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Leverage effect and relation between ROE and ROCE:

ROE and ROCE are two closely related notions, which seems intuitive enough since the return enjoyed by shareholders is that of the capital employed plus a correction resulting from the level of debt. The following formula gives an explicit expression for ROE as a function of ROCE plus a correcting factor:

ROE = ROCE + (ROCE – i) x Net Debt/Book value of equity, where i stands for the after-tax cost of debt. The correcting factor, (ROCE – i) x Debt / Book value of equity, is called leverage effect, while the ratio Net Debt / Book value of equity is called “financial leverage” (or “gearing”). You can observe that whenever ROCE > i, any increase in net debt will immediately trigger an increase in ROE: this is the virtuous impact of debt. However, such a boon comes at a price: when increasing its debt level, a company runs the risk that its ROCE will be lower than i, in which case its ROE will diminish because the correcting factor will then be negative. Note that this result is very intuitive because this just says that issuing debt increases ROE only when you are able to invest the proceeds at a rate which is higher that the after-tax interest rate paid on debt.

Derivation of the formula :

The above formula is trivial to derive:

Net Income = NOPAT – Interests paid on debt after tax

ROE x Book value of equity = ROCE x (Book value of equity + Net Debt) – i x Net Debt

ROE x Book value of equity = ROCE x Book value of equity + (ROCE – i) x Net Debt

ROCE = ROCE + (ROCE – i) x Net Debt / Book Value of equity

Short-termism versus long-term profitability:

One of the most severe problems posed by ROE is that this ratio only provides a snapshot of the profitability of the firm (for shareholders) over one fiscal exercise. In particular, this doesn’t say anything about past or future profitability. In this way, you should pay attention not to sacrifice long-term profitability for the sake of short-term ROE: imagine a company with two investment opportunities. The first one is assumed to bring a net profit of $1 this year and $1,000 next year, while the second one is assumed to bring $2 this year and nothing next year. A manager whose objective would be to maximize ROE for this year will be tempted to prefer the second investment opportunity, while it would be clearly preferable to invest in the first project. Why ? Because the Net Present Value of the first project is greater than that of the second one.