Mutual Fund Mastery puzzles, solved step by step

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All topicsCompounding and time value9Statistics, correlation and diversification8Bond maths and duration10Performance measurement and returns8Costs and fee drag8Valuation riddles11Logic and numeracy brainteasers6Estimation and market sizing7Probability and expected value8NAV, units and fund mechanics7Risk, volatility and drawdown8Behavioural traps6Withdrawals and after-tax arithmetic4
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  1. 024An investor puts Rs 50,000 into a fund at an NAV of Rs 25.40. A stamp duty of 0.005% is deducted from the amount first. How many units are allotted, and why is the answer not 1,968.504?NAV, units and fund mechanicsWarm upFund operationsRegistrars and transfer agents

    Try it first

    How many units are allotted?

    Show the worked solution

    1,968.406 units. Stamp duty of 0.005% on Rs 50,000 is Rs 2.50, so Rs 49,997.50 is actually invested. Divided by the NAV of 25.40, that is 1,968.4055, rounded to 1,968.406. The figure 1,968.504 divides the full Rs 50,000 by the NAV and ignores the duty; the 0.098 extra units are worth about Rs 2.49, the duty give or take rounding.

    Why does the charge come off before the units are counted?

    Think of buying petrol with a Rs 500 note when the pump adds a Rs 5 card fee: you get Rs 495 worth of litres, not Rs 500 worth. A purchase is converted to units only after any charge on the transaction is deducted, so the units equal the net amount divided by the NAV, not the gross amount. Here the charge is a stamp duty of 0.005%, as stated in the question; the rate is set by law and can change, so confirm the current rate before using it.

    Charges come off the rupees before the rupees become unitsAmount paidRs 50,000.00Stamp duty 0.005%- Rs 2.50Amount investedRs 49,997.50Divide by NAV 25.401,968.406 unitsExact: 49,997.50 / 25.40 = 1,968.4055, rounded to three decimalsThe slip: dividing the full amount50,000 / 25.40 = 1,968.504 units0.098 units too many, worth about Rs 2.49: the duty, to roundingAllotted1,968.406
    Rs 50,000 less Rs 2.50 of stamp duty leaves Rs 49,997.50, which buys 1,968.406 units at an NAV of 25.40, while dividing the full Rs 50,000 gives 1,968.504 units and over-allots by the value of the duty.

    How do you do the division cleanly?

    Work in two steps and check the gap. Fifty thousand over 25.40 is 1968.5039; the duty removes Rs 2.50, which at 25.40 is about 0.0984 of a unit, so the answer is 1,968.4055, shown as 1,968.406. Checking it that way tells you the difference between the two answers is exactly the duty converted into units, which is a useful sense check in any operations role.

    The relationship
    Units=A(1−s)NAV=50,000×(1−0.00005)25.40=49,997.5025.40=1,968.406\text{Units} = \frac{A(1 - s)}{NAV} = \frac{50{,}000 \times (1 - 0.00005)}{25.40} = \frac{49{,}997.50}{25.40} = 1{,}968.406
    Athe amount paid, Rs 50,000
    sthe stamp duty rate, 0.005%
    NAVthe applicable NAV, Rs 25.40
    What it says in wordsTake the charge off the amount, then divide what is left by the price of one unit.

    Two practical points complete the answer. Which NAV applies depends on when the application and the money reach the fund relative to the cut-off time, so 25.40 is the NAV for the day the purchase qualifies, not necessarily the day it was submitted. And units are shown to three decimals on the statement; the exact rounding convention is set out in the scheme's documents, which is where an operations team would check it.

    Where candidates lose it

    The common slip is dividing the gross Rs 50,000 by the NAV, which is precisely the wrong answer the question names. An operations interviewer asks this to see whether you know the order: charges first, units second.

    The other slip is rounding the units to a whole number, or treating the stamp duty as coming out of the units afterwards. Fund units are allotted in fractions, and the duty is a deduction from the rupee amount.

    What the interviewer asks next

    • If the same investor redeems all the units later at an NAV of 30, what amount is paid before any exit load or tax?
    • Why might two investors who submit the same amount on the same day get different NAVs?
    • How would an entry load, where one is permitted, change the calculation?
  2. 081Scheme A, with a NAV of Rs 42.00, is merged into scheme B, whose NAV is Rs 18.00. How many units of B does an investor holding 1,000 units of A receive, and has anyone gained or lost in the swap?NAV, units and fund mechanicsWarm upFund operationsRegistrars and transfer agents

    Try it first

    How many units of scheme B does the investor receive?

    Show the worked solution

    2,333.333 units, and nobody gains or loses on the day. The holding is worth 1,000 x Rs 42, or Rs 42,000. Divided by B's NAV of Rs 18, that is 2,333.333 units, and 2,333.333 x Rs 18 is Rs 42,000 again. The swap ratio, 42 over 18, is 2.333 units of B per unit of A. A merger changes the unit count and the scheme, not the value held.

    Why does a lower NAV not make scheme B cheaper?

    Change a Rs 500 note into Rs 100 notes and you get five of them. You now hold more notes, but you are no richer. A NAV is the value of one unit, so the number of units you hold only means something when multiplied by the NAV; a merger at NAV swaps notes of one size for notes of another. Scheme B's Rs 18 NAV only says its units started at a lower price or have grown less since launch. It says nothing about whether B is cheap, good or bad.

    The unit count changes; the value held does notUnits heldBefore: scheme A1,000 unitsAfter: scheme B2,333.333Value held, Rs1,000 x Rs 42.00Rs 42,0002,333.333 x Rs 18.00Rs 42,000Swap ratio = NAV of A / NAV of B = 42 / 18 = 2.333 units of B for every unit of A
    The investor's 1,000 units of A become 2,333.333 units of B, but both holdings are worth Rs 42,000, because the swap ratio of 2.333 is set by the two NAVs on the merger date.
    The relationship
    uB=uA×NAVANAVB=1,000×4218=2,333.333u_B = u_A \times \frac{NAV_A}{NAV_B} = 1{,}000 \times \frac{42}{18} = 2{,}333.333
    u_A, u_Bunits held in scheme A before and scheme B after
    NAV_A, NAV_Beach scheme's net asset value per unit on the merger date
    What it says in wordsThe new unit count is the old count times the ratio of the two NAVs, which keeps the rupee value unchanged.

    So can a merger leave an investor worse off?

    Not on the day of the swap, when both schemes are valued at their closing NAVs. What a merger can change is everything after the swap: a different portfolio, a different expense ratio, a different level of risk, and possibly a tax event. If scheme B charges more, holds riskier bonds or follows another strategy, the investor's future returns change even though the swap itself was fair. That is why investors in a scheme being merged are generally offered a window to exit without an exit load; confirm the current rules on how that window works before relying on it.

    The three decimals are not decoration. Registrars in India commonly allot units to three decimal places, so the answer is 2,333.333 and not a rounded 2,333. Rounding down to whole units would take about Rs 6 from this investor, and across lakhs of folios that adds up, so fractional units exist precisely to keep the swap exact.

    Where candidates lose it

    The fast wrong answer is 1,000 units, as if a merger were a change of name. It would leave the investor with Rs 18,000 in place of Rs 42,000. The next wrong answer inverts the ratio and gives about 429 units. Both come from working with unit counts instead of rupees.

    State the rupee value first, Rs 42,000, and divide by the new NAV. Then add the sentence that shows judgement: the swap is fair on the day, and the real question is what the investor now owns and what it costs.

    What the interviewer asks next

    • Scheme B's expense ratio is 0.5 points higher. Roughly what does that cost on Rs 42,000 over ten years?
    • In what circumstances could the merger be a taxable event for the investor, and what would you check?
    • The investor had a monthly systematic investment plan into scheme A. What should happen to it?