Question

Commonwealth Construction (CC) needs $3 million of assets to get started, and it expects to have a basic earning power ratio of 35%. CC will own no securities, so all of its income will be operating income. If it so chooses, CC can finance up to 30% of its assets with debt, which will have an 8% interest rate. If it chooses to use debt, the firm will finance using only debt and common equity, so no preferred stock will be used. Assuming a 40% tax rate on all taxable income, what is the difference between CC’s expected ROE if it finances these assets with 30% debt versus its expected ROE if it finances these assets entirely with common stock?

Answer 1

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.

Step-by-step 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

`BEP=(EBT)/(Assets)\\\\EBT=BEP*Assets=0.35*3,000,000=1,050,000`

Then, if we take into account the tax rate, we calculate the earnings after tax:

`EAT =EBT*(1-TaxRate)=1,050,000*(1-0.4)=630,000`

The ROE in this case is

`ROE=(EAT)/(Assets)=(630,000)/(3,000,000)  =0.21`

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

`I=i*Debt=0.08*(0.3*3,000,000)=0.08*900,000=72,000`

We can calculate now the EBT

`EBT=BEP*Assets-Interest\\\\EBT=0.35*3,000,000-72,000=978,000`

And the earning after tax

`EAT =EBT*(1-TaxRate)=978,000*(1-0.4)=586,800`

The ROE in this case is

`ROE=(EAT)/(Assets)=(586,800)/(3,000,000-900,000)  =(586,800)/(2,100,000)=0.28`

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.