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Time value of money

Before we go into any more detail with financial topics such as discounted cash-flow analysis, annuities, and perpetuities I need to explain to you the concept of "Time value of money". Once you have understood this principle a lot of the stuff that financial people talk and worry about will make far more sense. 

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Every explanation of the concept normally starts with: "a dollar now is worth more than a dollar in the future." Yes, this is true, but it misses the point of the concept a little bit. 

For me, "Time value of money" is fundamentally about making sound choices when faced with several alternatives. 

 

Let's quickly draw up 3 hypothetical examples to explain it:

  • You invest 10.000GBP in a company that pays an 8% dividend (money reward) in a year's time

  • You lend a friend 10.000GBP, and he promises to pay you 10.500 in a year. 

  • You give the 10,000 Pound to your bank, and they promise you a whopping 3% interest rate (not that such an account exists anymore)

The question is, which is the better alternative?

I quickly summarize a few abbreviations I am about to use for my calculations:

  • I stands for Investment 

  • R is the Interest rate

  • T equals the number of years

  • PV means Present Value

  • FV stands for Future Value

There are two approaches to choosing the best alternative: 

1.) Future Value:

This is probably the more straightforward method to use and also easier to grasp. Essentially you want to find out what will happen to your money in a year, hence the name future value.

Starting with the Investment into the company that pays you a dividend of 8%, you could calculate the Future value of this Investment by using the following formula: FV=I×(1+(R×T)).

In our example, after keying the figures quickly into excel, we would get a result of 10,800GBP, which equals a return (fancy word for reward) of 800GBP.

Do the same with the bank offer, and you will see that giving the money to your bank will get you 10.300GBP in 1 year.  

Now you can choose what Investment is best and rank them accordingly:

On pole position is the 8% dividend-paying company, followed by your friend in second place, and the bank finishes last in third place. 

2.) Present Value

You could also view it from a different angle. You know, your friend will pay you 10.500GBP in the future, but you wonder what better alternatives I have. Stupid question to ask, you might think; everything that gives me more than 10,500GP in a year!

 

 Well, this is true but not the correct answer to the question: You see, it is all about the 10.000GBP you have in your pocket now! And you could spend the quids wherever and on whatever you like, maybe a massive pub crawl, a trip to Greece, or skydiving with Elon Musk, it doesn't matter!

All of these choices sound pretty fun to me, and by missing such fun activities, you want to make sure that you at least make some rocking return on the 10.000GBP for the pleasure of waiting 1 year. 

You start with your friend who approached you with the offer of a guaranteed 10.500GBP in 1 year. And now comes the crucial part; is this worth the while, giving up the skydiving, the pub crawl, or the other investment alternatives? 

It gets a bit geeky here: For finance people to determine whether sth is worth the while, they try to find out what sth is in today's money, calling this exercise discounting: They take the offer to benchmark and work out the Present Value, given the alternatives at hand.

The formula is as follows: PV = FV / (1 + r)^T

The company with the 8% dividend: If you key the following values (PV = 10.500GBP / (1+8%)^1 into a spreadsheet, you get: 9,722GBP. 

The bank offer: you key in (PV = 10.500GBP / (1+3%)^1, instead of the 8% before we have now used the next best alternative, which is 3% by the bank. The result is: 10,194GBP

So what: It shows that your friend's offer loses against the dividend-paying company because worked backward, you end up with less than your investment amount of 10.000GBP. 

 

The bank offer: Your friend's proposal wins as you end up with more in today's money terms when you lend the money to your friend.

So basically, you can now decide what to do, and there are only 2 viable options: Option Nr.1 You blow your money today or Option 2. you put it into the dividend-paying stock as you at least get the best return out of the 3 choices available. 

I have another example. In real life, we make these choices almost daily! Have you ever heard of our nasty friend inflation? Switch on the news, and I guarantee you will listen to someone talking about it. Imagine the anchor says that the bank of England expects an inflation rate of 2% for next year. They should instead say that they expect things to get more expensive by 2% next year. So if you think of your 10.000GBP that you have now, if you leave it sitting, you can only buy goods worth 9803GBP in a year's time! SO: we are back at the beginning: "a dollar now is worth more than a dollar in the future, and I shall add: "and if you choose not to spend it now, make sure to put it somewhere where at least keeps its value."

The final verdict on this:

I hope it makes sense to you why the time value of money is such a valuable concept to understand. It is all about choice and opportunity and choosing the best way for your money in the here and now. See it as a compass that can guide you out of the numbers' jungle.

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