ROE vs the Price You Pay

1ROE is PAT divided by book equity

Return on equity (ROE) asks: how much profit did the business earn on the owners' book equity? Helio Year 1 PAT is 16. Opening book equity is 80. ROE = 16 / 80 = 20 percent. Some people use average equity (80 + 96) / 2 = 88, which gives 16 / 88 ≈ 18 percent. This lesson uses opening equity so the arithmetic stays one line.

Book equity is an accounting residual on the balance sheet — assets minus liabilities — not the stock-market value of Helio. The share price does not enter this fraction. If someone tells you 'ROE changed' because Helio's ticker doubled, they substituted a market number into a book formula.

Figure. ROE is the 16 of PAT standing on the 80 of book equity — 20 percent. The market price is not in the picture.

How it works

1. NumeratorPAT for the period — Helio 16.
2. DenominatorBook equity, usually opening — Helio 80.
3. Refuse the tickerMarket cap is not book equity.

2You buy at market price, not at book

When you buy Helio, you pay the market price, not the book value. With 10 crore shares and a price of ₹40, market cap is 40 × 10 = ₹400 crore. You are paying 400 for a business that earned 16. Your earnings yield is 16 / 400 = 4 percent — not the 20 percent ROE.

Earnings yield is PAT divided by market cap, or EPS divided by price. Helio EPS is 16 / 10 = ₹1.60. At ₹40, P/E is 40 / 1.60 = 25, and earnings yield is 1 / 25 = 4 percent. ROE told you what the business earned on book. Earnings yield tells you what that earning is relative to the price you actually pay.

Figure. Same 16 of PAT. On book 80 it is 20 percent ROE. On the 400 you pay it is 4 percent earnings yield. The height you paid is the one that sets your starting yield.

How it works

1. Market capPrice times shares — Helio 40 × 10 = 400.
2. Earnings yieldPAT / market cap = 16 / 400 = 4 percent.
3. Keep both20 percent is the business on book; 4 percent is you at this price.

3P/B is the bridge between ROE and earnings yield

Price-to-book is market price divided by book value per share, or market cap divided by book equity. Helio at ₹40: book value per share is ₹8, so P/B = 40 / 8 = 5. Equivalently 400 / 80 = 5.

When ROE uses opening book and the P/E uses the same PAT, earnings yield ≈ ROE / (P/B). Helio: 20 percent / 5 = 4 percent, which matches 16 / 400. A high-ROE business bought at a high P/B can be a low-yield purchase. The bridge is mechanical. It is not a buy or sell rule — Helio might still be able to reinvest at 20 percent, which can justify a P/B above 1. The arithmetic still holds.

Figure. Twenty divided by a P/B of 5 is 4. The first bar is the business on book; the third is what that business yields at today's price.

How it works

1. Compute P/BHelio 400 / 80 = 5.
2. DivideROE / P/B = 20 percent / 5 = 4 percent.
3. CheckThat 4 percent is earnings yield at this price.

4High ROE at a high price can be a poor buy

Helio's 20 percent ROE is a fact about the business on book. At P/B 5 you earn a 4 percent earnings yield on the price you pay. At P/B 1 — price ₹8, market cap 80 — earnings yield equals ROE: 16 / 80 = 20 percent. Same PAT, same book, very different purchase.

This is why a screen that sorts on ROE alone can trick you. The high-ROE name may already be priced so that your yield is ordinary. The cheap-looking low-ROE name may be priced at half of book. Neither fact is a recommendation. The lesson is to pair ROE with P/B (or with earnings yield) before calling a stock 'high quality at any price.' Quality of the business and quality of the purchase are two questions.

Figure. Same Helio, same 20 percent ROE. At book you start at a 20 percent earnings yield; at five times book you start at 4 percent. The missing height is the premium you paid.

How it works

1. BusinessHelio ROE 20 percent at both prices.
2. Purchase A₹40, P/B 5, yield 4 percent.
3. Purchase B₹8, P/B 1, yield 20 percent.

5When the chart moves, ROE usually did not

Suppose Helio's price doubles from ₹40 to ₹80 overnight with no new PAT and no new book equity. ROE is still 16 / 80 = 20 percent. Market cap is now 800, P/B is 10, earnings yield is 16 / 800 = 2 percent, P/E is 50. The chart changed. The business's ROE did not.

People still say 'ROE changed' for three honest mix-ups: they watched price return and named it ROE; a website plotted a market ratio and labelled it ROE; or book equity later changed because of new shares issued at the high price, which can move true ROE next year. The first two are labelling errors. The third is a real book-equity change — still not 'the ticker is the ROE.' If PAT and book did not move, ROE did not move.

How it works

1. Hold PAT and book16 and 80 — ROE locked at 20 percent.
2. Move only price₹40 → ₹80. P/B 5 → 10. Yield 4 percent → 2 percent.
3. Name the moverThe chart. Not ROE.