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Value Research: Calculation Error?

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Over email, Ravikiran Rao pointed out to an error in Value Research’s article by Dhirendra Kumar which mentions:

Consider a ten year investment that is yielding 20 per cent an year. In ten years an investment of Rs 1 lakh at this rate would grow to Rs 6.19 lakh. If the long-term capital gains are taxed at 15 per cent for your income bracket, you would end up with Rs 4.41 lakh post tax returns, an effective rate of return of 18.3 per cent. But if this investment was switched to a different share or fund just twice in those ten years, the final post tax return would be just Rs 2.24 lakh.

(Emphasis mine)

Ravi couldn’t get how he calculated this and then, neither could I. LTCG has an indexation benefit linked to inflation – so if you invest Rs. 100 today and exit one year later at 120, your cost is assumed to have become 106 at 6% inflation, and your real gain is just Rs. 14 – which is what gets taxed at the lower LTCG rate.

So if you made 20% per year and in 10 years got 6.19 lakh (profit is 5.19 lakhs), the cost will go to Rs. 1.79 lakhs (at 6% inflation). The tax on the inflation adjusted gain of 4.41 lakhs is only 66K. So you made 5.19 lakhs in profit, paid 66K in taxes and are left with 4.5 lakhs after 10 years.

But Dhirendra says if you exited twice in the interim, your gain would go to half that. I can’t seem to figure out how. Even if you exited every single year and paid 15% taxes on the gains, you will end up making 4.18 lakhs as profit, which is just 7.5% lower than staying the entire course.