# Reduction ab absurdum – Arthvigyan

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### Proof by Contradiction

Recently I came across a talk given by Professor Sanjay Bakshi. He talked about one mathematical concept of Proof by contradiction which is used by intelligent investor to invest in current fads.

As per Wikipedia –

In logic and mathematicsproof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction.

What it means, we should approach the problem by assuming the assumption implicate in the problem are correct and try to prove that these assumption leads to some absurd conclusion.

Let’s understand this concept with one example.

Company : D-mart

 Particulars Rs in Crores Current Mcap 1,40,000 PAT 1,414 PBT 1,902 Current Revenue 24,000 No of Stores 225 Revenue per Store 107 FD interest rate 8% PAT { Interest Income ( Mcap * 8%) } 11,200 Profit before tax ( PAT / 75% ) 14,933 PBT Margin 8.00% Expected Revenue 1,86,667 Total No of Stores 1750 Total Retail Area required (Million Sq. ft.) 59

As an investor, one must think like owner. So suppose investor decided to buy D-mart. He will have to pay Rs.1,40,000 crores for buying whole company. Investor should get minimum rate of return of 8% (FD interest rate). So he should expect profit after tax of Rs.11,200 crores and profit before tax of Rs.14,933 crores. By reverse calculation, company must earn revenue of Rs.1,86,667 crores. With further reduction, company has to open 1750 stores occupying the total area of 59 mn sq. ft.

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Is it Impossible? No. One can cite example of Wal-Mart. But the point I am driving is that it will take min 6-8 years for D-mart to reach this level of operation. At the same time It is very difficult to predict the future of retail industry due technological disruption, consumer preference etc. So considering all of these factors it is better to stay away from investing in the company whose valuation reflects 6-8 years future performance. Also if investor overpays, he is bound to get lower returns.

Investor can apply this concept to most of the emerging stocks or jackpot stocks recommended by experts in the media and reach a conclusion whether the company can achieve the revenue or profit implicit in the stock price.

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