Every percentage point paid as fee matters in long-term wealth growth

There is a bug in the human brain owing to which it rushes to the conclusion that a fee of 1 per cent per annum (pa) over any number of years totals up to 1 per cent of the amount. That is completely wrong. The brain struggles to understand that a fee of 1 per cent pa over 10 years becomes a total fee of about 10 per cent. Nobel Prize-winner William Sharpe correctly observed that minimising investment costs, along with diversification, are the two most important rules in investing. So, let us fix this bug.

The brain finds it comfortable to shut down when faced with too much complexity. To fix that, we have to simplify, even if that requires a small sacrifice in accuracy. 

Suppose you have a corpus of ₹10 crore, kept in physical cash at home. You agree to pay the security guard a fee of 1 per cent p.a. In the first year, you pay a fee of ₹10 lakh, leaving you with ₹9.9 crore. In the second year, the fee is ₹9.9 lakh. The total fee over two years is ₹19.9 lakh. This total fee of ₹19.9 lakh divided by ₹10 crore is 1.99 per cent over two years. This is close to 2 per cent. 

The easiest way to do this calculation, even if it is not fully accurate, is that 1 per cent in the first year plus 1 per cent in the second year equals a total of 2 per cent. The accurate way to do this calculation is that in the first year, you are left with 99 per cent of the amount. Ninety-nine per cent in decimals is 0.99. In the second year, you are left with 99 per cent (ie 0.99) of what you started the second year with. So, at the end of the second year, you are left with 0.99 multiplied by 0.99, which is 0.9801. This is 1.99 per cent less than what you began the first year with. 

Extending this to 10 years, the simple calculation implies a total fee of 10 per cent. The more accurate calculation shows a total fee of 9.56 per cent. The simple calculation is sufficient to think through most real-life decisions. So, let us stick to that. In the previous example, over 10 years the total fees would be ₹1 crore, and you would be left with ₹9 crore. 

Let us assume that there is a mutual fund (MF) scheme where the direct plan has a fee of 0.5 per cent pa and the regular plan has a fee of 1.5 per cent pa The difference between the two is 1 per cent pa For simplicity, let us assume that the fee does not change for the next 10 years; that your entire net worth is invested in this scheme; and you spend your entire salary on living expenses. With the regular plan, you will be 10 per cent poorer at the end of the 10 years, as compared to the direct plan. That is beyond dispute. The only decision you have to make is whether using the regular plan provides you with so much benefit or convenience that it justifies being 10 per cent poorer at the end of 10 years. Inflation and returns do not change this conclusion. Including them only distracts the brain from understanding it. 

If a balanced fund (direct plan) generates 1 per cent pa return net  of inflation and taxes, then giving up 1 per cent pa in additional fees in a regular plan is giving up 100 per cent of the increase in our purchasing power. Hence, every 1 per cent pa of investment costs is a matter of life or death. 

 

The writer is an hourly-fee  financial planner and a Sebi RIA at Fiduciaries.in. He was a private-equity investor for 12 years.