Debt Capital Markets puzzles, solved step by step

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All topicsLeverage, coverage and cash flow9Mental maths and numeracy8Estimation and market sizing7Logic and brainteasers8Cost of capital and valuation riddles7Bond pricing and yield7Compounding, PIK and fees6Issuance and refinancing arithmetic8Credit spreads and default probability8Duration and convexity8Capital structure and recovery8Probability and expected value10Yield curve and forward rates6
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  1. 075Revenue is Rs 800 crore, up 10% on last year's Rs 727.3 crore. The EBITDA margin is 18%, depreciation is Rs 30 crore, the tax rate is 25%, capex is Rs 45 crore, and the net working capital build is 12% of the change in revenue. Walk from revenue to unlevered free cash flow.Leverage, coverage and cash flowCoreRBC Capital MarketsLondon · 2026

    Try it first

    Roughly what is unlevered free cash flow?

    Show the worked solution

    Unlevered free cash flow is about Rs 61.8 crore. EBITDA is 18% of Rs 800 crore, Rs 144 crore. Less Rs 30 crore of depreciation gives EBIT of Rs 114 crore, and tax at 25% leaves NOPAT of Rs 85.5 crore. Add back depreciation, which is not cash, to reach Rs 115.5 crore, then take off capex of Rs 45 crore and the working capital build of 12% of the Rs 72.7 crore revenue increase, Rs 8.7 crore.

    What order do you walk the lines in?

    Think of a shopkeeper's year: sales come in, stock and staff are paid, the taxman takes a share, some money goes on a new fridge, and more stock sits on the shelves because the shop is busier. What is left is what the owner could take out. Unlevered free cash flow follows the same order: operating profit, less tax on that profit, plus non-cash charges, less investment in fixed assets and in working capital. It is unlevered because interest is left out: the cash belongs to lenders and shareholders together.

    From Rs 800 crore of revenue to Rs 61.8 crore of free cash144EBITDA-30D&A114EBIT-28.5Tax85.5NOPAT+30Add D&A-45Capex-8.7NWC61.8FCFRevenue 800 x 18% margin = EBITDA 144Working capital: 12% x (800 - 727.3) = 8.7Only 43% of EBITDA reaches free cash flow; lenders are paid from the lime bar, not the first one
    EBITDA of Rs 144 crore loses Rs 30 crore of depreciation and Rs 28.5 crore of tax to reach NOPAT of Rs 85.5 crore, gets the depreciation back, then loses Rs 45 crore of capex and Rs 8.7 crore of working capital, leaving Rs 61.8 crore of unlevered free cash flow.
    LineRs crore
    Revenue800.0
    EBITDA at 18%144.0
    Less depreciation(30.0)
    EBIT114.0
    Less tax at 25% of EBIT(28.5)
    NOPAT85.5
    Add back depreciation30.0
    Less capex(45.0)
    Less working capital build, 12% x 72.7(8.7)
    Unlevered free cash flow61.8
    Unlevered free cash flow is Rs 61.8 crore, 43% of EBITDA, after tax on operating profit, capex of 1.5 times depreciation and a working capital build on the Rs 72.7 crore rise in revenue.

    Why tax EBIT rather than profit after interest?

    Unlevered cash flow is the cash the business makes before any financing choice, so tax is charged as if there were no debt: 25% of EBIT, Rs 28.5 crore. Real tax is lower when there is interest to deduct, and that saving is counted elsewhere, in the discount rate or in a separate tax shield line. Taxing profit after interest and then discounting at a rate that already includes the shield counts the same benefit twice.

    Where does the cash go between EBITDA and free cash flow?

    Of Rs 144 crore of EBITDA, only Rs 61.8 crore, about 43%, becomes unlevered free cash flow: tax takes 28.5, capex 45 and working capital 8.7. Capex is 1.5 times depreciation, so the company is investing to grow, and working capital rises with sales because more revenue means more receivables and stock. A lender sizing debt on EBITDA should look at this conversion, because interest and repayments are paid from the Rs 61.8 crore, not the Rs 144 crore. The limit: one year of cash conversion can mislead when capex is lumpy.

    Where candidates lose it

    The common slip is stopping at EBITDA less capex and calling it free cash flow, forgetting tax and working capital; that gives Rs 99 crore, well above the true Rs 61.8 crore.

    The second is charging working capital on the whole revenue, 12% of Rs 800 crore, instead of on the change. Working capital is a balance; only the increase uses cash this year.

    What the interviewer asks next

    • Revenue falls 10% next year instead. What happens to the working capital line?
    • How would you get from unlevered to levered free cash flow?
    • Capex falls to the level of depreciation. What is free cash flow now, and is that sustainable?

    Asked at RBC Capital Markets, Leveraged Finance, London, 2026 (Wall Street Oasis): Walk me through Revenue to unleveraged FCF

  2. 096Two Rs 1,000 crore loans are sold in the broadly syndicated market. A term loan A amortises 20% a year over 5 years. A term loan B amortises 1% a year and repays the rest as a bullet at year 7. What is the weighted average life of each?Leverage, coverage and cash flowCoreScotiabankNew York · 2026

    Try it first

    Before calculating: roughly what is term loan B's weighted average life?

    Show the worked solution

    Term loan A has a weighted average life of 3.0 years and term loan B about 6.8 years. Term loan A repays 200 in each of years 1 to 5, so its average is (1 + 2 + 3 + 4 + 5) x 200 / 1,000 = 3.0. Term loan B repays 10 in each of years 1 to 6 and 940 in year 7: (210 + 6,580) / 1,000 = 6.79. Amortisation, not maturity, sets how long the lender's money is out.

    What are the two loans, and why do they amortise so differently?

    That is the question a candidate reported being asked, and the arithmetic is the best way to answer it. A term loan A is built for banks: it amortises steadily, so the lender's exposure shrinks every year. A term loan B is built for institutional investors such as loan funds: it amortises only nominally and returns almost everything at maturity, which suits investors who want to stay invested. The difference in structure shows up as a difference in weighted average life, and that number drives pricing, investor appetite and how long the credit risk lasts.

    Where the principal comes back sets how long the money is outTerm loan A: 20% a yearWAL 3.0 years2002002002002001234567yearTerm loan B: 1% a year, then bulletWAL 6.79 years1010101010109401234567year
    Term loan A returns 200 of principal every year and has a weighted average life of 3.0 years, while term loan B returns only 10 a year before a 940 bullet in year 7, giving a weighted average life of 6.79 years.

    How is weighted average life calculated?

    Think of lending a friend Rs 1,000 who repays Rs 200 a year: on average your money is out about three years, even though the last rupee comes back in year five. Weighted average life weights each repayment date by the share of principal repaid on it, and ignores interest. For term loan B: six payments of 10 contribute 10 x (1 + 2 + 3 + 4 + 5 + 6) = 210 year-rupees, and the bullet contributes 940 x 7 = 6,580. Total 6,790 over 1,000 is 6.79 years.

    The relationship
    WAL=∑tt⋅Pt∑tPt:A=200(1+2+3+4+5)1,000=3.0B=10(1+⋯+6)+940×71,000=6.79WAL = \frac{\sum_t t \cdot P_t}{\sum_t P_t}: \quad A = \frac{200(1+2+3+4+5)}{1{,}000} = 3.0 \qquad B = \frac{10(1+\dots+6) + 940 \times 7}{1{,}000} = 6.79
    P_tprincipal repaid in year t
    tthe year of repayment
    What it says in wordsWeighted average life is the average repayment date, weighted by how much principal comes back on each date.

    Why does the desk care?

    A loan's pricing is spread over its weighted average life, not its stated maturity, so an upfront fee or discount is spread over 3 years on term loan A and nearly 7 on term loan B. In practice term loans B are often repaid early from refinancings or cash sweeps: if this one were refinanced in full at year 4, its weighted average life would fall to 3.94 years. Weighted average life is also not duration; it ignores interest and discounting, so it always sits above the loan's duration.

    Where candidates lose it

    The common error is quoting maturity: 5 years and 7 years. The question is about how long the money is out on average, and the answer for term loan A is two years shorter than its maturity.

    The second is guessing term loan B's life at half its term because it amortises. It amortises so little that the bullet dominates. Say the 94% bullet share first and the answer follows.

    What the interviewer asks next

    • If term loan A amortised 5%, 10%, 15%, 20% and 50% over the five years, what is its weighted average life?
    • Why do institutional loan investors prefer the term loan B structure?
    • A 2 point upfront fee is spread over the weighted average life. What does it add to the yield on each loan?

    Asked at Scotiabank, Debt Capital Markets, New York, 2026 (Wall Street Oasis): Tell me about the two different types of loans in the broadly syndicated loan market.