# Game Theory and Dominant Strategies

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Most people in India, especially her investors, have welcomed Indian Government’s Corporate Tax Rate-cut with fanfare. While first level thoughts may deceive us into believing all that extra money directly adds to the value of all companies, a deeper level thought process provides a more accurate understanding.

## The Tax Rate Cut

1. For existing domestic companies, the corporate tax rate is reduced from around 35 percent to 25 percent (for domestic entities that do not avail of any exemptions or incentives, the effective tax rate could be as low as 22 percent);
2. For manufacturing firms incorporated after October 1, 2019 and beginning operations before March 31, 2023, the corporate tax rate is slashed from 25 percent to 15 percent (this will amount to an effective tax rate near 17 percent, including surcharge and cess):
3. For companies that continue to avail of exemptions or incentives, the rate of minimum alternate tax (MAT) is reduced to 15 percent from the current 18.5 percent (the effective MAT will lower from 21 to 22 percent to 17 percent, including surcharge and cess).

While points #2 and #3 are equally welcome, the big news is #1: A 28% reduction in Corporate Tax Rates for Indian companies–from 35% to 25% (Which can go to as low as 22%).

The markets cheered the move with a 10%+ gain in the BSE SENSEX in a matter of mere days.

But how excited should investors be about the rate cut? Does it benefit all companies equally? If not, which companies do gain in value and which companies do not? To answer all these questions, we should turn our attention to a very famous and influential mathematician from 1928.

## John Von Nuemann and the ‘Theory of Games’

John Von Nuemann, born in Budapest, Hungary, in 1903 had an eidetic memory and aced every course in school. By the age of 16, he was already publishing his research work in mathematics. By 1926, at the young age of 23, he was awarded a Doctorate in Mathematics (With minors in Physics and Chemistry).

Here’s a particularly revealing quote from the former paper:

The fate of each player depends not only on his actions but also on those of the others, and their behavior is motivated by the same selfish interests as the behavior of the first player. We feel that the situation is inherently circular.”

John Von Nuemann, Zur Theorie der Gesellschaftsspiele (On the Theory of Games of Strategy).

Simply put, in Strategy-based games like Chess or Poker, you will have to base your decisions on not only how you think you should make a move, but also based on how you think your opponent will make a move.

I always say that investing is neither like Chess, nor like Poker, but somewhere in between. So, suffice it to say that Game Theory very much applies to the world of business and investing too.

A corollary to Game Theory is the ‘Nash Equilibrium’ in Dominant Strategies. But don’t worry. We’ll get to it eventually.

## Game Theory Example: The Payoff Matrix and the Nash Equilibrium

Now let’s get specific. Let’s assume that the Tax Rate-cut has reached all industries. For the moment, let’s assume that Company A and Company B are in an oligopoly in a commodity-based industry (Let’s say the production and sale of Steel and allied products).

How do you think both the companies will decide to utilize the tax savings? Apart from paying out the entire tax savings as Dividends, which is a neutral sort of decision, there are two other ways in which companies can make use of the extra cash:

1. Protect Sales: Reduce price in the anticipation that the competitors will also reduce his price. This way, the overall Margin difference between the competitors remain the same. Customers are not enticed to go with one or the other competitor solely based on price.
2. Increase Capacity: Reinvest the money into more capacity in the anticipation that the competitor will also try to increase his capacity and capture more Market Share in the future.

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Since both Company A and Company B can employ either Strategy, we can build a Matrix of Strategies. This is generally called the ‘Payoff Matrix’:
The numbers you see are completely assumed, of course. For a thorough understanding, let’s take one quartile at a time.

### Quartile 1: Company A Reduces Price (Protects Sales) and Company B Reduces Price (Protects Sales)

Both Company A and Company B have anticipated that the other will opt to reduce prices. Since both the players have done this, the value creation for both of them will be equal, so to speak. Hence, I’ve given them the average score of 5 each.

### Quartile 2: Company A Reinvests (Increases Capacity) and Company B Reduces Price (Protects Sales)

In this scenario, although Company B reduced prices in the anticipation that Company A will also reduce price, thereby taking customers away from them, Company A in fact chose to not reduce prices. They decided to increase their capacity instead. What will be the impact of this?

Imagine yourself as the Inventory Manager of some large conglomerate who purchases Steel on a regular basis. You get the news that Company A’s Steel production capacity is being increased, but Company B’s Steel is available at a flat 20% discount. Do you really care that Company A is able to produce more Steel? Not really. You’d much rather go with the 20% discount offered by Company B.

So Company A loses some customers immediately, who are readily taken up by Company B. This leads to Company B realizing more value than Company A.

### Quartile 3: Company A Reduces Price (Protects Sales) and Company B Reinvests (Increases Capacity)

Quartile 3 is exactly like Quartile 2, but this time Company A realizes more value than Company B.

### Quartile 4: Company A Reinvests (Increases Capacity) and Company B Reinvests (Increases Capacity)

This is a lose-lose situation. Both the companies have increased capacity, but neither have passed on any of the tax cut benefit to their customers. So both of them gain only the least amount of value.

### The Nash Equilibrium

Now if you look at which strategy offers the most payoff for both Company A and Company B, you will quickly understand something interesting:

For Company A, Reducing Prices has a 20 Payoff and Reinvesting has a 16 Payoff. For Company B, the Payoff is similar as well for both strategies. In essence, if both the competitors are smart, neither of them will Reinvest. They will both choose to Reduce Prices in order retain their customers.

So Reducing Price, in this case, is the ‘Nash Equilibrium‘. Simply put, a Nash Equilibrium is a state in which neither competitors can gain anything by changing their strategy (Here, changing from Reducing Price to Reinvesting) provided the other competitors doesn’t change their strategy (Here, Reducing Price). In Chess terms, it is a ‘Stale Mate’ in which neither player can win and neither can lose.

## The Impact in Value due to Tax Cuts for Companies in Nash Equilibrium

But how can we put a value on this? I’m going to consider a similar industry in India – the two wheeler industry and specifically Hero Motocorp. The payoff matrix with a competitor like Bajaj Auto will look like this:

I will value the company once like I normally would (Without considering the tax cut) and then once more with the tax cut, keeping in mind that Margins may also have to take a dip (Like we discussed above).

DisclaimerI have not done any fundamental analysis of Hero Motocorp. The following valuation is based solely on the numbers, averages and informed guesses.

What’s the result?

As you can see, the value falls around the same levels despite the tax cut (It is actually about 1% less – but you get the point). This is what we expect for industries / companies in the Nash Equilibrium. You can try to experiment with the Margin and Tax assumptions. You can even try to do this for a comparable competitor (Ex: Bajaj Auto). But you will more or less arrive at the same conclusion.

## The Impact in Value due to Tax Cuts for Companies not in Nash Equilibrium, but cannot Reinvest to Increase Sales

Wow, that heading is a mouthful.

But essentially these are the set of ‘neutral’ companies we talk about a bit earlier. These are companies that are either dealing with a huge Total Addressable Market (The proverbial ‘glass ceiling’ is very tall) or companies having their own niches and Pricing Power. This way, their Margins need not take a downgrade. However, there’s a catch. These companies cannot really reinvest to increase their Sales in any meaningful way.

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Can you think of any examples in the Indian context? For this exercise, I have chosen the Asset Management industry in India. Clearly, the TAM in the India AMC industry is massive for lack of a better word. Competitors need not necessarily compete on Margins. You’re not going to switch from one investment fund to another if they promise a 10% less TER. It’s just not worth the hassle. But also, when was the last time you got attracted to an AMC solely based on advertising or banding? If you’re a rational investor, you’re looking at performance, fund manager history, convenience, grievance redressal among many other things.

Don’t trust me? Go ahead and look at the Balance Sheet of any pure Asset Management Company (Say, HDFC AMC or Reliance Nippon). Their ‘Investments’ will be multiple times the ‘Fixed Assets’. They simply cannot generate more Sales by reinvesting. That’s a fact. So they often have a high Dividend Payout Ratio (DPR) and whatever Cash is left, they invest in financial securities.

So, how might HDFC AMC fare in Pre Tax-cut and Post Tax-cut value? Here’s how:

Disclaimer: Contrary to the above Hero Motocorp exercise, I have done some fundamental analysis of HDFC AMC is an earlier blog post: HDFC AMC IPO Valuation: Speed DemonSo all I had to do here was replace the numbers with the latest figures and touch up a very limited extent on some assumptions.

There’s roughly a 7% increase in value. Once again, I’m not here to debate whether the valuation is correct or not. We can do that in a separate post if I ever revalue HDFC AMC in the future. The point here is that the restriction on reinvestment does have a visible impact on how value transpires to the shareholders.

Obviously, I have no idea how HDFC AMC or for that matter, their competitors will choose to pass on the tax cuts. But regardless of the way they choose, you should only be ~7-10% more excited for companies like HDFC AMC as you did before the tax cut. That is still far better than the nil increase we got for companies like Hero Motocorp.

There are exceptions to the rule as well. CDSL (CDSL Valuation: How Much Cash is Too Much Cash?), for instance, has a considerable grip on its Margins and cannot reinvest to increase Sales. But there’s a third catch. CDSL already pays very low Taxes, averaging at about 27% or so. Although CDSL is a perfect candidate for this category, the value creation due to tax cuts is negligible.

You see how we’re going up the ladder with this thing. What do you think will the next and final rung on this value creation ladder?

## The Impact in Value due to Tax Cuts for Companies not in Nash Equilibrium, but can Reinvest to Increase Sales

Obvious, isn’t it? We are now going to look at companies that have both a high Pricing Power (No need to compromise on Margins) and can reinvest to boost Sales considerably.

Many names pop up immediately: Pidilite, Asian Paints and the likes. But a dash above all of these, the most prominent examples in my head right now are Private Banks.

Private Banks have a massive TAM, can reinvest virtually unlimited amounts of capital (Or for instance, in the case of IndusInd Bank, they have chosen to use the tax cuts to increase their Provision Coverage Ratio (PCR), which again indirectly leads to more lending in the future).

For this exercise, I’m going to choose a fan favorite: HDFC Bank. Unfortunately, I still have not done any meaningful study on HDFC Bank, so I’m going to have to add the disclaimer:

DisclaimerI have not done any fundamental analysis of HDFC Bank. The following valuation is based solely on the numbers, averages and informed guesses.

Here’s how the cookie crumbles:

That’s a ~26% increase in value! Great, but what’s the math behind this? Well, it’s very crude, I have to warn you.

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I considered the ~10% increase in Sales / Net Profits solely due to the tax cut. Then, in a self-admitted half-ass attempt, I took HDFC Bank’s Equity Gearing Ratio (Units of Sales produced per Unit of Equity Capital), which turned out to be 0.82 on average for 10 years. The average leverage over the same period is about 8.49. So, a crude multiplication of 0.82 x 10 x 1.1 gave me a 66% increase. But this 66% ‘capacity’ isn’t likely to be utilized over a single or even a medium term time period. It is likely to unravel over many, many years ahead. So I averaged it over the 20 year High Growth Period I have assumed and voila, I got a 2.60% (Rounded off to 3.00%) CAGR. This is added to the 10% to arrive at a 13% increase in HDFC Bank’s Net Profits for several years together. So once again, please take this with a bucket of salt. This exercise is just to show you the impact of the tax cuts, not to arrive at a precise value for HDFC Bank.

The ~15% rally in Bank NIFTY post the tax cut announcement clearly stands justified:

Why only 15% and not 25%? I generally try not to reason with the markets. But probably noteworthy is the fact that Bank NIFTY also contains Public Banks, which may not create as much value in this case for reasons well known to many investors.

## Jeff Bezos Vs. You

Are you are doubtful about tax cuts improving an economy? You are not alone. There are people who bat for Supply-side Economics (Like Corporate Tax Cuts) and there are those who vehemently oppose it in favor of Demand-side Economics. Regardless of whether you’re right-leaning or left-leaning, my conclusions for the time being will remain the same:

If you are having a difficult time processing this conclusion, I have a fun thought experiment for you. Imagine that both you and Jeff Bezos are handed Rs. 1,00,00,000 (Rs. 1 Crore) free of cost. Who do you think will create the most value out of this hand-out money?

I whole-heartedly hope you can beat Bezos. But we all know that the logical answer is Jeff Bezos. Why is that? For starters, he can put it back into Amazon, which is a capital turnover machine. By the time you even increase your money’s value by 30% (Say), Bezos would have doubled it and the difference would only get worse over time (i.e. In favor of Bezos). Even if we implement the restriction that Bezos can’t invest in any of his companies, his sheer entrepreneurial brilliance will simply enable him to create a new (Alebit tiny) startup, which will eventually beat you at the compounding game. The only way you can come close to beating Beozs is to invest with him, in his own companies.

Everyone will agree with this outcome at least, I’m sure. The next logical question to ask is, why should it be any different for a company like Hero Motocorp Vs. HDFC Bank? I’m not trying to take away anything from Hero Motocorp, which has done this country tremendous service. But when it comes to compounding incremental amounts of money, HDFC Bank emerges the clear winner.

Ultimately though, it’s all about Price Vs. Value. HDFC Bank ran up quite a bit after the tax cut, so the 25% ‘gap’ may have already been bridged to some extent. In fact, in my opinion, many companies that do not seem to have additional value creation abilities have also run up. Hence, it’s difficult to pick out a good company which still offers value solely owing to the tax cut.

Last but not the least, in Warren Buffett’s 2017 Berkshire Hathaway Chairman’s Letter to Shareholders, he talks a bit about how Corporate tax cuts work and how they end up creating value for shareholders. Despite the lack of Indian context, it’s a wonderful read. I highly recommend it for your perusal.

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