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My guess would be (ROCE - (Total Debt x Cost of debt(1-tax rate))).
but then in % terms it would be infinite % profit (coz of division by zero.) so return would only be defined in $ terms
OK, I see this equation in Tim Koller's (McKinsey & Co) Valuation book, Chapter 7:
ROE=ROIC + [ROIC-(1-T)K]D/E where K is cost of debt and T is tax rate.
When E is zero, D/E will be infinity. Hence the right hand side will be infinity.
Basically, even if ROIC is negative, ROE will be infinity.
What gives? Professor, can you help explain this?
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If ROIC is negative, then right hand side will be negative infinity.
Ok, I think, I get it.
Can you really have a number for the ROE when there is no equity? Return on equity is a number that tells you how much equity holders get in earnings for every equity dollar invested. If there is no equity, how could there be a meaningful number for the return on equity?
Your question has a fundamental flaw. The purpose of equity is to bear the residual risk. If there is no one to bear the residual risk, how can debt get a guaranteed payment. Who is guaranteeing the payment to them? In other words, debt ratios can be high and approach 100% but not be 100%.
Great point professor. You have rightly exposed the flaw in the business model of some house-flippers.
During the recent housing boom, some house flippers got 95% loan from the bank and 5% from friends and relatives. Thay had put in zero equity.
Some of them made money ( infinite ROI) and many of them lost ( infinite ROI).