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  1. 017Free cash flow of Rs 100 crore arrives every year for five years and the discount rate is 10%. How much does the mid-year convention add to the value, and why?DCF and cost of capitalCoreLazardNew York · 2026

    Try it first

    How much does the mid-year convention add?

    Show the worked solution

    It adds about Rs 18.5 crore, or 4.9%, taking the value from Rs 379.1 crore to Rs 397.6 crore. The mid-year convention assumes each year's cash arrives evenly through the year, so on average halfway through rather than at the end. Every cash flow is then discounted for half a year less, which multiplies each present value by 1.10 to the power of one half, 1.0488.

    Why would cash arrive in the middle of the year?

    A shop does not collect its year's takings in one lump on the last day of March; money comes in every day. A DCF that discounts each year's cash flow as if it all arrived on the final day is too harsh. The mid-year convention treats each year's cash flow as arriving, on average, halfway through the year, so it is discounted for t minus one half years instead of t. For a business with steady receipts that is the more accurate assumption, and it is the default in many banks' models.

    Same cash, six months earlier: every discount factor improves by the same ratioTodayYear 1Year 2Year 3Year 4Year 5Year-end100x 0.90990.9100x 0.82682.6100x 0.75175.1100x 0.68368.3100x 0.62162.1Mid-year100x 0.95395.3100x 0.86786.7100x 0.78878.8100x 0.71671.6100x 0.65165.1each cash flow 6 months earlierYear-end total379.08Mid-year total397.58Uplift+18.50 = +4.88%square root of 1.10, less 1the same for every cash flow
    Moving each Rs 100 crore cash flow from the end of its year to the middle lifts its discount factor by the same ratio, so the five-year value rises from Rs 379.08 crore to Rs 397.58 crore, an uplift of 4.88%.
    The relationship
    ∑t=151001.10 t−0.5=1.100.5×∑t=151001.10 t=1.0488×379.08=397.58\sum_{t=1}^{5} \frac{100}{1.10^{\,t-0.5}} = 1.10^{0.5} \times \sum_{t=1}^{5} \frac{100}{1.10^{\,t}} = 1.0488 \times 379.08 = 397.58
    t - 0.5each year's cash treated as arriving at the middle of the year
    1.10^0.5the gain from discounting every cash flow for half a year less
    What it says in wordsShifting every cash flow six months earlier multiplies the whole value by the square root of one plus the discount rate.

    Why is the uplift exactly the square root of 1.10 minus one?

    Because the shift is the same for every cash flow. Moving a payment six months earlier multiplies its present value by 1.10 to the power of one half, whatever year it sits in. Since every cash flow gets the same uplift, the whole value rises by the same 4.88%, and neither the size nor the pattern of the cash flows changes that. Half the discount rate, 5%, is a fair first approximation to say out loud; at a 20% rate the exact uplift is 9.5%, against the 10% the approximation would give, so the shortcut weakens as rates rise.

    Where should you not apply it?

    Two cautions. A terminal valueThe value of all cash flows beyond the forecast years, usually from a growing perpetuity or an exit multiple. built on a perpetuity of flows is usually discounted on the same mid-year basis, but one built on an exit multiple is not, because a sale happens at a point in time, the end of the final year. Shifting an exit-multiple terminal value half a year earlier overstates the answer, and an interviewer who asks about the convention is often fishing for exactly that. For seasonal businesses that collect most cash late in the year, the convention itself flatters the value.

    Where candidates lose it

    The usual slip is to say the convention changes the cash flows, or that it only affects the first year. It changes timing only, and it moves every cash flow by the same six months, so the uplift applies to all of them.

    The second slip is applying it to a terminal value built on an exit multiple. A sale happens at a moment, so that value stays discounted for the full five years; candidates who shift it too overstate the value and get caught on the follow-up.

    What the interviewer asks next

    • If the discount rate were 20%, what would the convention add?
    • Should the mid-year convention apply to a terminal value built on an exit multiple?
    • For a business that bills most customers in its final quarter, is the convention still appropriate?

    Asked at Lazard, Investment Banking, New York, 2026 (Wall Street Oasis): Asked about SBC, LBOs, Advanced accounting questions and mid-year conventions

  2. 043Comparable companies have an unlevered beta of 0.8. Your target will run at a debt-to-equity ratio of 50% with a 25% tax rate. The risk-free rate is 7% and the equity risk premium 6%. What is the target's cost of equity?DCF and cost of capitalCoreMoelis & CompanyLos Angeles · 2026

    Try it first

    What cost of equity do you get?

    Show the worked solution

    About 13.6%. The peers' 0.8 is an unlevered beta, the risk of the business with no debt. The target carries debt equal to 50% of its equity, so relever it: 0.8 times (1 plus 75% times 0.5) is 1.1. CAPM then gives 7% plus 1.1 times 6%, which is 13.6%. Using the unlevered 0.8 directly would understate the cost at 11.8%.

    Why can you not use the peer beta as it is?

    Think of two people with the same job and salary, one with no loan and one with a large home loan. A pay cut hurts the borrower more, because the loan payment does not shrink. Debt magnifies the swings that reach shareholders, so the same business carries a higher equity beta the more it borrows. Peers' betas are first stripped of their own debt to give an unlevered betaThe beta a business would have with no debt: the risk of its operations alone., then relevered at the target's own mix of debt and equity.

    Relever the peer beta to the target's own debt, then apply CAPMPeer unlevered beta0.8Relever at D/E 50%x 1.375Target levered beta1.1CAPM: 7% + 1.1 x 6%13.6%1 + (1 - 25%) x 0.5 = 1.375Cost of equity under each slip, axis starts at 10%Unlevered beta used as is11.8%Debt over total capital13.0%Correct: D/E, after tax13.6%Tax shield ignored14.2%10%11%12%13%14%15%
    The peers' unlevered beta of 0.8 relevers to 1.1 at a 50% debt-to-equity ratio and a 25% tax rate, giving a cost of equity of 13.6%, while the three common slips give 11.8%, 13.0% and 14.2%.

    How does the relevering work?

    Use the standard formula, which assumes the debt itself carries no market risk. Levered beta equals unlevered beta times one plus (one minus the tax rate) times debt over equity: 0.8 times (1 + 0.75 x 0.5), which is 0.8 times 1.375, or 1.1. The tax term is there because interest is tax deductible, so the tax saving softens a quarter of the debt's burden on shareholders. Then CAPM: 7% plus 1.1 times 6% is 13.6%.

    The relationship
    βL=βU[1+(1−t)DE]=0.8×1.375=1.1ke=7%+1.1×6%=13.6%\beta_L = \beta_U\left[1 + (1-t)\frac{D}{E}\right] = 0.8 \times 1.375 = 1.1 \qquad k_e = 7\% + 1.1 \times 6\% = 13.6\%
    beta_Uthe peers' unlevered beta, 0.8
    tthe tax rate, 25%
    D/Ethe target's debt divided by its equity, 50%
    What it says in wordsAdd back the target's own debt to the business risk, then price that risk with CAPM.

    Which slips change the answer?

    Three, each worth naming. Skipping the relevering gives 11.8%, using debt over total capital instead of debt over equity gives 13.0%, and ignoring tax gives 14.2%. A spread of 2.4 points in the cost of equity moves a DCF a long way, so the interviewer wants to hear which ratio you are plugging in. State the limit too: the rates here are illustrations, and a live model takes the current government bond yield and the premium the bank uses.

    Where candidates lose it

    The fast loss is plugging 0.8 straight into CAPM. The peers' beta has been cleaned of debt, so using it unadjusted values the target as if it had none, and the cost of equity comes out too low.

    The quieter loss is the ratio. The formula takes debt over equity, 50%, not debt over total capital, one third. Say the ratio out loud before you multiply.

    What the interviewer asks next

    • The target's debt rises to 100% of equity. What is the cost of equity now?
    • What is the WACC if the target's debt costs 10% before tax?
    • Why do you unlever each peer before averaging, rather than averaging the levered betas?

    Asked at Moelis & Company, Investment Banking, Los Angeles, 2026 (Wall Street Oasis): high-level technical questions aimed at accounting (NWC) and valuation topics (EV, DCF, UFCF, Cost of Equity)