The two kinds of claim
Money comes into a company on one of two terms, and almost everything on this page follows from the difference.
A lender has a fixed claim. They are owed a stated amount of interest, and they are owed it whether the year was good or bad. They get no more if it was excellent.
A shareholder has a residual claim. They get whatever is left after the fixed claims are met — which may be a great deal, nothing, or less than nothing.
Gearing is the proportion of the capital that carries the fixed claim. Raise it and you have not changed what the business earns; you have changed how the earnings are divided, and specifically you have put a bigger fixed slice ahead of a smaller residual slice.
The mechanism, in one sentence
The business earns a return on all of its capital. The lenders take a fixed rate on their part. Everything above that fixed rate, on the borrowed money, belongs to the shareholders — and so does everything below it.
That is the whole of gearing, and it can be written down exactly. Let ROCE be the return on capital employed, i the interest rate on the debt, D the debt and E the equity. Then
Read the second term carefully, because it contains three separate pieces of information.
The sign is the sign of (ROCE − i). Borrowing helps the shareholder only while the business earns more on the money than the money costs. Not sometimes — always, and only.
The size is set by D ÷ E. The gap between ROCE and the interest rate is multiplied by the amount of debt per rupee of equity. Double the gearing and you double the stretch, up and down alike.
When ROCE equals i the term vanishes. At that one operating profit, gearing makes no difference at all. Below it, borrowing is actively destroying the shareholders' return.
The worked example below builds a table of four trading outcomes for two capital structures, then reproduces every single figure from this formula.
What gearing really costs
A student who sees the good-year row concludes that companies should borrow as much as they can. Three things stop them, and they are not the same thing.
The return becomes more volatile
This is the amplification itself, and it is the honest cost. The shareholder in a geared company holds a claim on a more variable stream, and a more variable stream is worth less per rupee of expected return. You have not been given something for nothing; you have been given a higher expected return for a higher risk.
There is a point where the business cannot pay
Interest is a legal obligation. Miss it and the lenders can act — demand security, impose conditions, appoint a receiver, force a sale. Volatility in a return is unpleasant; insolvency is terminal, and the whole of a company's value can be destroyed by a shortfall far smaller than the company. This is why interest cover, operating profit divided by interest, is read alongside gearing: gearing says how much is owed, cover says how close the company is to not being able to pay it.
Borrowing gets dearer as you do more of it
The interest rate i in the formula is not a constant. A lender arriving after a lot of other lenders is further back in the queue and prices accordingly. So the gap (ROCE − i) narrows exactly as the multiplier D ÷ E grows, and the two effects fight. That is the real reason there is an optimum rather than a corner solution.
Two ways to measure it, and why the answer differs
Gearing is quoted either as debt over equity or as debt over total capital. For debt of 500 against equity of 500 the first gives 100% and the second 50%, and both are correct. A ratio with no stated definition is unusable, so state yours.
Two further judgements change the figure, and a question will usually expect you to notice them. Market or book values? The theory wants market values, because that is what a shareholder could sell for; the balance sheet offers book values, and for a company whose shares trade well above book the two gearings are very different. What counts as debt? A long-term loan obviously does. A renewed-every-year overdraft, a finance lease, a pension deficit and a parent company guarantee all behave like debt and may not be sitting where you would look for them.
Why an actuary is made to learn this
A general insurer's capital is geared by its liabilities in the same way, and reinsurance is in part a way of managing that gearing. More directly: the amplification above is why a regulator cares about the capital structure of an insurer and not only about its assets, and why a pension scheme's deficit changes the risk of the sponsoring company's shares. In every case the business has not changed and the claim on it has.
Where marks are lost
Saying gearing increases returns. It increases the spread of returns. Write both directions or the statement is wrong half the time.
Using profit after interest in ROCE. It breaks the formula on this page, because the formula's ROCE is the return on all the capital, before anybody has been paid.
Quoting gearing without interest cover. Two companies at the same gearing, one earning four times its interest and one earning 1.1 times, are not in comparable positions.
Forgetting tax. This page deliberately ignores it, to keep one mechanism on show. Interest is normally deductible and dividends are not, which gives debt a genuine tax advantage on top of everything here. That is the subject of the tax page, and an exam answer about the optimal structure that omits it is incomplete.
Questions students ask
If ROCE beats the interest rate, why not borrow everything?
Because the three costs above all grow with gearing, and the last one bites hardest: as debt rises the interest rate rises, so the gap being multiplied shrinks. Add the risk of not being able to pay at all, and there is an interior optimum.
Does gearing change the value of the whole company?
This is the deep question in the topic, and the useful first answer is: not by itself. Dividing the same earnings differently does not create any. What can change the total is real: the tax relief on interest adds value, and the cost of getting into financial distress subtracts it. The familiar conclusion — that there is a best mix — comes from those two real effects, not from the amplification on this page.
Is preference share capital debt or equity?
For this mechanism, treat it by its behaviour rather than its name. A fixed, prior dividend behaves like interest and belongs in the geared slice; whether the dividend is legally compulsory and whether it is tax-deductible are separate questions that change the arithmetic. Say which treatment you have chosen.
A worked example
An invented example, built for this page. One business, two capital structures, ₹1,000 lakh of capital employed in both. All figures are made up, and tax is ignored throughout so that one mechanism is on show.
- Structure A, ungeared: equity ₹1,000 lakh, no debt.
- Structure B, geared: equity ₹500 lakh, debt ₹500 lakh at 10% — so interest is ₹50 lakh every year, good or bad.
Four trading outcomes
Operating profit is the same in both structures, because the structure does not change the business.
| Operating profit | ROCE | A: ROE | B: profit after interest | B: ROE |
|---|---|---|---|---|
| ₹200 lakh | 20% | 200 ÷ 1,000 = 20% | 200 − 50 = ₹150 lakh | 150 ÷ 500 = 30% |
| ₹100 lakh | 10% | 100 ÷ 1,000 = 10% | 100 − 50 = ₹50 lakh | 50 ÷ 500 = 10% |
| ₹60 lakh | 6% | 60 ÷ 1,000 = 6% | 60 − 50 = ₹10 lakh | 10 ÷ 500 = 2% |
| ₹40 lakh | 4% | 40 ÷ 1,000 = 4% | 40 − 50 = (₹10 lakh) | −10 ÷ 500 = −2% |
In the good year the geared shareholders earn 30% where the ungeared earn 20%. In the poor year they earn 2% where the ungeared earn 6%, and in the worst row they lose money on a business that is still trading at a profit. Nothing about the trading differed between the columns.
Every row again, from the formula
Here D ÷ E = 500 ÷ 500 = 1 and i = 10%, so ROE = ROCE + 1 × (ROCE − 10%). Using the ROCE figures printed in the table:
| ROCE | Formula | Gives | Table says |
|---|---|---|---|
| 20% | 20 + 1 × (20 − 10) | 30% | 30% |
| 10% | 10 + 1 × (10 − 10) | 10% | 10% |
| 6% | 6 + 1 × (6 − 10) | 2% | 2% |
| 4% | 4 + 1 × (4 − 10) | −2% | −2% |
Four for four. The formula is not a separate fact to memorise; it is the table rearranged, and the agreement is the check.
The break-even, found two ways
Row two is the pivot: at a ROCE of 10% the two structures give the same 10%, because the business is earning exactly what the borrowing costs. In money, that is an operating profit of
Reach it from the other direction as a check. The structures are equal when operating profit ÷ 1,000 = (operating profit − 50) ÷ 500. Cross-multiplying gives 500P = 1,000P − 50,000, so 500P = 50,000 and P = ₹100 lakh. The same figure, and it is also exactly the interest bill divided by the proportion of the capital that is borrowed: 50 ÷ 0.5 = ₹100 lakh. Three routes, one answer.
So ₹100 lakh of operating profit is the line this company is betting on. Above it, borrowing pays the shareholders; below it, borrowing costs them.
Now gear it harder
Structure C: equity ₹250 lakh, debt ₹750 lakh at the same 10%, so interest is ₹75 lakh and D ÷ E = 3.
| Operating profit | ROCE | After interest | ROE, directly | ROE, from the formula |
|---|---|---|---|---|
| ₹200 lakh | 20% | 200 − 75 = ₹125 lakh | 125 ÷ 250 = 50% | 20 + 3 × (20 − 10) = 50% |
| ₹60 lakh | 6% | 60 − 75 = (₹15 lakh) | −15 ÷ 250 = −6% | 6 + 3 × (6 − 10) = −6% |
Tripling the multiplier tripled the stretch in both directions: the good-year premium over ROCE went from 10 points to 30, and the poor-year shortfall from 4 points to 12. The direct calculation and the formula agree in both rows.
Interest cover, which is the number that matters at the bottom
Using the printed operating profits and interest bills:
| Operating profit | B, interest ₹50 lakh | C, interest ₹75 lakh |
|---|---|---|
| ₹200 lakh | 4.0 times | 2.7 times |
| ₹60 lakh | 1.2 times | 0.8 times |
The 2.7 is 200 ÷ 75 = 2.666…, printed to one decimal. The row that matters is the last cell: at a cover below 1.0 the company cannot pay its interest out of its trading at all, and must find the money from cash, from a sale or from its lenders' goodwill. The ROE of −6% in the table above understates that situation badly, because it describes a loss to shareholders in a year when the real question was survival.
Where this fits in CB1
This page explains one idea from CB1 Business Finance. The full CB1 syllabus, with what each part is examined on, sits on the course page, and past-paper style mock exams with full solutions are where you find out whether the idea has stuck under time pressure.
Other CB1 topics explained
- Why financial reporting is regulated, and who it is regulated for
- Share capital and loan capital: why each source costs what it does
- Leasing against buying, and the only comparison that settles it
- Profit is not cash, and why a growing company can run out of money
- Return on capital employed, and the two things that drive it
- Modigliani-Miller: why gearing does not create value, and what does
- Dividend irrelevance, and the four reasons dividends still matter
- The cost of capital, and why a project must beat the whole pot
- NPV against IRR, and the three times IRR gives the wrong answer
- Working capital: the days between paying out and being paid
- Valuing a company: discounted cash flow against comparable multiples
- Synergies and the takeover premium: who actually gets the gain
- Company tax in an appraisal, and the relief that reverses the answer
- Interest rate swaps: fixing a floating cost, and where the saving comes from
- Hedging currency risk: the forward contract and the money-market hedge
Stuck on a term rather than the idea? The actuarial glossary defines the notation used above. If something here is wrong or unclear, tell us — these pages get corrected.