Hi!

Recently Nishith asked some questions on what discount rate to use in the valuation of stocks. Thought of sharing the original comment and the reply with you.

Dear Satyajeet – One question that I always wanted to ask value investors is that: “What discount rate one should use? Should it be the rate of return that you want from the particular stock? or The WACC of that particular company? or Something in line with 10 year G-Sec yield?. Your insight would be really helpful. Thanks.

Dear Nishith:

Very good question. One that has kept leading researchers in finance busy for the last several decades. All three alternatives have followers.

The **first option** – your want – is formally called “utility function”. How do you react to the chances of gains & losses at different levels of wealth? Economists at the turn of the 20th century and now behavioural economists take this approach to discount rates.

The **second option** – risk free rate + risk premium – is formally called “no arbitrage pricing”. CAPM is a well-known variant (there are others). Prices of various financial assets are seamlessly inter-connected. The base is set by the price of risk free asset. Every other (i.e risky asset) is priced in reference to the risk free asset, plus the risky asset’s unique risk premium. Any other price leads to arbitrage opportunities and is unsustainable. Economists from the 1950s onwards took this approach to discount rates.

The **third option** – risk free rate only – is sometimes called the “Fed model”. It was observed that the long term returns in the US stock markets merely match those of US Treasury bonds. That is surprising, because the riskier stock market is supposed to give higher returns than the much safer bonds. Some say, Alan Greenspan was referring to the Fed model when he made that famous comment about “irrational exuberance” in 1996.

**Which option?**

So then, which discount rate should you use? The first two alternatives have theoretical merits but are difficult to estimate with confidence in practice. The third alternative is easier to implement, but doesn’t have the required theoretical backing. It works only when you use it in conjunction with “certainty-equivalent cash flows” i.e. adjust for the risk in the cash flows instead of in the discount rates. It seems Warren Buffett, the patron saint of value investing, uses this method.

Consider a **fourth option** – reverse-engineering. Stephen Penman explains how to finesse the difficult estimation issues. You normally input a discount rate to get your DCF valuation as an output. Why not reverse-engineer the process? Take the current stock price, plug in the other inputs (i.e. cash flow projections) to derive the missing variable i.e. discount rate. You can compare the stock market’s discount rate thus found, with your required rate of return. Buy the stock if the discount rate is greater than your required rate of return. Sell the stock if the discount rate is less than your required rate of return.

Hope that answers your query, Nishith.

NishithDear Satyajeet,

Thank you for your valuable insights. I really appreciate your effort to put things in to perspective. I did read on some occasions that Warren Buffett uses the treasury rate (roughly though) while he is doing his “mental accounting”. Is it possible to club the risk free rate on long term government bonds with the rate of inflation to derive “your own discount rate”?. I feel that could be a starting point because it takes 2 things. 1st you are asking for at least the risk free rate of return and second the rate of inflation in our country is reasonably high so you are “discounting the risk of inflation also” in your discount rate.

The final product (our discount rate) hence gives us a rate that shields you from both financial risk free rate and the purchasing power. I don’t know how much this little theory of mine is practical. But anyways, just thought to share it with you. Would like your comments on it.

By the way there is a good site “buffettfaq.com” where you can find teachings of warrenn buffett online. I am sure you must have gone through the site, but just in case if you haven’t it’s a good one to glance through.

Thanks again..

Satya MishraHi Nishith,

Firstly, my apologies for the delayed response.

There are two separate things:

1. Required rate of return = Risk free rate + Risk premium

2. Nominal interest rate = (1 + Real interest rate) * (1 + Inflation)

So at first glance, mixing risk-free rate and inflation is “intellecutual cross-dressing” (to borrow Buffett’s term).

However, given that risk-free rate, risk premium, real interest rate and inflation are very important terms in economics, there is a case to be made for studying economics in-depth to see whether/how they are related. And to check whether your statement is tenable at all.

Great economists (Irving Fisher comes to mind) have thought about these issues in fundamental terms. But I’m afraid my knowledge is shallow in that area. Will be interesting to explore though.

nishithvyasThanks for your reply Praveen. Actually initially i was of the same opinion as you but some how after talking to a lot of small business owners i feel that the real inflation in the sense that input costs of materials and labour are actually much higher than the long term G-Sec yields and hence I thought if it might be a good idea to add inflation over and above the prevalent G-Sec yield. Again it must be a recency bias among business owners as current conditions are quite distorted.

Regards

Nishith

K Praveen KumarHi,

I believe risk free rate takes care of the inflationary situation in the country. Risk free rate only identifies that there is a certainty in the cash flow/ receipt of interest and principal.

Adding inflation to the risk free rate would lead to double counting.

regards

Praveen

AnonymousFinally a blog, that I can relate to and enjoy.

Just a question if you would care to reply….Although a thorough analysis is extremely imp. before investing in a stock..What do you think of the use of or reliance on intuition or gut feeling when investing.For example a decade ago I was in high school and just knew that the stock market was an investment option, I bought a notebook made by ITC ltd..then I had a friend tell me about the ITC welcome group hotels acquiring Sheraton hotels in India..and somehow I knew this company was full of new ideas and I liked its products…I even suggested to my dad to buy their stock..which of course he completely ignored..and a look at its charts now shows I was not off the mark…anyways what is ypour opinion??

Satya MishraHi,

Thanks for the kind words!

Was it only intuition or was it ‘consumer’s edge’ that Peter Lynch talks about in ‘One Up on Wall Street’? He talks about how common folk can generate stock ideas from their everyday life. I completely buy that argument. In fact, one of my earliest stock purchases was Balaji Telefilms. A few years back, its soap operas were all pervasive on the telly. And, just like ITC – its stock did well.

Until, one day it didn’t. And that’s the catch. I had no robust mechanism to analyze and track the unfolding story.

Intuition or consumer’s edge is an excellent place to start/generate leads. But it must be backed by rigorous quantitative (financial) and qualitative (strategic) analysis. Of course, you have already prefaced your comment with that point. Peter Lynch also emphasizes it in his book. Although one has to look beyond his book to learn ‘how to analyze’ well.

Taha MerchantHey Satyajeet,

Loved the way you systematically organize your thoughts in your post. Brings clarity to the subject of discussion; helping stimulate further thinking on it.

While thinking about discount rates in the context of ‘value investors’, I think it is important to emphasize that value investors are looking to buy something not at its fair value, but when it is undervalued. Because they themselves would not generally buy something at its fair value, they are in effect looking for not their own discount rate, but someone else’s discount rate while estimating fair value.

Who is that someone else? What is that fair value? It is the price a prudent business man would be willing to pay for purchasing the entire business if he could buy it. And because different such businessmen may come with different shades of optimism toward that business (and consequently place increasingly higher ‘fair values’ on it), we are looking for the ‘minimum’ a such a businessman would be willing to pay.

Now, remember that the risk-free rate of return on capital is accessible to anyone in an economy, without doing any work or needing any special skills/knowledge to be able to earn that rate of return. Thus the essential reason for anyone to take the trouble of venturing into business of any kind, new or existing, is to earn a rate of return on his capital higher than the passive risk-free rate of return. So it seems reasonable that a prudent businessman will arrive at his fair value for any business with this in mind.

If our businessman can arrive at a figure of annual earnings for a particular business such that he can conclude that it is extremely unlikely that future earnings will average below that figure, then that would offer him a great starting point for his valuation. In the case of an already well established, financially sound business with an already demonstrated track record of profitability through business cycles and no reason to doubt the future of the business, it becomes much less tricky to arrive at such a figure.

Once such a figure is arrived at, it would seem reasonable that for the average business (one earning ROEs in the region of 15%), the minimum fair value a businessman is likely to place on it would be that arrived at by discounting such an earnings figure by the after tax risk-free rate of return of about 7%.

That’s because if he purchases the business at such a price, he is buying into a likely upside, with a low probability of downside. The upside being that he earns an earnings yield of higher than 7% on his buying price in future and the downside being that he earns one that is lower. The downside is low because of the nature of this earnings figure that we have arrived at as described earlier. The upside is likely because while he will get an earnings yield of 7% on his purchase price to start off with, he is going to also get the right to invest a part of his earnings back into the business every year (retained earnings). And since the business is expected to earn ROEs which are much higher that 7% (15% for the average business), he will earn such higher returns-on-capital on the earnings which are retained on his account in future years. In this manner, as the years go by, his aggregate return on capital will keep marching closer to the ROEs that the business earns.

I think that there is scope for adjusting the discount rate higher/lower than 7% for businesses of below-average/above-average profitability, within a band of 10% and 5% respectively.

So that is about the fair value discount rate, or the minimum price a conservative and prudent should be willing to pay to buy the entire company. And which in a value investor’s case coincides with his ‘Sell price’ discount rate. Obviously, a value investors ‘Buy price’ discount rate is going to be much higher since he is looking to buy at a price much below fair value. And in that sense, a value investor by definition cannot use his own required rate of return as a guidepost to discovering the fair value of a business.

Satya MishraHi, Taha!

Great to hear from you after a long time. Like I’ve told you many times before, you should consider blogging/voicing your opinion more often.

I actually had to read the post and the series of comments from the beginning to place your comment in context.

First, some background to my post: At the time of writing the post, I was reading Stephen Penman’s book

Accounting for Value. The opening chapters of the book give a sweeping overview of the journey of theory of finance. I followed up with some of the references he gives. He refers to a fascinating book by Mark Rubinstein calledA History of the Theory of Investments. Turns out discount rates have received a lot of attention from a wide spectrum of academics/theorists.Penman, who perhaps is the only mainstream academician who embraces value investing, chooses to finesse/bypass the issue of discount rates by the reverse-engineering valuation (to arrive at implied discount rate as opposed to prescribing one).

However, you are taking a more prescriptive stance compared to Penman. Sort of keeping the skeletal framework of CAPM (risk-free rate + risk premium), while replacing the guts with value investing logic.

I have no quarrel with that.

Taha MerchantTwo things I dont fully understand with the reverse engineering approach –

1. If estimating the market’s discount rate at a particular market price, as you’ve said one would have to plug in the other inputs – again as the market estimates them – at that point it time. The market’s excessive swings between optimism and pessimism also see manifestation in its earnings projections among other things. Its not just the market discount rates that fluctuate to silly levels, but so do the perceptions about the future of the business which get discounted at those rates. So discovering and comparing market discount rates with your own seems a tricky thing to do.

2. Even if one assumes that one has discovered the comparable market discount rate in a given situation, that still doesn’t bypass the need to have your own independent view of the approximate fair value discount rate. That important reference is would still be equally needed for a comparison to judge both the presence and extent of undervaluation in that situation.

Satya MishraHi Taha!

1. Why do you say that “one would have to plug in the other inputs – again as the market estimates them”? The idea is to plug your inputs (and not Mr Market’s) in order to find the discount rate implied in the market price.

We do this simply because estimating discount rates (using something like a CAPM) is a notoriously difficult. So we try to isolate the missing variable – the discount rate – given our inputs.

2. Yes, we do need a benchmark to compare the implied discount rate with. A minimum return which signals the undervaluation.

Taha MerchantThere’s –

1) The market’s inputs @ market’s discount rate = market price

2) Your inputs @ your discount rate = your price

3) Your inputs @ discount rate implied in market price considering your inputs = market price

I would say that 1) and 3) are not the same

Satya MishraIndeed, they’re not the same. The issue is about unknown variables and whether it is possible to mathematically triangulate them. Given two knowns – your earning estimates and the market price, the unknown implied discount rate can be triangulated. It’s not a trivial result.

With unknown market estimates, the unknown discount rate can’t be triangulated.