I have 10000 units of currency. I invest them in Debt and Equity in the ratio 75:25 respectively. Debt and Equity grow at different rates hence the proportion changes accordingly. Suppose I need to re-balance the appreciated Debt and Equity investments at end of year 1 such that they are back in the ratio 75:25, I need to either redeem my investment from either of them (whichever has grown greater than their required proportion) and invested back into the other. The problem is however whenever I redeem from either of them they are taxed hence the resulting re-balancing leaves me Debt to Equity not in 75:25 proportion. How much do I redeem from either of them at once so that after paying the tax the resulting re-balancing is in 75:25 proportion.
e.g.10000 invested in Debt and Equity as 7500 and 2500 respectively and get 75 units of Debt and 25 units of Equity. Tax rates for Debt and Equity are 30% and 10% on gains respectively. Thus suppose Debt value rises to 8000 and Equity value to 2800, how do I re-balance it to 75:25 after paying necessary tax? Here since Equity has risen greater than its proportion, I need to redeem their respective units, pay tax and invest in Debt which again leaves me without 75:25 ratio (because of taxation).
Point to note is I redeem individual units which can be fractions and each redeemed unit has corresponding investment value as well as gains and hence redeeming it does not entail redeeming only gains as that is the part that is taxed.
What formula do I use for calculation to re-balance considering taxation as well?
$\frac{8000 + \frac{9x}{10}}{2800-x}=3$
We have 8000 +$\frac{9x}{10}$ = 8400 - 3x
So 39x=4000
There transfer $\frac{4000}{39}$ rupees from equity