Mutual Fund Mastery puzzles, solved step by step

One third of each withdrawal, about Rs 16,667, is gain, and only that part is taxable. Rs 50,000 at NAV 60 redeems 833.33 units that cost 40 each, so Rs 33,333 is the investor's own capital returning. Deposit interest of Rs 50,000 is income in full. At any single assumed rate t, tax on the SWP is t times Rs 16,667 against t times Rs 50,000.

Is a withdrawal income?

Think of selling three of your own mangoes that you bought at Rs 40 each and can now sell at Rs 60. You receive Rs 180, but only Rs 60 of it is profit; Rs 120 is your money coming back. An SWP is a monthly sale of units, and each unit sold returns its purchase cost plus the gain on it, so only the gain portion is a taxable gain. At cost 40 and NAV 60, the gain is 20 out of 60, one third of every rupee withdrawn.

Why does it hold at any tax rate?

Apply one assumed rate t to both. The SWP's taxable amount is Rs 16,667 and the deposit's is Rs 50,000, so whatever t is, the SWP's tax is one third of the deposit's. At an assumed 30%, that is Rs 5,000 against Rs 15,000 a month. In practice the two are taxed under different heads and can face different rates and holding-period rules, so confirm the current rules; the structural point is that a withdrawal is mostly capital and interest is entirely income.

Now say the limitation honestly. The comparison is not like with like: the deposit's Rs 50,000 leaves the principal untouched, while the SWP is selling units, so the holding shrinks unless the fund grows faster than the withdrawals. And the gain share rises over time: as the NAV climbs, a larger part of every unit sold is gain, so the tax advantage narrows the longer the plan runs. A light tax bill early on is not a measure of whether the withdrawal rate is sustainable.

The deposit, by about Rs 1,418 on Rs 10 lakh. Taxed yearly, the deposit compounds at 7.2% x 0.7 = 5.04% and reaches Rs 11,58,949. The fund grows to Rs 12,25,043 and keeps 70% of its gain: Rs 11,57,530. Deferral alone is worth about Rs 3,399, roughly the cost of a 0.14% yield gap, so a 0.2% lower yield more than uses it up. Tax rates here are assumptions; confirm the current rules.

Where does the value of deferral come from?

Think of a shop that lets you pay your bill at the end of the year instead of every month. You keep the money a little longer and can earn something on it, but over a short time that is a small favour. Tax deferral is the same favour: the tax you would have paid each year stays invested and earns until redemption, so the gain comes from interest on money that would otherwise have gone to the tax office. Over three years at 7% that extra earning is modest. Over twenty years it is large, because it compounds.

Work both. The deposit pays 7.2%, of which 30% goes in tax each year, so it compounds at 5.04%: Rs 10 lakh becomes Rs 11,58,949. The fund compounds untaxed at 7.0% to Rs 12,25,043; on redemption 30% of the Rs 2,25,043 gain goes in tax, leaving Rs 11,57,530. The deposit is Rs 1,418 ahead.

How do you separate the deferral from the yield gap?

Give the fund the same 7.2% and the only difference left is the timing of tax. It would end at Rs 11,62,348, Rs 3,399 above the deposit: that is the value of deferral. Then the fund's 0.2% lower yield takes away Rs 4,818, slightly more than the deferral gave, which is why the deposit edges ahead. The fund would break even at a yield of about 7.06%, so the deferral is worth roughly 0.14% a year over three years.

The limits matter more than the arithmetic here. The tax treatment of debt funds has changed in India in recent years, and slab rates, surcharge and cess all move the answer, so confirm the current rules before using any rate. A deposit has no price risk, while a debt fund's NAV moves with interest rates and credit events. And deferral grows with time: over fifteen years the same set-up would give the fund a clear lead.