Question 1149063: I have a basic formula to calculate "weighted average cost of capital" which is this
WACC = E / (E + D) * Ce + D / (E + D) * Cd * (100% - T)
E is the equity,
D is the debt,
Ce is the cost of equity,
Cd is the cost of debt, and
T is the corporate tax rate
Now from this formula i want to drive formulas for the following
"cost of equity ", "equity", "cost of debt", "debt" , "corporate tax rate"
How can i drive those formulas?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula needs to be modified somewhat to make it accurate.
it should be:
WACC = E / (E + D) * Ce + D / (E + D) * Cd * (1 - T).
E is value of the equity.
D is the value of the debt.
Ce is the cost of equity as a rate, not as a percent.
Cd is the cost of debt as a rate, not as a percent.
T is the federal tax rate as a rate, not as a percent.
it''s not 100% - T.
it's 1 - T.
once you get the average cost of capital, you multiply it by 100 to get the percent.
i'll derive the formulas for you and then give you an example that will show you how it works.
i'll do it on a manually generated worksheet since it's a real pain to have to type the formulas.
the first worksheet derives the cost of equity.
the second worksheet derives the equity.
the third worksheet derives the cost of debt.
the fourth worksheet derives the debt.
the fifth worksheet derives the corporate tax rate.
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.
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.
you do that by multiplying or dividing both sides of the equation or adding to or subtracting from both sides of the equation.
note that if a = b, then b = a.
i used that to skip some steps.
otherwise the worksheets would have become unwieldy and i would have had to write more than i cared to.
anyway, here's your formulas.
cost of equity:
Ce = (E + D) / E * WACC - D / E * Cd * (1 - T)
equity:
E = D * (WACC - Cd * (1 - T) / (Ce - WACC)
cost of debt:
Cd = ((E + D) / E * WACC - E / D * Ce) / (1 - T)
debt:
D = (E * (WACC - Ce)) / (Cd * (1 - T) - WACC)
tax rate:
T = 1 - ((E + D) / D * WACC - E / D * Ce) / Cd
to check if the formulas were correct, i used the following example.
E = 100
D = 100
Ce = .15
Cd = .07
T = .2
using the WACC formula, i got:
WACC = 100 / 200 * .15 + 100 / 200 * .07 * (1 - .2)
= .103
my test figures were:
E = 100
D = 100
Ce = .15
Cd = .07
T = .2
WACC = .103
cost of equity formula was:
Ce = (E + D) / E * WACC - D / E * Cd * (1 - T)
this became:
Ce = 200 / 100 * .103 - 100 / 100 * .07 * (1 - .2) = .15 which is correct.
equity formula was:
E = (D * (WACC - Cd * (1 - T)) / (Ce - WACC)
this became:
E = 100 * (.103 - .07 * (1 - .2)) / (.15 - .103)) = 100 which is correct.
cost of debt formula was:
Cd = ((E + D) / E * WACC - E / D * Ce) / (1 - T)
this became:
Cd = ((100 + 100) / 100 * .103 - 100 / 100 * .15) / (1 - .2) = .07 which is correct.
debt formula was:
D = (E * (WACC - Ce)) / (Cd * (1 - T) - WACC)
this became:
D = (100 * (.103 - .15)) / (.07 * (1 - .2) - .103) = 100 which is correct.
corporate tax rate formula was:
T = 1 - ((E + D) / D * WACC - E / D * Ce) / Cd
this became:
T = 1 - ((100 + 100) / 100 * .103 - 100 / 100 * .15) / .07 = .2 which is correct.
as best i can determine, these formulas are good.
hopefully, you can follow along with what i did in the worksheets.
if you have some questions, feel free to ask.
i can't promise to get back to you right away since i have a busy schedule through the weekend.
the numbers are all there.
see what you can do and ask what you need to ask.
i'll answer as soon as i can.
|
|
|
