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  1. 076A bank has book equity of Rs 20,000 crore, a sustainable return on equity of 15%, a cost of equity of 12% and long-run growth of 6%. Estimate its market capitalisation.Capital and leverageCoreScotiabankToronto · 2025

    Try it first

    Before any formula: is this bank worth more or less than its Rs 20,000 crore book?

    Show the worked solution

    About Rs 30,000 crore, 1.5 times book. For a bank growing steadily, price to book equals ROE less growth, over cost of equity less growth: (15 - 6) / (12 - 6) = 1.5. Book of Rs 20,000 crore times 1.5 gives Rs 30,000 crore. A cross-check: earnings of Rs 3,000 crore at a P/E of 10 gives the same figure.

    Why does ROE against cost of equity decide the answer?

    Imagine a fixed deposit that pays exactly the return you demand. Nobody would pay more than its face value, and nobody would sell it for less. A deposit paying more than you demand is worth a premium; one paying less sells at a discount. A bank's book equity is that deposit. A bank that earns exactly its cost of equity is worth its book, and every point of ROE above that cost is priced as a premium to book. Here the bank earns 15% on capital that shareholders price at 12%, so you already know the answer is above Rs 20,000 crore before touching the arithmetic.

    A bank is worth more than its book only when ROE beats the cost of equity0.5x1.0x1.5x2.0x2.5x0ROE 12% = cost of equity: 1.0xROE 15%: 1.5x bookEarns less than it costs:trades below bookEarns more than it costs:trades above book6%9%12%15%18%21%Return on equityPrice to book(ROE - g) / (ke - g)= (15 - 6) / (12 - 6)= 1.5x bookBook Rs 20,000 crx 1.5Rs 30,000 crmarket cap
    With a 12% cost of equity and 6% growth, price to book crosses 1.0 at an ROE of 12% and reaches 1.5 at 15%, so the bank's Rs 20,000 crore of book equity is worth about Rs 30,000 crore.

    Where does the formula come from, so you can rebuild it under pressure?

    Start from a dividend growth model. To grow book at 6% while earning 15%, the bank must keep 6 over 15, or 40%, of its profit, and it can pay out the other 60%. That means the dividend is book times ROE less growth, and dividing by cost of equity less growth gives the price. Earnings are Rs 3,000 crore, the payout is Rs 1,800 crore, and Rs 1,800 crore divided by 12% less 6% is Rs 30,000 crore.

    The relationship
    PB=ROE−gke−g=0.15−0.060.12−0.06=1.5\frac{P}{B} = \frac{ROE - g}{k_e - g} = \frac{0.15 - 0.06}{0.12 - 0.06} = 1.5
    P/Bmarket capitalisation over book equity
    ROEsustainable return on book equity, 15%
    k_ecost of equity, 12%
    glong-run growth in book and dividends, 6%
    What it says in wordsPrice to book is the excess of ROE over growth, divided by the excess of the cost of equity over growth.

    What would a risk interviewer want you to add?

    Say how fragile the number is. The denominator is only 6 points wide, so a one point rise in the cost of equity to 13% cuts price to book from 1.5 to 1.29, a fall of 14% in market value. The word sustainable is also doing work: a 15% ROE earned in a benign credit year, before loan losses normalise, is not the same as 15% through a cycle. A stress-testing team cares because a bank trading below book is telling you the market doubts its ROE or its asset values.

    Where candidates lose it

    The common miss is answering Rs 20,000 crore, treating book value as the value of a bank. Book is only the starting point; the premium or discount comes entirely from ROE against the cost of equity.

    The second is plugging 15% and 12% into a P/E formula without growth and getting lost. Say the price to book shortcut out loud, then back it up with earnings of Rs 3,000 crore at a P/E of 10.

    What the interviewer asks next

    • Loan losses rise and sustainable ROE falls to 10%. What happens to the market capitalisation?
    • What does a bank trading at 0.6 times book tell you about how the market views its loan book?
    • Why might a bank with a high CET1 ratio still earn a low ROE?

    Asked at Scotiabank, Risk, Toronto, 2025 (Wall Street Oasis): The market cap of the bank