Return on equity under leverage
How borrowing changes the return an investor earns on their own money — in the workbook's own caselet, a 10% yielding asset bought with 1.4 times leverage returns 11.4% on the investor's own funds.
In plain language
Borrowing money to invest changes the return an investor earns on their own cash. It does not just add risk. It changes the number itself.
Return on equity, in this sense, is the return earned on the investor's own money alone, not on the total amount invested. Leverage can push this number above the return the underlying asset earns, or below it, depending on what the loan costs.
How it works
The workbook's own caselet: Ms T invests Rs 60,000 in an asset yielding 10%, using leverage of 1.4 times, borrowing at 9% a year. A leverage ratio of 1.4 means the borrowed amount is 1.4 times her own funds — not that the total invested is 1.4 times her own funds.
Own funds = Rs 60,000 ÷ (1 + 1.4) = Rs 25,000. Borrowed = Rs 60,000 − Rs 25,000 = Rs 35,000.
Interest paid = Rs 35,000 × 9% = Rs 3,150. Gross return on the asset = Rs 60,000 × 10% = Rs 6,000. Net return = Rs 6,000 − Rs 3,150 = Rs 2,850.
Return on equity = Rs 2,850 ÷ Rs 25,000 = 11.4% — higher than the asset's own 10% yield, because the 9% cost of borrowing is lower than the 10% the borrowed money earned.
The formula
Own funds = Total investment / (1 + leverage ratio)
Borrowed = Total investment - Own funds
Interest = Borrowed x borrowing rate
Gross return = Total investment x asset yield
Net return = Gross return - Interest
Return on equity = Net return / Own funds
A worked example
This is the workbook's own Module 12 caselet, put as four linked multiple-choice sub-questions.
| Question | Options given | Worked answer |
|---|---|---|
| Own funds invested | Rs 35,000 / Rs 25,000 / Rs 42,857 / Rs 17,143 | Rs 25,000 |
| Interest paid | Rs 2,250 / Rs 5,400 / Rs 3,150 / Rs 3,500 | Rs 3,150 |
| Net return | Rs 6,000 / Rs 2,850 / Rs 3,750 / Rs 2,500 | Rs 2,850 |
| Return on equity | 1% / 10.4% / 10.9% / 11.4% | 11.4% |
Every option in the caselet matches this single, consistent calculation. Leverage of 1.4 times means Rs 1.40 of borrowing for every Rs 1 of Ms T's own money, not a total exposure of 1.4 times her own funds. Reading leverage the other way round changes all four answers.
Why NISM asks about it
Module 12 (Comprehensive Investment Advice I), Module-end Question 3, sets out Ms T's leverage caselet as four linked sub-questions on own funds, interest, net return and return on equity. Expect all four to be tested together, since getting the leverage ratio wrong at the first step throws off every answer that follows.
Common exam traps
- Leverage of 1.4 times means borrowed ÷ own funds = 1.4, not total ÷ own funds = 1.4. Reading it the second way gives a different, wrong own-funds figure.
- Leverage cuts both ways. Because the asset's 10% yield beat the 9% cost of borrowing, leverage raised the return above 10%. Had the borrowing rate exceeded the yield, leverage would have pulled return on equity below it instead.
- This return on equity is specific to one leveraged trade, not the company balance-sheet ratio of profit after tax over net worth tested elsewhere in the syllabus — the mechanics are related, but the inputs are different.