DCF PRIMER

FUNDAMENTAL ANALYSIS.

The Stock Price

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.

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.

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.

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.