The r for Equity
Let’s first pretend that our company was going to be all equity financed. The way we might determine our “r” is to look at other companies and what their r is for equity. There is one problem, however. Debt tends to make equity riskier. This is because debt holders have first dibs to any assets if a company were to go bankrupt; additionally large amounts of debt can be dangerous for companies.
The way we get rid of the effects of debt on equity is through a process called unlevering. Before we begin with unlevering, let’s look at how the rate of return on assets is defined.
Equation
a
= r
e
* E/(D+E) + r
d
* D/(D+E)
r
a
= Return on Assets
r
e
= Return on Equity
r
d
= Return on Debt
E = Equity Value
D = Debt Value
Theoretically our rate for debt shouldn’t be changing, so as you can see from this equation the more debt you take on, the higher the return on equity will have to be to balance the lower return on debt. This same idea applies to betas as well!
Equation
a
= B
e
* E/(D+E) + B
d
* D/(D+E)
B
a
= Beta for Assets
B
e
= Beta for Equity
B
d
= Beta for Debt
E = Equity Value
D = Debt Value
Thankfully, to unlever the rate and the beta, all you need to do is re-arrange these equations
Equation
e
= r
a
+ (r
a
– r
d
) * D/E
r
a
= Return on Assets
r
e
= Return on Equity
r
d
= Return on Debt
E = Equity Value
D = Debt Value
Equation
e
= B
a
+ (B
a
– B
d
) * D/E
B
a
= Beta for Assets
B
e
= Beta for Equity
B
d
= Beta for Debt
E = Equity Value
D = Debt Value
Challenge
|
r e |
r a |
r d | E | D | |||
| ? | .08 | .04 | 100 | 0 | |||
| ? | .08 | .04 | 100 | 100 | |||
| ? | .08 | .04 | 100 | 200 | |||
| ? | .08 | .02 | 100 | 200 |