by elmads

Introduction

“To me, saving was as natural as breathing: I knew when I saved $10, I was really saving $100 or $1,000 because of the future growth”.

—Charlie Mungers

In my previous blog “A Dollar Today is Worth More Than a Dollar Tomorrow – The Time Value of Money”, I wrote about the following:

• The importance of compound interest, that every amount we save has the potential to be worth more in the future.
• All projected future values of a sum of money correspond to its present value equivalent. For instance, the $1,030 you anticipate having next year from a savings account yielding 3% per year ($1,000 times 3% = $30) is equivalent to the current $1,000 you have today.
  
  Think of it this way: a student named XYZ who diligently studies for an exam today is the same student who successfully passes the exam tomorrow. The only difference between today and tomorrow is the value of the grade achieved. Just like in finances, the value of money changes over time, but its essence remains the same.
• Know the present value of the future cash flows of an asset and project investments, and how to use it to weigh which investment would provide a better return on our cash today.

But what if there are different amounts of cash flows coming in and out at different points in time?

Let’s take, for example, a bank savings account. You’ve deposited $10,000 in a 5-year fixed term bank savings account that gives 5% a year. This means that you’ll be receiving $500 a year for 5 years. What will then be the present value of your deposited money after 5 years, including the total interest received on your deposits?

The Net Present Value (NPV)

Just a quick refresher before we go ahead with NPV. To get the future value of an initial investment through compounding, we need to use the following formula below.

The future value and the present value are directly related. 

This becomes complicated when there are different cash inflows and outflows over various periods of time. This is where net present value comes in. It is, as the name suggests, the NET value of all present values of future cash flows.

Coming back to the fixed-term bank savings account example at the start of this blog.

Let’s take, for example, a bank savings account. You’ve deposited $10,000 in a 5-year fixed-term bank savings account that gives 5% a year. This means that you’ll be receiving $500 a year for five years. What will then be the present value of your deposited money after 5 years, including the total interest received on your deposits?

As expected, the total present value of your savings account is equal to its initial deposited amount in year 0 which is $10,000, since the deposit interest rate is equal to the discount rate. This happens because the bank guarantees a 5% interest rate on your principal deposit. They give you certainty about the returns you will receive.

We have to discount every cash inflow we receive each year. The number of years depends on when we receive the cash flow. In the NPV table form above, in row “Year 3”, we received a $500 cash inflow from our savings account. We’ll use 3 for our variable “n”, which is for the number of years. 

📝 NOTE: I’ll just explain how we arrived at the cashflows in the table image above. You placed an initial $10,000 to open the 5-year fixed rate savings account; though the money is still yours, you won’t be able to use it until the 5-year period is completed. Therefore, it is a cash outflow in your finances. You have received a yearly cash inflow worth $500 for 5 years. As the 5-year period is completed, the bank will give back your initial deposited amount of $10,000, which then becomes a cash inflow. That’s the gist of it.

What if there’s no fixed amount that you’ll receive on your investments? Just like with businesses. How will NPV help decide if an investment is worth taking or not?

Let’s say a business plans to buy $20,000 worth of machinery, and the management expects to generate $5,000 in years 1, 2, 3, and 4, and $5,000 in year 5 + $500 (the company will scrap the machinery in the same year). What would be the net present value of all cash flows if the management assumed a 6% discount rate (based on inflation, the risk associated with this investment, and the cost of money when taking this investment) for those future cash flows? Is the machinery worth taking or not?

Assessing Net Present Value (NPV) Across Varying Cash Flows

Let’s say a business plans to buy $20,000 worth of machinery, and the management expects to generate $5,000 in years 1, 2, 3, and 4, and $5,000 in year 5 + $500 (the company will scrap the machinery in the same year). What would be the net present value of all cash flows if the management assumed a 6% discount rate (based on inflation, the risk associated with this investment, and the cost of money when taking this investment) for those future cash flows? Is the machinery worth taking or not?

What we need to do here is get the present value of each projected yearly cash inflow. Same as with the bank savings account we used previously.

We would still use the formula: PV = FV/(1+r)^t.

But in this case, we’ll do it each year. It’ll be like this:

The net present value of our example above is $1,435.45, which means that the management should go ahead with buying the machinery as it would give them a positive investment return. Only if! Their projected cash flow for the machinery will materialise; what do I mean by this?

Recall that these cash flows are only projections of the management on what they would receive from the $20,000 investment, and the discount rate (6% in our example) reflects their assessment of risks, inflation, and investment opportunities moving forward.

• If the NPV is positive, the project is financially viable. It indicates that the project’s expected future cash flows are higher than the initial investment and the cost of capital. This suggests that the project has the potential to generate more value over time than it costs to implement, making it financially viable and potentially a good investment opportunity.
• If NPV is zero, the project breaks even.
• If the NPV is negative, the project is financially unviable. It shows that the expected cash flow is lower than the initial investment. The project would be paying more on its costs than making actual positive cash flow in the future, which in turn could destroy value over time.

Using our machinery example above, I’ll show you a projected cash flow to illustrate what would give a NPV of zero and a NPV of negative.

As you can see from the above, your decision about whether to take an investment or not is based on your own projected cash flows for the project or asset and how much it can generate for you in the future. And making such projections is one of the hardest things to do because we’re talking about being comfortable with uncertainty and backing your own judgement and conviction by putting money on the line.

“One of the major difficulties with present values is the estimation of interest rates and annual cash flows… As you project further into the future, the cash flows and rates become more and more speculative.”

—Kaplan

Leveraging Discounted Cash Flow for Comparative Investment Analysis and Informed Decision-Making

There is always an opportunity cost for every investment.

Using discounting is very helpful to find out what investment we should choose.

An investor has three options that he can choose from, of which he can only choose one. The investor estimates a discount factor of 10% for the lifetime of each investment. Which one should he choose?

• Investment A: An initial investment of $10,500 with a projected cash flow of $3,000 each year for 5 years
• Investments B: An initial investment of $9,000 that pays $4,250, $3,750, and $3,500 in years 1, 2, and 3, respectively.
• Investment C: An initial investment of $7,000 with a pay of $1,000 in year 1, $1,500 in year 2, and keeping on growing $500 each year until it reaches $3,000 in year 5.

As Investment A has the highest positive NPV, it is the clear winner compared to others. That said, the initial investment required is worth $10,500, which is a large sum of money, or not, depending on an individual’s financial circumstances.

In every investment decision, not all opportunities are applicable to us because, like with personal finance, we must tailor our current life circumstances, financial goals, time frame, personality, knowledge, and skills to the investment opportunities presented to us.

Take the one that you deem well-suited for yourself and your family. If you’re able to invest the required amount for Investment B or C, then you can take either one as well because their NPVs are both positive. That said, you can just continue to save money and wait for another buying opportunity to come with a better and higher return.

Discounted Cash Flow To Find The Estimated Value Of A Public Company

The above image shows the real cash flows generated by Alphabet Inc., the parent company of Google. Year 1 in the image above was the actual free cash flow obtained by Alphabet Inc. in fiscal year 2013. Therefore, the free cash flows were from 2013 to 2022.

📝 NOTE: All free cash flows (FCF) generated are in millions of dollars. Using the FCF number for fiscal year 2013, we read it as 11 billion 301 million USD.

I won’t confuse you about the other variables in the photograph above. To relay my information clearly, we must take ourselves back to 2013. By the way, where were you in 2013? What were you doing? Were you a student or already in the workforce? What was your job back then? Anyway, just think of going back to 2013, and let’s just say you made discounted cash flow projections for Google back then.

You projected 10 years of Google’s cash flow, from 2013 to 2022. You did your best, and tada! You were able to do it, which is approximately near the numbers in the image above.

As you did the net present value of all your projected cash flows for Alphabet Inc.,  the terminal rates, and the projected possible number of shares in the future, basically you did all of the nuances in doing valuations.

You arrived at the fair value of $31.29 per share of the company. This means that based on your future cash flow estimates that you assume the company will make in the future, its net present value is worth $31.29 per share.

Today is the 31^st of December 2013. Alphabet Inc.’s current stock price is $28.04 per share. This means that Alphabet’s current stock price is undervalued by 10.38% based on your free cash flow projections that the company will generate in the future.

If you buy now, then you might realize a 10% increase in the value of your investments. Let’s say you’ve bought $10,000 worth of Alphabet Inc. at $28.04 per share. If the company’s stock price reaches your fair value calculation of $31.29 per share, then your initial $10,000 invested will become approximately $11,038.

Fast-forward to today: Alphabet’s stock price is hovering around $120 per share. If you bought it in 2013 and sold it today, you would still quadruple your invested money.

Does it sound easy? Well, it isn’t. Don’t get your hopes up that easily. You see, we’re looking at hindsight.

“In the financial markets, hindsight is forever 20/20, but foresight is legally blind.”

— Benjamin Graham

Maybe your own valuation superseded your own expectations! But that’s only a small portion of your analysis because every year you have to update your thesis and see things moving forward. As the actual number of your projections materialises in the future, your valuation will show a higher price per share. 

Furthermore, do you think, back in 2013, you would strongly believe your own valuation? How likely and how unlikely do you think your projections will happen? Also, is that a worst-case, most likely-case, or best-case scenario projection? If you believe in what you’ve done, then what percentage of your money would you invest in that one stock? Will you go all in? or 50%? 20%? 5% of your total net worth? Recall that in investing, you back up your beliefs and decision-making with money, not just with empty words.

The past free cash flow generated by Google holds no significance anymore as those funds have already been utilized and reinvested by the company. What’s important is the future cash flow.

Now, in 2023, can you make a valuation for what they will probably generate in the future? From today to, let’s say, 5 years? Or 10 years? Then, with your own understanding of the company, its business model, their competitive advantage, and the competence of the management, you can make an informed decision about whether it’s a buy now or not, or whether you should look for other investment opportunities in the market.

To The Next>>>

Now we’re here, in the intricacies of discounted cash flow modelling for valuing public companies.

Let’s go deeper into the rabbit hole, shall we? Let’s talk about forever cash flow projections, the terminal values and rate, and what is an asset that has 0% risk?

Evan I thought all assets have risk. That’s what I thought before too, but in theory, there is one that is almost risk free.

Let’s go!!! 😁😁😁

This blog is for informational purposes only and not a Financial Recommendation. Not all information will be accurate. Consult an independent financial professional before making any major financial decisions.