LeverCo is financed entirely by equity. The company generates operating profit e

Question

LeverCo is financed entirely by equity. The company generates operating profit equal to $80 million. LeverCO currently trades at an equity value of $900 million. At a tax rate of 25 percent, what is the price-to-earnings multiple for LeverCo? New management decides to increase leverage through a share repurchase. The company issues $400 million in bonds to retire $400 million in equity. If the bonds pay interest at 5 percent, what is the company’s new price-to-earnings ratio? Could you predict the direction the P/E ratio would move without performing this calculation?

Explanation / Answer

Initially:

Operating Profit=80 million

Taxes=80*25%=20 million

Net Income=60 million

P/E=900/60=15

After share repurchase:

Operating Profit=80 million

Interest 400*5%=20 million

Profit Before Taxes=80-20=60 million

Taxes=60*25%=15 million

Net Income=45 million

New Equity=900-400=500

P/E=500/57=8.772

Yes, we can predict that P/E would go down without performing the calculation

In the below calculatins, Equity means initial equity before debt

As, P/E after Debt=(Equity-Debt)/(Operating Profit*(1-tax rate)-Debt*Interest Rate*(1-tax rate))=(Equity-Debt)/((1-tax rate)*(Operating Profit-Debt*Interest Rate))

P/E before Debt=(Equity)/(Operating Profit*(1-tax rate))

P/E before Debt-P/E after Debt=(Equity)/(Operating Profit*(1-tax rate))-(Equity-Debt)/((1-tax rate)*(Operating Profit*-Debt*Interest Rate))=1/(1-tax rate)*(Equity/Operating Profit-(Equity-Debt)/(Operating Profit*-Debt*Interest Rate))

=(Equity*Operating profit-Equity*Debt*Interest Rate-Equity*Operating Profit+Debt*Operating profit)/(Operating Profit*(Operating Profit*-Debt*Interest Rate)*(1-tax rate))

=Debt*(-Equity*Interest Rate+Operating Profit)/((1-tax rate)*Operating Profit*(Operating Profit-Debt*Interest Rate))

So, if Operating Profit>Equity*Interest Rate and Debt*Interest Rate, then P/E would decrease

or if Operating Profit<Equity*Interest Rate and Debt*Interest Rate, then P/E would decrease

However if Operating Profit>Equity*Interest Rate and <Debt*Interest Rate, then P/E would increase

Operating Profit<Equity*Interest Rate and > Debt*Interest Rate, then P/E would increase

In our case, Equity*Interest Rate=900*5%=45 and Debt*Interest Rate=400*5%=20

Operating Profit at 80 is >Equity*Interest Rate and is >Debt*Interest Rate so, P/E would decrease

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