Introduction and Net Present Value

When I recently joined this community, I noticed that there are a lot of articles about investing in cryptocurrencies (makes sense considering the platform ;)). My aim here is to contribute to your understanding of investing in general. What are the basics of accepted valuation & investing theory?
In my opinion it is always useful to start from the foundations. The articles will very much be aimed at finance/investing novices. If you are a seasoned hedge fund manager, this is not for you :). There will be some math, which I consider unavoidable. I will try to illustrate any formula with some examples however. I hope to give you a feel for the concepts.

Here is how I envision the content of this series of articles:
• Basics of valuation
a) Net present value intro
b) Equity Only
c) Equity & Debt
d) IRR & Ratio analysis versus NPV
e) Decision Trees
• Introduction to financial products (derivatives)
a) Bonds
b) Swaps
c) Options
• Introduction to risk management
a) General thoughts
b) Value At Risk
• Investing theory
a) Indifference curve; risk vs return
b) Modern Portfolio Theory
c) Practical considerations
d) How does crypto fit in?

If I make it this far, and there is interest I can go in depth on some of these topics. A single point might get chopped up into multiple articles.

With the practical information out of the way, let’s start with an introduction to what I consider the hearth of modern finance: Net Present Value (NPV). Almost every traditional valuation technique is built on NPV. So what is the idea? If I give you $100 right now, how much is that worth to you? Seems like a stupid question. $100 dollars of course. Now let’s say that I sign a contract with you that states that I will pay you $100 exactly one year from now. It is a written agreement, so you can enforce it by legal means if needed. I have a stable job, so the chances of me not being able to pay are pretty slim. To keep it simple, we will assume you can be 100% certain that I will pay. So how much is this $100 in one year worth to you? Still $100? Probably a bit less, but how much?

If we go back to the $100 you get right now, we can evaluate what you can do with it. If you don’t want to take any risk, you could go with the $100 dollar to the bank, and collect some interest when you withdraw it in one year. In my country you can get around 0.1% right now on such a deposit account (thanks quantative easing). It is insured by the government for amounts up to $100,000. We will again assume that we have 0% risk of not getting our money back.

So if we do the math: an increase with 0.1% (0.1% = 0.001) is multiplying with 1.001. You get $100.1 in a year. Hurray! If we then work backwards we can say that getting $100.1 in a year is worth $100.1/1.001 = $100 today. So following the same logic: $100 in a year is then $100/1.001 = $99.9. What about $100 that you receive in 2 or 10 years? $100/(1.001)^2 and $100/(1.001)^10. Where did that come from? Well before we saw that to go back one year we need to divide by 1 + 0.001. If you go back 10 years we simply divide our $100 10 times by this number.

In finance the 1/(1+r)^n is called the discount factor. r is the (discount) rate that we use for a certain project, company, … In this case the r in the example is the risk-free rate, as we aren’t taking any risk. n is the amount of time between now and when we receive the money. For our example n is expressed in years. $99.9 is the Net Present Value (NPV) of the $100 that we receive next year. If CF is the nominal cash flow, in this case $100 (nominal = what you actually get, no extra calculations needed), then the NPV = CF * 1/(1+r)^n.

The NPV of different amounts in different years can simply be added. Let’s revisit our contract. I was going to give you $100 in one year. However I don’t think that is very fair and at some point I would certainly like it back. Let’s say I would get it back in 20 years. What is the value of this contract to you?
If we break it down in two parts:

1. As we calculated: The NPV of $100 in one year is $99.9.
2. The NPV of $100 in 20 years is $100*1/(1+1.001)^20 = $98.02.
   You receive the money in one year, and pay the money in 20 years. By calculating the NPV we have projected the cash flows to today. The total worth of the contract to you is $99.9 - $98.02 = $1.88. Of course this means that I’m losing money on it. How much? Exactly $1.88.

But wait! Maybe you have a super awesome cryptocurrency that will give you 120% each year. Or you consider US government bonds quite safe (not an unreasonable assumption) and you might get 2% or more? So why would we discount with 0.1%? The answer to this is risk. We assumed that our contract was totally risk free. This means that we need to discount with the return we can get on a 100% risk free investment. Is this ever going to be 100% in practice? No. The project isn’t going to be risk free, and neither is the rate that we use to calculate the discount factor. We will still make the assumption that we have a risk-free rate. A different (riskier) contract, project or a business would of course need a different rate. But more on that later. Until we revisit the discount rate, we will the appropriate rate known for now.

This concludes the first article in the series. In the next instalment we will have a look at how to value a simple company using these techniques. I know it is a slow start. It is however very important that you always think of any cash flow in the future as having another, discounted value when projected to today.

Any questions or corrections? Let me know in the comments below.

Best Regards,

AdmiralEnthalpy