Including Taxes
def unlever(r_a,r_d,E,D):
return r_a + (r_a-r_d)*(D/E)
print(unlever(.08,.04,100,0))
print(unlever(.08,.04,100,100))
print(unlever(.08,.04,100,200))
print(unlever(.08,.02,100,200))You should notice that the required return on equity is 8% when there is no debt, and that it keeps going up as we take more debt on and/or the rate of debt goes down.
The final part of this lesson, is how to include taxes. As you should remember, there is a tax shield associated with debt interest payments and we need to include it in our analysis. The revised equations including tax are below:
Equation
a
= r
e
* E/(D+E) + r
d
* D/(D+E) * (1-T)
r
a
= Return on Assets
r
e
= Return on Equity
r
d
= Return on Debt
E = Equity Value
D = Debt Value
T = Tax Rate
Equation
a
= B
e
* E/(D+E) + B
d
* D/(D+E) * (1-T)
B
a
= Beta for Assets
B
e
= Beta for Equity
B
d
= Beta for Debt
E = Equity Value
D = Debt Value
T = Tax Rate
Equation
e
= r
a
+ (r
a
– r
d
) * D/E * (1-T)
r
a
= Return on Assets
r
e
= Return on Equity
r
d
= Return on Debt
E = Equity Value
D = Debt Value
T = Tax Rate
Equation
e
= B
a
+ (B
a
– B
d
) * D/E * (1-T)
B
a
= Beta for Assets
B
e
= Beta for Equity
B
d
= Beta for Debt
E = Equity Value
D = Debt Value
T = Tax Rate
Another important thing to consider is net debt. Net debt is the debt we use for D considering cash on hand. The idea is that the cash balances off debt, and even more so can make your equity less risky if there is more cash than debt
For this example, let’s say the return on assets is .08, the return on debt is .04, equity is 100 and debt is 100. We are going to see what happens when the cash on hand it 0,100, and 150.
print(unlever(.08,.04,100,100-0))
print(unlever(.08,.04,100,100-100))
print(unlever(.08,.04,100,100-150))When cash perfectly balances out debt (example 2), the equity r is equal to the r for assets. When there is more cash, then the net debt is actually negative, and the rate for equity is lower than the rate for assets.
Source Code