Module 3 Fundamental Analysis

Chapter 14

DCF Primer

92

14.1 – The Stock Price

In the previous chapter we understood stage 1 and stage 2 of equity research. Stage 1 dealt with understanding the business and stage 2 dealt with understanding the financial performance of the company. One can proceed to stage 3, only if he is convinced with the findings of both the earlier stages. Stage 3 deals with the stock price valuation.

An investment is considered a great investment only if a great business is bought at a great price. In fact, I would even stretch to say that it is perfectly fine to buy a mediocre business, as long as you are buying it at a great price. This only shows the significance of ‘the price’ when it comes to investing.

The objective of the next two chapters is to help you understand “the price”. The price of a stock can be estimated by a valuation technique. Valuation per say helps you determine the ‘intrinsic value’ of the company. We use a valuation technique called the “Discounted Cash Flow (DCF)” method to calculate the intrinsic value of the company. The intrinsic value as per the DCF method is the evaluation of the ‘perceived stock price’ of a company, keeping all the future cash flows in perspective.

The DCF model is made up of several concepts which are interwoven with one another. Naturally we need to understand each of these concepts individually and then place it in the context of DCF.  In this chapter we will understand the core concept of DCF called “The Net Present Value (NPV)” and then we will proceed to understand the other concepts involved in DCF, before understanding the DCF as a whole.

M3-Ch14-title

14.2 – The future cash flow

The concept of future cash flow is the crux of the DCF model. We will understand this with the help of a simple example.

Assume Vishal is a pizza vendor who serves the best pizza’s in town. His passion for baking pizzas leads him to an innovation. He invents an automatic pizza maker which automatically bakes pizzas. All he has to do is, pour the ingredients required for making a pizza in the slots provided and within 5 minutes a fresh pizza pops out. He figures out that with this machine, he can earn an annual revenue of Rs.500,000/- and the machine has a life span of 10 years.

His friend George is very impressed with Vishal’s pizza machine. So much so that, George offers to buy this machine from Vishal.

Now here is a question for you – What do you think is the minimum price that George should pay Vishal to buy this machine? Well, obviously to answer this question we need to see how economically useful this machine is going to be for George. Assuming he buys this machine today (2014), over the next 10 years, the machine will earn him Rs.500,000/- each year.

Here is how George’s cash flow in the future looks like –

2015 2016 2017 2018 2019 2020 2021 2022 2023 2024
500,000 500,000 500,000 500,000 500,000 500,000 500,000 500,000 500,000 500,000

Do note, for the sake of convenience, I have assumed the machine will start generating cash starting from 2015.

Clearly, George is going to earn Rs.50,00,000/- (10 x 500,000) over the next 10 years, after which the machine is worthless. One thing is clear at this stage, whatever is the cost of this machine, it cannot cost more than Rs.50,00,000/-. Think about it – Does it make sense to pay an entity a price which is more than the economic benefit it offers?

To go ahead with our calculation, assume Vishal asks George to pay “Rs.X” towards the machine. At this stage, assume George has two options – either pay Rs.X and buy the machine or invest the same Rs.X in a fixed deposit scheme which not only guarantees his capital but also pays him an interest of 8.5%. Let us assume that George decides to buy the machine instead of the fixed deposit alternative. This implies, George has foregone an opportunity to earn 8.5% risk free interest. This is the ‘opportunity cost’ for having decided to buy the machine.

So far, in our quest to price the automatic pizza maker we have deduced three crucial bits of information –

  1. The total cash flow from the pizza maker over the next 10 years – Rs.50,00,000/-
  2. Since the total cash flow is known, it also implies that the cost of the machine should be less than the total cash flow from the machine
  3. The opportunity cost for buying the pizza machine is, an investment option that earns 8.5% interest

Keeping the above three points in perspective, let us move ahead. We will now focus on the cash flows. We know that George will earn Rs.500,000/- every year from the machine for the next 10 years. So think about this – George in 2014, is looking at the future –

  1. How much is the Rs.500,000/- that he receives in 2016 worth in today’s terms?
  2. How much is the Rs.500,000/- that he receives in 2018 worth in today’s terms?
  3. How much is the Rs.500,000/- that he receives in 2020 worth in today’s terms?
  4. To generalize, how much is the cash flow of the future worth in today’s terms?

The answer to these questions lies in the realms of the “Time value of money”. In simpler words, if I can calculate the value of all the future cash flows from that machine in terms of today’s value, then I would be in a better situation to price that machine.

Please note – in the next section we will digress/move away from the pizza problem, but we will eventually get back to it.

14.3 – Time Value of Money (TMV)

Time value of money plays an extremely crucial role in finance. The TMV finds its application in almost all the financial concepts. Be it discounted cash flow analysis, financial derivatives pricing, project finance, calculation of annuities etc, the time value of money is applicable. Think of the ‘Time value of money’ as the engine of a car, with the car itself being the “Financial World”.

The concept of time value of money revolves around the fact that, the value of money does not remain the same across time. Meaning, the value of Rs.100 today is not really Rs.100, 2 years from now. Inversely, the value of Rs.100, 2 years from now is not really Rs.100 as of today. Whenever there is passage of time, there is an element of opportunity. Money has to be accounted (adjusted) for that opportunity.

If we have to evaluate, what would be the value of money that we have today sometime in the future, then we need to move the ‘money today’ through the future. This is called the “Future Value (FV)” of the money.  Likewise, if we have to evaluate the value of money that we are expected to receive in the future in today’s terms, then we have to move the future money back to today’s terms. This is called the “Present Value (PV)” of money.

In both the cases, as there is a passage of time, the money has to be adjusted for the opportunity cost. This adjustment is called “Compounding” when we have to calculate the future value of money. It is called “Discounting” when we have to calculate the present value of money.

Without getting into the mathematics involved (which by the way is really simple) I will give you the formula required to calculate the FV and PV.

Example 1 – How much is Rs.5000/- in today’s terms (2014) worth five years later assuming an opportunity cost of 8.5%?

This is a case of Future Value (FV) computation, as we are trying to evaluate the future value of the money that we have today –

Future Value = Amount * (1+ opportunity cost rate) ^ Number of years.

= 5000 *(1 + 8.5%) ^ 5

= 7518.3

This means Rs.5000 today is comparable with Rs.7518.3 after 5 years, assuming an opportunity cost of 8.5%.

Example 2 – How much is Rs.10,000/- receivable after 6 years, worth in today’s terms assuming an opportunity cost of 8.5%?

This is clearly the case of Present Value (PV) computation as we are trying to evaluate the present value of cash receivable in future in terms of today’s value.

Present Value = Amount / (1+Discount Rate) ^ Number of years

= 10,000 / (1+ 8.5% ) ^ 6

= 6129.5

This means Rs.10,000/- receivable after 6 years in future is comparable to  Rs.6,129.5 in today’s terms assuming a discount rate of 8.5%.

Example 3 – If I reframe the question in the first example – How much is Rs.7518.3 receivable in 5 years worth in today’s terms given an opportunity cost @ 8.5%?

We know this requires us to calculate the present value. Also, since we have done the reverse of this in example 1, we know the answer should be Rs.5000/- . Let us calculate the present value to check this –

= 7518.3 / (1 + 8.5%) ^ 5

= 5000.0

Assuming you are clear with the concept of time value of money, I guess we are now equipped to go back to the pizza problem.

14.4 – The Net Present Value of cash flows

We are still in the process of evaluating the price of the pizza machine. We know George is entitled to receive a stream of cash flows (by virtue of owning the pizza machine) in the future. The cash flow structure is as follows

2015 2016 2017 2018 2019 2020 2021 2022 2023 2024
500,000 500,000 500,000 500,000 500,000 500,000 500,000 500,000 500,000 500,000

We posted this question earlier, let me repost it again – How much is the cash flow of the future worth in today’s terms?

As we can see, the cash flow is uniformly spread across time. We need to calculate the present value of each cash flow (receivable in the future) by discounting it with the opportunity cost.

Here is a table that calculates the PV of each cash flow keeping the discount rate of 8.5% –

Year Cash Flow (INR) Receivable in (years) Present Value (INR)
2015 500,000 1 460,829
2016 500,000 2 424808
2017 500,000 3 391481
2018 500,000 4 360802
2019 500,000 5 332535
2020 500,000 6 306485
2021 500,000 7 282470
2022 500,000 8 260,335
2023 500,000 9 239,946
2024 500,000 10 221151
Total 50,00,000 32,80,842

The sum of all the present values of the future cash flow is called “The Net Present Value (NPV)”. The NPV in this case is Rs. 32,80,842 This also means, the value of all the future cash flows from the pizza machine in today’s terms is Rs. 32,80,842. So if George has to buy the pizza machine from Vishal, he has to ensure the price is Rs. 32,80,842 or lesser, but definitely not more than that and this is roughly how much the pizza machine should cost George.

Now, think about this – What if we replace the pizza machine with a company? Can we discount all future cash flows that the company earns with an intention to evaluate the company’s stock price? Yes, we can and in fact this is exactly what will we do in the “Discounted Cash Flow” model.


Key takeaways from this chapter

  1. A valuation model such as the DCF model helps us estimate the price of a stock
  2. The DCF model is made up of several inter woven financial concepts
  3. The ‘Time Value of Money’ is one of the most crucial concept in finance, as it finds its application in several financial concepts including the DCF method
  4. The value of money cannot be treated the same across the time scale – which means the value of money in today’s terms is not really the same at some point in the future
  5. To compare money across time we have to ‘time travel the money’ after accounting for the opportunity cost
  6. Future Value of money is the estimation of the value of money we have today at some point in the future
  7. Present value of money is the estimation of the value of money receivable in the future in terms of today’s value
  8. The Net Present Value (NPV) of money is the sum of all the present values of the future cash flows

 

92 comments

  1. Harshad Salvi says:

    What are other valuation models which are used in equity research or say M&As?
    Hope my question is not ambiguous..

    • Karthik Rangappa says:

      There are basically two valuation techniques – Intrinsic valuation and relative valuations. DCF is the best way to do intrinsic valuations, which is what we have explained here. Relative valuation is a bit dicey as you are essentially comparing two companies by assuming they are similar. But in reality no 2 companies are similar. Not that DCF is a very clean technique..both have its drawbacks. The industry practices both these techniques.

      • Avinish Sarvaiya says:

        Hi,
        Do we take opportunity cost always as current fixed deposit’s rate of return at the time of calculations?
        Waiting for the reply

        • Karthik Rangappa says:

          Yes, you can.

          • Avinish Sarvaiya says:

            Hello,
            I have to ask one more question I hope you wouldn’t mind answering it too..😋
            As you said FD rates at the time of calculations must be taken as opportunity cost.
            So the question is what about the Discount rate ?( which is cost of capital itself,right? ) As you have taken it same as the opportunity cost. Is it always the same I.e. FD rate only?
            I hope you get my point..😊😊

          • Karthik Rangappa says:

            Considering FD rates have fallen quite a bit, I think we need to have a better discount rate :). I have a tendency to take conservative numbers, hence something like 10-12% should be alright.

  2. Sameer says:

    Little typing mistake noticed
    No. 14.3 is missing where as 14.2 is double
    🙂

  3. Abhimanyu Jamaiyar says:

    i am interested in a career in equity research. i do not have any prior experience but i am very keen to learn. Is it possible to get trained under zerodha? I am willing to join you as a fresher or even as a trainee.

    • Karthik Rangappa says:

      Thanks for the interest expressed. I’m afraid we have no such openings in Equity Research as such. Would the support desk interest you?

      • Abhimanyu Jamaiyar says:

        Dear Sir,
        Thanks a lot for your reply. Yes, i would like to go ahead with the support desk profile. Kindly share the details.Waiting for your reply.
        Regards,
        Abhimanyu Jamaiyar

  4. SUBHANKAR says:

    How to calculate the fair price of usd/inr currency pair? Explain with example.

  5. Sanat says:

    I am unable to understand PV properly…………please help

    • Karthik Rangappa says:

      Present value is the current value of the future payment. For example assume you are expected to receive Rs.100,000/- 10 years from now. PV helps you answer find out the worth of that Rs.100,000/- in today’s terms.

  6. BM says:

    Price of Amararaja has gone up 🙂 do you have other analysis could be shared ?? Thanks for the investor education …priceless

  7. Hitesh says:

    Shouldn’t we account inflation while calculating the present value of money?

  8. Karan Samal says:

    While calculating the Free Cash Flow, the formula is Cash Generated From Operations – Purchase of Fixed Assets
    Do we also add ‘Sale of Fixed Assets’ figure in this formula??

    • Karthik Rangappa says:

      Cash flow from ‘Sale of fixed asset’ could be a one off event. Hence, its best to ignore this one.

      • Karan Samal says:

        Thank you. While analyzing the fundamentals using all the ratios, I found a few companies that are fundamentally very sound. While doing the DCF analysis that too using very conservative assumptions (Growth rate 8% for each year till 10 years, opportunity cost @ 9%) , I found that the CMP of those stocks are less than the margin of safety price (30% discounted price from the lower intrinsic price). Shall I go ahead and accumulate these stocks?

  9. Govinda Daga says:

    please provide description of formula of finiding pv fv

  10. sammandar khan says:

    Dear Karthik
    How did you calculate the amount 7518.30? didn’t understand it
    thanks

  11. Sanjay limbu chongbang says:

    Respected sir! How should I evaluate an NPV with different negative and positive cash flow? What sense does it make?

  12. Abhilash says:

    Hi Karthik, I have joined your last Live Webinar @ 12 … It was simply Superb.
    How Dividend payout coming under Financial activities, Is it operational activity ?

    • Karthik Rangappa says:

      Thanks! I’m glad you liked the webinar 🙂

      OA consists of activites which are core to the company, where as div is an optional thing for companies.

  13. KARANVEEER SINGH JAGGI says:

    sir thanks for this module ! it was nice to learn new things
    and sir please can you share the excel sheet format of the dcf model ?

  14. chetan says:

    hi..can i have the dcf excel sheet plz

  15. shabaz says:

    sir,
    current p/e ratio is on 23.66 and current p/b is on 3.56
    is it the time that good investors doesn’t invest money and the nifty has made its top.
    Not confirm about p/b as it hasn’t crossed 4 but it still may be considered overbought and p/e should also be considered as overvalued.
    Am i right?

  16. Ajay says:

    Sir,
    Different websites (like Economic Times, NDTV Profit, Moneycontrol) having different P/E ratio, P/B value for SAME COMPANY. Why it is so??? Please share how to calculate P/E ratio, P/B values ACCURATELY from financial statements. Should we focus on Standalone balance sheet or consolidated balance sheet of company while buying a stock?? P/E ratio, P/B values are very important in fundamental analysis. Please provide detail guidance regarding this. Your help will be very useful to me. Thank you very much.

    • Karthik Rangappa says:

      Difference could be due to consolidated and standalone data? You should look at consolidated financial data. Will share a note on how to calculate these ratios sometime soon.

  17. Ajay says:

    Sir,
    I am studying your module 2 of fundamental analysis. I think that there is small mistake in calculating EBITDA . Please share your email id so that I can contact you. This is very important. You have taken financial cost twice.
    Total Expense – Finance Cost – Depreciation & Amortization .
    In the total Expense financial cost is already added (I think) and again Finance cost. Please clarify

  18. Ashish Gade says:

    Thanks a lot for the detailed DCF primer. I learned a lot. One question I have is :- the (reserves/Outstanding) is not added to NPV? Is it a norm or can we add it?

  19. Gourav Jha says:

    Thanks a ton for this knowledgeble detailed Varsity.
    I am willing to know that how can be accumulate data like future cash flows, discount rates etc in real practical scenarios for a company to calculate its intrinsic values.

    Is there a way to gather these data ? if so can it vary basis the assumptions of investor?

    • Karthik Rangappa says:

      This data is best if you can calculate them yourself. This is where the skill of the investor comes into play. So as a long term investor, its best if you develop these skills yourself.

      • Gourav Jha says:

        Thank you for the reply.
        But as a new investor, if I think to take a first step for valuation of any company. What factors needs to be taken into consideration? If you can give example once as to how you proceed for this exercise.

  20. Gurudutt says:

    Considering more than 3000 companies listed in the Indian stock market how to do analysis of all these stocks?

  21. Sriram Srinivasan says:

    Hi Karthick,

    Excellent work!!

    I have 2 questions :

    1.Once I start valuating a company based on DCF with annual reports for last 3 years and arrived at good MOS to buy, how can i keep check on the price based on quarterly results that will be published by the company in coming financial year? is there any data from quarterly reports that can help in DCF else I will have to wait another year to ascertain based on annual report published by the company.

    2. With growth stocks, its very difficult to value a company by DCF. In that case i just try to do reverse DCF to find out how much of growth is implied in current price or the market values it. Say for eg : Avanti feeds from reverse DCF gives me 31% growth for next 10 years in current price of 1886( TGR : 3.5%, Discount rate : 12 %,Growth I & II : 32% & 30%). Whats your take on DCF for growth stocks? How do you value growth stocks? Do you use earnings power?

    Thanks in advance.

    • Karthik Rangappa says:

      1) You will have to track new for quarterly result announcement
      2) Yes, that does make sense. Earning power, business moat, market size – these are few things that help.

      • Sriram Srinivasan says:

        Thanks for the quick reply. Regarding 1st question again: But the attributes used in DCF are not available from quarterly results report given by companies like cash from operations, CAPEX, non current debt, current debt or is it given somewhere? Please help me here.

        • Karthik Rangappa says:

          True, balance sheet items are not available during the year. But you don’t really need them as well. Once you develop the valuation model, you will have a fair idea of how much the stock is (should be) worth.

  22. Dinesh Kukreja says:

    Karthik you write the content in a very lucid manner. Thanks for helping millions understand for free!!!!

  23. Sanjay Dubey says:

    First of all, Awesome work Karthikji!
    I’m completely new to Trading/Share Market but your systematic approach has boosted my confidence in learning it.
    Second, pleasantly surprised to see the thread to be alive even after 3 years!!

    Superb work!

  24. jyotshna says:

    Hi Karthik,
    In kite we have charts of stocks, it is provided by 3rd party, It will be good if zerodha adds 1 more tab where we can get different ratios of that stock, when we click on chart- chart displays for different time frame. Similarly with the help of 3rd party or by your own 1 fundamental tab’s implantation will be very helpful.
    Thanks,
    Jyotshna

    • Karthik Rangappa says:

      We have taken a step towards that, have you checked out the stock widget? Click on a stock widget option next to the stock name. Its in the same place where you get the options for Buy/sell/market depth etc.

      • jyotshna says:

        This suggestion is for fundamental analysis related. If a button is implemented near chart button then by clicking on that button we can get data like PE ratio, EPS, Dividend etc. of that stock.

  25. Anup Padamwar says:

    How can we use this(DCF Primer) to calculate the future price of a Stock or to know that the current price is over / undervalued.
    eg. Current price of ARBL is 771, how can we calculate the future price suppose after 2 years or , how can we say that at 771 ARBL is over valued or undervalued?

  26. tarun says:

    sir mail me the excel file of DCF MODEL.

  27. Azeem says:

    Why have you assumed that the machine will generate 5,00,000 Rs worth of revenue every year? As inflation increases price of pizza will also increase so the revenue generated will also increase from the machine. Shouldnt the revenue generated also grow at the average rate of inflation?

  28. Amith says:

    This concept is good, but It would be more helpful if the following are addressed.

    1. How to calculate the cost of a share after calculating DCF?
    2. 8.5 is a constant?
    3. How does inflation impact the model?
    4. How do we account for other risks involved in the business?
    5. What is the best source to feed in the model?

    Thanks
    Amith

    • Karthik Rangappa says:

      1) Its explained in the chapter
      2) No, varies based on the company
      3) Yes – especially when you take the discount rate
      4) That is outside the purview of DCF, however, you can take conservative growth numbers to accommodate for this
      5) Not sure about this

  29. l_earn_err says:

    Sir, Why is impact of inflation not taken into account along with opportunity cost while calculating FV/PV?
    OR
    Is it like that opportunity cost rate of 8.5% is considered equivalent to inflation rate only?
    Need to confirm whether inflation has no role in DCF model?

  30. Dheepak says:

    Hello Karthick, As usual it is a great and easy explanation and I am reading this chapter to know about present value for Greek Calculator. And I noticed that at “14.3 – Time Value of Money (TMV)” it is mentioned as TMV instead of TVM, correct if I am wrong. Thank you.

  31. anmol says:

    thanku sir for sharing ur knowledge……..i had one qusestion, in DCF how toidentify growth rate of different companies

  32. Binu Varghese says:

    Hello karthik,

    Thanks for this excellent article..!! Just have a confusion..

    Discount rate (which is given as 8.5%) is constant or it is varies depends on the company?

    If it varies, then how to calculate it?

    Some other website shows a term called WACC as discount rate with a formulae while you assumed that discount rate is simply 8.5 – 9% relative to the FD interest rate..

    Could you please help me understand this further?

    • Karthik Rangappa says:

      The general thumb rule is that the discount rate depends on the risk-free rate prevailing in the economy.

      • Binu Varghese says:

        So you say discount rate would be same for all companies in general?

        • Karthik Rangappa says:

          Binu, in a sense yes. This is an easy approximation. The discount rate is the prevailing rates in the economy, so it remains same for all companies. However, you can also use CAPM model to arrive at the exact rate.

  33. Sagar says:

    In below formula how can I calculate capital expenditure? I did visit moneycontrol.com website to see capex but didn’t find.
    FCF = Cash from Operating Activities – Capital Expenditures

    • Karthik Rangappa says:

      I’d suggest you look for CAPEX number as indicated in “Cash flow from investing activities”, in the cash flow.

      • Sagar says:

        Thank you sir for your valuable suggestion.
        When I look for “Net Cash Used In Investing Activities” (sorry I can’t find “cash flow from investing”) of ARBL for year 2013, 2014, values showing -120.51 & -344.84 respectively. & in example those values are 72.47 & 330.3 for year 2012-13 & 2013-14.
        Can you suggest which website is good to get all values for DCF.

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