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