Analysis Of Financial Options - Maths Puzzle

Let's assume we have invested Rs 30 lacs in a particular debt instrument which used to give about 8% annual return. 

Now LTCG (Long term capital gains) tax on debt instruments is 20%. For the time being let's avoid the complexity of indexation. This means if a fund grew from Rs 100 to Rs 140 over a 4 year period, the gain is Rs 40. And the LTCG tax is 20% of Rs 40.

Now let's come to the problem.

I find that the debt fund returns have fallen from 8% to 6%. This means that while I used to get 8% returns till today,  the return from today to days in future wilI be 6%. I have another financial instrument which gives me the same 6% return but it does not attract any income tax - meaning the returns are tax exempt.

I am considering moving the funds from the first instrument to the second one. But if I move now, I will have to pay LTCG tax in Apr 2018. If I were to wait till Apr 1, 2018 and then make the switch, the LTCG would have happened only in the FY (Financial year) 2018-19 and the tax would have to be paid only in April 2019. We assume for the sake of simplicity that all tax is payable in April meaning the month following the end of the FY. So if I wait 4 months, I can postpone the tax by a year. 

Assume that the 2nd fund will remain tax exempt and that the return percentages will hold good for the next year or so.

Now the question:

Should I make the switch now or wait till Apr 2018?

Intermediate questions you need to answer:

1. Is the exact date that I made the original investment relevant (I assure you the date is such that the transaction will be termed Long Term).
2. Is the exact amount of original investment and the rates of return from the beginning till now relevant? Is the exact amount of LTCG till now relevant?

Assumptions:

• The LTCG tax payable on debt funds does not depend on your income. Even if you had zero income in a FY, you still have to pay the LTCG tax on debt funds that you redeemed (sold) and made a profit on in the FY.
• I do not know any IT assessor whom I can bribe. Answers pertaining to illegal methods not accepted.

Solution:

• The amount and date of original investment as well as the history of returns till now are same for both options - whether i switch right now or I switch on Apr 1, 2018. I need not hence bother with these values.
• What happens on Apr 2, 2018 or later is again not relevant since it is the same for both options.

• It is like saying you and I go on a trip.  For the 1st four days we travel together, then we split up. You go north, I go south. Then we meet up on Apr 1st 2018. Then travel together for the rest of the trip. How many more places did you visit than me? Would we start finding out how many places you saw and I saw before we split up and again after we rejoined? We need not, right? We need focus only on that portion of the trip when we were not together.

• The debt fund gives 6% but taxed @ 20%, hence nett it gives 4.8%. The other option gives 6% nett. Hence the "sell right now option" gives me 1.2% extra for 1/3 year (=4months). If the amount I have now is x, I get 1.2%*x* 1/3 more if I switch right now vis-a-vis waiting till Apr 2018 to switch.
• If y is the LTCG incurred till now in the debt fund then, if I switch now, I have to pay 20%*y as tax in Apr 2018. Remember, there is no tax on the fund I switch to. Now If I wait till Apr 2018 and then switch then my total tax will still be 20%*y (note that by using nett 4.8% as the return for the next 4 months, I have already considered tax) but I will pay the 20%*y in Apr 2019. If the cost of money is 6%, I get 20%*y*6% as interest on the tax I have deferred by a year till 2019 in case I wait till Apr 2018 to switch.
• Note that for finding out the cost of tax payment earlier I DO need to know the amount of LTCG (directly, if available, or indirectly through the amount of original investment and the avg rate or return from the date of original investment till now).
• Hence if I switch right now, I get 1.2%*x*1/3 (=30Lacs/3*1.2/100=12k) more because of higher return and 20%*y*6% less because of non-deferment of tax payment. Which is higher? Can't say.  It depends on the exact value of y. If for example y = 5Lacs, then 20%*y*6% = 6k. In such a case I should switch right now because 12 lacs > 6lacs. But if y is high enough the the expression with y will become higher then I should wait till Apr 2018 to switch. 
• If y=12Lacs, 20%*y*6% = 14.4k. In that case it may make more sense to wait until Apr 2018 to switch. This means that the 18Lacs of original investment became 30Lacs with a CG of 12Lacs. That means that the investment was held for many years so that the interest or LTCG is sizeable compared to the original principal. This also provides an instance where decision to switch to a more lucrative instrument (the second one) depends on an external forced factor of when the tax is payable - this is counter intuitive.