Private Wealth Management puzzles, solved step by step
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005A client needs Rs 10 lakh in hand from a mutual fund redemption. Forty per cent of every rupee he redeems is capital gain, taxed at an illustrative 12.5%. How much must he redeem?Mutual fund distributionIndian wealth management
Try it first
Which redemption gives exactly Rs 10 lakh after tax?
Show the worked solution
About Rs 10.53 lakh. Each rupee redeemed is 40 paise of gain, and 12.5% tax on that is 5 paise, so he keeps 95 paise per rupee. Dividing Rs 10 lakh by 0.95 gives Rs 10.5263 lakh. Tax is Rs 52,632 and he is left with exactly Rs 10 lakh. The rate is illustrative; check the current rules and any exemption before advising.
Why does adding the tax on top fall short?
Imagine a shop that adds a 5% delivery charge on the order total. If you want Rs 100 of goods delivered and add Rs 5 for delivery, the shop charges delivery on Rs 105, and you are short. When the tax falls on the amount you withdraw, the withdrawal must be grossed up by dividing, not by adding a percentage. Here every rupee redeemed carries 0.40 times 12.5%, which is 5 paise, of tax.
A redemption of Rs 10.53 lakh is 60% principal and 40% gain; tax at 12.5% of the gain is Rs 52,632, leaving exactly Rs 10 lakh, while redeeming Rs 10.50 lakh leaves Rs 2,500 short. Why is the gain share of each rupee the same across the redemption?
Because the question fixes it: 40% of every rupee is gain. In practice the gain share depends on which units are sold first, which follows a first-in, first-out order for mutual fund units, and on the cost of acquisitionThe price paid for the units being sold, set against the sale value to find the capital gain. of each lot. The grossing up works for any tax rate and gain share: divide the need by one minus the gain share times the rate. Say that general form after the number.
The relationshipN the amount needed in hand, Rs 10 lakh g the share of each redeemed rupee that is gain, 0.40 t the illustrative tax rate on the gain, 12.5% G the gross redemption, Rs lakh What it says in wordsDivide the cash needed by the share of each rupee that survives tax.Say the boundary plainly. Real capital gains tax has holding-period rules, an annual exemption on some gains, and surcharge and cess on top, and the rates change with budgets. The desk wants the method; the client file needs the current rules confirmed before a single unit is sold.
Where candidates lose it
The trap is adding 5% and saying Rs 10.50 lakh. It feels right because 5 paise per rupee is the tax, but the extra Rs 50,000 is itself taxed, and the client ends up Rs 2,500 short on the day he needs the money.
The second loss is quoting a tax rate as fact. Call it illustrative, give the method, and say the current rate and exemption need to be checked.
What the interviewer asks next
- If only 20% of each rupee were gain, how much would he redeem?
- What if the first Rs 1 lakh of gain were exempt? How does the calculation change?
- Why might you redeem from a different fund to raise the same Rs 10 lakh?
043A client in an illustrative 30% tax slab holds an equity fund and earns Rs 1 lakh of return in a year. He can take it through the IDCW payout option, taxed at his slab, or leave it in the growth option and pay an illustrative 12.5% capital gains rate when he sells. How much does the option choice cost him?Mutual fund distributionIndian wealth management
Try it first
On Rs 1 lakh of return, how much more tax does the payout option cost him?
Show the worked solution
About Rs 17,500 on every Rs 1 lakh of return, before the benefit of deferral. Paid out as IDCW, the Rs 1 lakh is taxed at his illustrative 30% slab: Rs 30,000. Left in the growth option and later sold as a long-term gain, it is taxed at an illustrative 12.5%: Rs 12,500. The return is identical; only its tax label changes. Over ten years on Rs 10 lakh the gap compounds to about Rs 4.27 lakh.
Is the IDCW payout extra money?
No, and that misunderstanding is where most of the damage starts. Taking water out of your own tank does not give you more water. An IDCW payout is paid out of the fund's NAV, so the NAV falls by the amount paid; the client receives part of his own money, and in the payout option that money is taxed as income. The growth option leaves the same return inside the fund, where it is taxed only when units are sold and, if held long enough, at the capital gains rate.
The same Rs 1 lakh of return costs Rs 30,000 in tax in the payout option at an illustrative 30% slab, against Rs 12,500 in the growth option at an illustrative 12.5% gains rate, a difference of Rs 17,500. Over ten years on Rs 10 lakh at 10% the gap compounds to Rs 4.27 lakh. The relationshipR the return in the year, Rs 1 lakh t_slab the client's illustrative income tax slab, 30% t_cg the illustrative long-term capital gains rate, 12.5% What it says in wordsThe cost of the payout option is the return times the gap between the two tax rates.Why does the gap grow over time?
Because the payout option is taxed every year, so the reinvested amount compounds at 7% after tax, while the growth option compounds at the full 10% and is taxed once at the end. Rs 10 lakh for ten years becomes about Rs 19.67 lakh in the payout option, even with every payout reinvested, against about Rs 23.95 lakh in the growth option after its tax. The rate gap and the deferral work in the same direction.
The payout option can still suit a client who needs regular cash and sits in a low slab. The rates here are illustrative: slab rates, capital gains rates, holding periods, exemption limits and deduction of tax at source all change, so confirm the current rules before advising on them.
Where candidates lose it
Candidates often treat the payout as income on top of the return, or say the option choice cannot matter because the fund is the same. Both miss that the option changes the tax treatment of an identical return.
Give the Rs 17,500 per Rs 1 lakh, then add deferral as the second effect, and flag that the rates are illustrative. That last line matters on a desk that answers to a compliance team.
What the interviewer asks next
- For a client in a 5% slab, which option costs less tax?
- How would you set up regular cash for a retiree without using the IDCW option?
- Why might a fund's NAV fall sharply on a record date?
081A client holds three lots of the same mutual fund, 1,000 units each, bought at NAV 100, 150 and 180. The NAV is now 170 and he redeems one lot's worth of units. What is his taxable gain under first in, first out, and what would it be if he could choose which lot to sell?Mutual fund distributionIndian wealth management
Try it first
Under first in, first out, what gain does he book?
Show the worked solution
Rs 70,000 under first in, first out, against a loss of Rs 10,000 if he could pick the lot bought at 180. FIFO sells the NAV 100 units: 70 a unit on 1,000 units. Picking the newest lot books 170 minus 180, a loss of 10 a unit. The gap is Rs 80,000 of taxable gain, Rs 16,000 of tax at an illustrative 20%, though only a shift in timing.
Why does it matter which lot is sold?
Think of a shop selling rice it bought in three batches at three prices. Its profit on today's sale depends on which batch it says it sold. Units of one fund are identical in the market but not in the tax records: each lot carries its own cost, so the lot matched to a sale decides the gain. The oldest lot here has the lowest cost and the biggest gain.
Against today's NAV of 170 the lot bought at 100 carries a Rs 70,000 gain, the lot at 150 a Rs 20,000 gain and the lot at 180 a Rs 10,000 loss, so first in, first out books Rs 70,000 of gain where picking the newest lot would book a loss. In India, redemptions of units of the same scheme are generally matched first in, first out, so the client cannot usually pick the lot; confirm the current rule before relying on it. The puzzle asks for both numbers so you can show the cost of the rule, Rs 80,000 of gain brought forward.
Does picking the lot actually save tax?
Mostly it moves tax in time. The three lots carry Rs 80,000 of gain in total at 170, whatever the order. Choosing the high-cost lot defers gains rather than erasing them, so its value is the time value of the deferred tax plus any loss he can set against other gains now. Two things can change that: the oldest lot may qualify for a lower long-term rate because it has been held longer, and a loss booked today may offset gains elsewhere in the same year.
The relationship170 today's NAV, the sale price per unit cost the NAV each lot was bought at: 100, 150 or 180 1,000 units per lot What it says in wordsEach lot's gain is the sale price less that lot's cost, times its units.Where candidates lose it
Candidates reach for the average cost, 143.3, and book a gain of about Rs 26,667. That is how many people track a holding, but it is not how the redemption is matched here.
The second slip is saying lot choice saves Rs 16,000 of tax outright. It mostly defers it; say the total gain is Rs 80,000 whichever order, and name the holding period as the thing that can change the rate.
What the interviewer asks next
- The NAV falls to 140. Which lots are at a loss, and what does first in, first out book now?
- How could the client use the loss on the newest lot this year?
- Why might selling the oldest lot be cheaper in tax even with the largest gain?