## 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.

## 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 –

- The total cash flow from the pizza maker over the next 10 years – Rs.50,00,000/-
- 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
- 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 –

- How much is the Rs.500,000/- that he receives in 2016 worth in today’s terms?
- How much is the Rs.500,000/- that he receives in 2018 worth in today’s terms?
- How much is the Rs.500,000/- that he receives in 2020 worth in today’s terms?
**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

- A valuation model such as the DCF model helps us estimate the price of a stock
- The DCF model is made up of several inter woven financial concepts
- 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
- 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
- To compare money across time we have to ‘time travel the money’ after accounting for the opportunity cost
- Future Value of money is the estimation of the value of money we have today at some point in the future
- Present value of money is the estimation of the value of money receivable in the future in terms of today’s value
- The Net Present Value (NPV) of money is the sum of all the present values of the future cash flows

What are other valuation models which are used in equity research or say M&As?

Hope my question is not ambiguous..

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.

Little typing mistake noticed

No. 14.3 is missing where as 14.2 is double

🙂

Missed seeing your comment! Thanks for pointing out, made the changes 🙂

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.

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

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

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

Unfortunately I’m not to familiar with currency valuation techniques. But my guess is that this is largely market driven.

Please suggest me from where i get information about that?

This should help you with a start – http://blogs.wsj.com/economics/2011/10/03/guest-contribution-how-to-value-a-currency/

Good luck.

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

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.

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

Nothing worth sharing as of now 🙂

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

You kind of factor in this when you take a very conservative discount rate.

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??

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

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?

Yes, you should. But please make sure you are thoroughly convinced with the business model and management quality.

Yes, Management Quality is something that has to be focused on. Thanks Karthik for your insight.

Welcome and good luck!

please provide description of formula of finiding pv fv

PV = Cash Flow / (1 + discount rate)^(time)

FV = Cash Flow * (1 + expected return)^(time)

How do you find/calculate the discount rate and expected return rate?

The discount rate is usually close to the risk-free rate in the economy. Expected return – https://zerodha.com/varsity/chapter/expected-returns/

Dear Karthik

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

thanks

Its the future value of Rs.5000 when compounded at 8.5%.

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

There is no NPV of -ve cashflows.

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 ?

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.

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 ?

Glad you liked it Jaggi 🙂

I guess the excel is available at the end of the chapter.

hi..can i have the dcf excel sheet plz

We will soon start a module on Financial modelling, you will have DCF and more.

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?

It really depends on your time frame, Shabaz. There is no harm investing on a selective basis.

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.

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.

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

Thanks for pointing this, Ajay. Let me check this again.

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?

Yup, reserves is not really considered for NPV and DCF calculations.

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?

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.

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.

Everything documented in this chapter is important Gourav, you cannot afford to ignore one over the other.

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

Exactly why companies like Smallcase has useful tools like Screener. Check this out – https://screener.smallcase.com/welcome

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.

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.

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.

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.

Yes I am able to sense it.Thanks.. I am eagerly waiting for your module on Financial modelling. Keep up the good work!!!!

Hopefully soon 🙂

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

Happy learning, Dinesh!

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!

Happy learning, Sanjay 🙂