Respuesta :
Answer:
The difference of the ROE between financing with 30% debt and the ROE of financing only with common stocks is 0.07, in favor of financing with debt.
This difference is because it has an operational leverage: the return on assets is bigger than the interest paid for debt.
Explanation:
We have to calculate the return on equity (ROE) for two situations:
1) No debt
In this case, all $3 millions of assets will be financed by common equity.
The EBT can be calculated as
[tex]BEP=\frac{EBT}{Assets}\\\\EBT=BEP*Assets=0.35*3,000,000=1,050,000[/tex]
Then, if we take into account the tax rate, we calculate the earnings after tax:
[tex]EAT =EBT*(1-TaxRate)=1,050,000*(1-0.4)=630,000[/tex]
The ROE in this case is
[tex]ROE=\frac{EAT}{Assets}=\frac{630,000}{3,000,000} =0.21[/tex]
The return on equity (ROE) is 21% or $0.21 per $1 of equity.
2) With 30% debt
In this case, the assets are financed 30% by debt and 70% by common stocks.
The annual interest of this debt are
[tex]I=i*Debt=0.08*(0.3*3,000,000)=0.08*900,000=72,000[/tex]
We can calculate now the EBT
[tex]EBT=BEP*Assets-Interest\\\\EBT=0.35*3,000,000-72,000=978,000[/tex]
And the earning after tax
[tex]EAT =EBT*(1-TaxRate)=978,000*(1-0.4)=586,800[/tex]
The ROE in this case is
[tex]ROE=\frac{EAT}{Assets}=\frac{586,800}{3,000,000-900,000} =\frac{586,800}{2,100,000}=0.28[/tex]
The return on equity (ROE) is 28% or $0.28 per $1 of equity.
The difference is because it has an operational leverage: the return on assets is bigger than the interest paid for debt.
