Debt Capital Markets puzzles, solved step by step

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  1. 046A company has 50 of debt and 50 of equity at market value, trades at 10x earnings and pays 6% on its debt. What is its WACC before and after a 25% tax rate on interest?Cost of capital and valuation riddlesWarm upCitiNew York · 2026

    Try it first

    What cost of equity does a P/E of 10 suggest, as a quick proxy?

    Show the worked solution

    WACC is 8.0% before tax and 7.25% after. Read the cost of equity as the earnings yield, 1 over a P/E of 10, which is 10%. Half the capital costs 10% and half costs 6%, so the blend is 8.0%. The tax shield cuts debt to 6% x 0.75 = 4.5%, and the blend falls to 7.25%. The P/E shortcut assumes no growth; with growth the true cost of equity is higher.

    Where does the cost of equity come from when you are not given a beta?

    If a shop earns Rs 10,000 a year and sells for Rs 1 lakh, a buyer earns 10% on the price. Nobody would pay more unless they expected growth, so 10% is roughly what buyers of such a shop demand. A P/E of 10 means earnings are a tenth of the price, an earnings yield of 10%, and with no growth that is a quick proxy for the cost of equity. Say out loud that it is a proxy: it is the fastest honest route when the interviewer gives you only a multiple.

    The relationship
    WACC=EVke+DVkd(1−t)=0.5×10%+0.5×6%×0.75=7.25%WACC = \tfrac{E}{V}k_e + \tfrac{D}{V}k_d(1-t) = 0.5 \times 10\% + 0.5 \times 6\% \times 0.75 = 7.25\%
    E/V, D/Vequity and debt as shares of total capital at market value, 0.5 each
    k_ecost of equity, here the earnings yield 1 / 10 = 10%
    k_dcost of debt, 6%
    ttax rate on interest, 25%
    What it says in wordsWeight each funder's required return by its share of the capital, and cut the debt cost by the tax it saves.
    Weight each funder's cost by its share of the capitalEquity 50cost 10% = 1 / P/EDebt 50cost 6%, 4.5% after taxMarket valuesBefore tax: 0.5 x 10% + 0.5 x 6%equity 5.0debt 3.0= 8.00%After tax: 0.5 x 10% + 0.5 x 4.5%equity 5.0debt 2.25= 7.25%0%5%10%The tax shield on interest takes 0.75 points off the blend
    Equity of 50 costing 10% and debt of 50 costing 6% blend to 8.0% before tax, and to 7.25% once interest is deducted at 25%, because the debt's after-tax cost falls to 4.5%.

    Why does tax only touch the debt half?

    Interest is paid before tax and dividends after it. Every rupee of interest reduces taxable profit, so the government in effect pays a quarter of the interest bill at a 25% tax rate, and debt that costs 6% on paper costs 4.5% to the company. Equity gets no such relief. That is why the after-tax WACC is 0.75 points lower: half the capital times the 1.5 point shield. The difference compounds into valuation, since a lower discount rate raises the value of every future cash flow.

    State the limit of the shortcut before the interviewer does. The earnings yield equals the cost of equity only for a company that does not grow and pays out all its earnings. If earnings grow at 3% a year, investors paying 10x are expecting roughly 10% plus 3%, about 13%, and the WACC rises with it. For a real company you would build the cost of equity from a risk-free rate, a beta and a market premium instead.

    Where candidates lose it

    The common error is using 10 as a percentage or treating the P/E itself as a cost. Invert it: a multiple becomes a yield only when you flip it.

    The second loss is giving one WACC and not saying whether it is before or after tax. The question asked for both on purpose; give 8.0% and 7.25% and say where the 0.75 points went.

    What the interviewer asks next

    • The company re-levers to 70% debt at a 7% cost. What happens to WACC, and what should happen to the cost of equity?
    • If earnings grow at 4% a year, what cost of equity does a P/E of 10 imply?
    • Why do you use market values rather than book values for the weights?

    Asked at Citi, Capital Markets, New York, 2026 (Wall Street Oasis): $50 debt, $50 equity, P/E 10x, Cost of Debt 6%, what is WACC

  2. 076A conglomerate owns three businesses worth Rs 1,200 crore, Rs 800 crore and Rs 500 crore of enterprise value. The market applies a 15% holding company discount to the sum of the parts. Net debt is Rs 600 crore and there are 50 crore shares. What is the value per share, and what would it be with no discount?Cost of capital and valuation riddlesCoreDeutsche BankMumbai · 2024

    Try it first

    Before you calculate: the discount is 15% of enterprise value. How much does the value per share fall?

    Show the worked solution

    Rs 30.5 per share with the discount and Rs 38.0 without it. The parts add to Rs 2,500 crore. A 15% discount takes off Rs 375 crore, leaving Rs 2,125 crore of enterprise value. Less Rs 600 crore of net debt gives equity of Rs 1,525 crore over 50 crore shares. With no discount equity is Rs 1,900 crore, or Rs 38.0. A 15% discount costs shareholders 19.7%.

    Why does the discount come off before the debt?

    Think of a house worth Rs 1 crore with a Rs 60 lakh home loan on it. If buyers suddenly pay 15% less for houses on that street, the house is worth Rs 85 lakh, the bank is still owed Rs 60 lakh, and the owner's share drops from Rs 40 lakh to Rs 25 lakh. A conglomerate works the same way. The holding company discount is a haircut on what the whole group is worth, and the lenders' claim is a fixed number that sits ahead of the shareholders, so the haircut is taken from enterprise value and passes through to equity untouched.

    So the order is: value each business, add them to get the sum of the partsValuing each business on its own, usually against its own peers, and adding the values together., apply the holding company discountThe gap between what a group trades at and what its businesses would be worth separately, often blamed on head office costs, capital allocation or tax leakage. to the total, subtract net debt, and divide by shares. Rs 2,500 crore less Rs 375 crore is Rs 2,125 crore; less Rs 600 crore is Rs 1,525 crore; over 50 crore shares is Rs 30.5.

    The discount comes off the whole group, then the debt comes off in full1,200Unit A800Unit B500Unit C2,500Sum-375Discount-600Net debt1,525Equityless 15%, then less debtEnterprise value falls 15.0%Equity falls 19.7%Rs 38.0no discountRs 30.515% discountvalue per share
    The three businesses add to Rs 2,500 crore; the 15% discount removes Rs 375 crore and net debt removes Rs 600 crore, leaving equity of Rs 1,525 crore, or Rs 30.5 a share against Rs 38.0 with no discount.
    The relationship
    Value per share=(1−d)∑EVi−NDN=0.85×2,500−60050=30.5\text{Value per share} = \frac{(1-d)\sum EV_i - ND}{N} = \frac{0.85 \times 2{,}500 - 600}{50} = 30.5
    dthe holding company discount, 15%
    EV_ithe enterprise value of each business
    NDnet debt, Rs 600 crore
    Nshares outstanding, 50 crore
    What it says in wordsDiscount the sum of the businesses, take off what the lenders are owed, and share what is left.

    Why does a 15% discount cost the shareholders more than 15%?

    Equity is the thin slice left after debt, so any fall in enterprise value is a bigger fall as a share of equity. The Rs 375 crore haircut is 15% of Rs 2,500 crore but 19.7% of Rs 1,900 crore. Push net debt to Rs 1,500 crore and the same haircut takes 37.5% of the equity. This is why a credit analyst reading a holding company cares about the discount even though no lender ever sees it on a statement: it is a measure of how much equity cushion the market will actually pay for.

    What should you say about where the discount is applied?

    Some desks apply the discount to equity value instead of enterprise value. On equity of Rs 1,900 crore, 15% gives Rs 1,615 crore and Rs 32.3 a share. The two conventions differ by Rs 1.8 a share here, so name your convention in the first sentence rather than let the interviewer find it. The enterprise value version is the more common reading when the discount is described as a discount to the sum of the parts, and it is the one that treats the lenders' claim as fixed.

    Where candidates lose it

    The frequent slip is subtracting the net debt first and then taking 15% off what is left. That gives Rs 32.3 a share and quietly assumes the lenders share the discount, which they do not when the discount is on the sum of the parts. Interviewers accept either convention only if you name it.

    The second slip is telling the interviewer that shareholders lose 15%. Say 19.7%, and give the reason in one line: the debt does not shrink, so the whole haircut falls on equity.

    What the interviewer asks next

    • With net debt of Rs 1,500 crore, what discount would halve the equity value?
    • The group sells unit C for Rs 500 crore of cash and repays debt. If the discount stays at 15% on what remains, what happens to value per share?
    • Why would a lender to the holding company watch the discount at all?

    Asked at Deutsche Bank, Equity Capital Markets, Mumbai, 2024 (Wall Street Oasis): working capital, leases and SOTP with conglomerate discount question