a = b, then b = a.<BR>\n" );
document.write( "i used that to skip some steps.<BR>\n" );
document.write( "otherwise the worksheets would have become unwieldy and i would have had to write more than i cared to.\r<BR>\n" );
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document.write( "anyway, here's your formulas.\r<BR>\n" );
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document.write( "cost of equity:\r<BR>\n" );
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document.write( "Ce = (E + D) / E * WACC - D / E * Cd * (1 - T)\r<BR>\n" );
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document.write( "equity:\r<BR>\n" );
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document.write( "E = D * (WACC - Cd * (1 - T) / (Ce - WACC)\r<BR>\n" );
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document.write( "cost of debt:\r<BR>\n" );
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document.write( "Cd = ((E + D) / E * WACC - E / D * Ce) / (1 - T)\r<BR>\n" );
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document.write( "debt:\r<BR>\n" );
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document.write( "D = (E * (WACC - Ce)) / (Cd * (1 - T) - WACC)\r<BR>\n" );
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document.write( "tax rate:\r<BR>\n" );
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document.write( "T = 1 - ((E + D) / D * WACC - E / D * Ce) / Cd\r<BR>\n" );
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document.write( "to check if the formulas were correct, i used the following example.\r<BR>\n" );
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document.write( "E = 100<BR>\n" );
document.write( "D = 100<BR>\n" );
document.write( "Ce = .15<BR>\n" );
document.write( "Cd = .07<BR>\n" );
document.write( "T = .2\r<BR>\n" );
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document.write( "using the WACC formula, i got:\r<BR>\n" );
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document.write( "WACC = 100 / 200 * .15 + 100 / 200 * .07 * (1 - .2)<BR>\n" );
document.write( " = .103\r<BR>\n" );
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document.write( "my test figures were:\r<BR>\n" );
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document.write( "E = 100<BR>\n" );
document.write( "D = 100<BR>\n" );
document.write( "Ce = .15<BR>\n" );
document.write( "Cd = .07<BR>\n" );
document.write( "T = .2<BR>\n" );
document.write( "WACC = .103\r<BR>\n" );
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document.write( "cost of equity formula was:\r<BR>\n" );
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document.write( "Ce = (E + D) / E * WACC - D / E * Cd * (1 - T)\r<BR>\n" );
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document.write( "this became:\r<BR>\n" );
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document.write( "Ce = 200 / 100 * .103 - 100 / 100 * .07 * (1 - .2) = .15 which is correct.\r<BR>\n" );
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document.write( "equity formula was:\r<BR>\n" );
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document.write( "E = (D * (WACC - Cd * (1 - T)) / (Ce - WACC)\r<BR>\n" );
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document.write( "this became:\r<BR>\n" );
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document.write( "E = 100 * (.103 - .07 * (1 - .2)) / (.15 - .103)) = 100 which is correct.\r<BR>\n" );
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document.write( "cost of debt formula was:\r<BR>\n" );
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document.write( "Cd = ((E + D) / E * WACC - E / D * Ce) / (1 - T)\r<BR>\n" );
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document.write( "this became:\r<BR>\n" );
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document.write( "Cd = ((100 + 100) / 100 * .103 - 100 / 100 * .15) / (1 - .2) = .07 which is correct.\r<BR>\n" );
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document.write( "debt formula was:\r<BR>\n" );
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document.write( "D = (E * (WACC - Ce)) / (Cd * (1 - T) - WACC)\r<BR>\n" );
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document.write( "this became:\r<BR>\n" );
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document.write( "D = (100 * (.103 - .15)) / (.07 * (1 - .2) - .103) = 100 which is correct.\r<BR>\n" );
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document.write( "corporate tax rate formula was:\r<BR>\n" );
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document.write( "T = 1 - ((E + D) / D * WACC - E / D * Ce) / Cd\r<BR>\n" );
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document.write( "this became:\r<BR>\n" );
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document.write( "T = 1 - ((100 + 100) / 100 * .103 - 100 / 100 * .15) / .07 = .2 which is correct.\r<BR>\n" );
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document.write( "as best i can determine, these formulas are good.\r<BR>\n" );
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document.write( "hopefully, you can follow along with what i did in the worksheets.\r<BR>\n" );
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document.write( "if you have some questions, feel free to ask.\r<BR>\n" );
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document.write( "i can't promise to get back to you right away since i have a busy schedule through the weekend.\r<BR>\n" );
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document.write( "the numbers are all there.\r<BR>\n" );
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document.write( "see what you can do and ask what you need to ask.\r<BR>\n" );
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document.write( "i'll answer as soon as i can.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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