Towers of Hanoi, Russian dolls and Kirloskar

What is common among Towers of Hanoi, Russian Dolls and Kirloskar group of companies?

Those among you who did computer programming probably can guess the answer. Hint: Recursion.

A set of matryoshkas (Russian dolls) consists of a wooden figure which can be pulled apart to reveal another figure of the same sort inside. It has in turn another figure inside, and so on.


The Tower of Hanoi or Towers of Hanoi is a mathematical game or puzzle. It consists of three pegs, and a number of disks of different sizes which can slide onto any peg. The puzzle starts with the disks neatly stacked in order of size on one peg, smallest at the top, thus making a conical shape.


Look at Share holding of Kirloskar Brothers (KBL) and Kirloskar Oil Engines (KOEL).

A) KOEL market cap is 3145 Cr. Now watch carefully at Russian Doll No. 1.
KBL owns 38 % of KOEL.

B) KBL market caps is 4548 Cr. Now for the Russian doll no. 2. KOEL owns 10% of KBL.
But as we have seen above, KBL owns 38% of KOEL. So, in effect, KOEL owns 38% * 10% = 3.8 % of itself.

Let me illustrate with a concrete example:
Suppose KOEL market cap increases by 1000 Cr, then KBL market cap should increase by 380 Cr. This follows from A as KBL owns 38% of KOEL.

When KBL market cap increases by 380 Cr, KOEL market cap should increase by 38 Cr. This follows from B.

Now, since KOEL market cap increases by 38 Cr, the KBL market cap should increase by 14 Cr.
Since KBL market cap increases by 14 Cr, KOEL market cap should increase by 1.4 Cr.

If KOEL market cap increases by 1.4 Cr, ..., so on, ad infinitum.(I can hear you, Enough, ENOUGH!)


Fortunately, all recursion cases have a terminal case which ultimately resolves the recursion. As the numbers get smaller, it is less and less meaningful to keep up with the recursion. Let's leave the elegance of recursion to programming classes and get down to the valuation of Kirloskar Oil Engines (KOEL).

The balance sheet of KOEL is as conservative as you could ask for.

The quoted investments are treated at cost (example: KOEL stake of KBL is on the books at 9 Cr. The market value at today's prices is 474 Cr. Stake in Kirolskar Ferrous is on books at 27 Cr. Current Market value: 108 Cr).

The investments which have gone bad are promptly written off (example: investments in Mysore Kirloskar and Ghatage Patil).

Result: Balance sheet significantly understates the investments. The book value of investments is 500 Cr where as, in my opinion, the current market value is at least 1000 Cr.
Subtract this 1000 Cr from KOEL market cap of 3145 Cr and you are getting a business which is growing by 25% per annum at PE of around 10.

Pictures Courtesy Wikipedia.