Post No.: 0065
If you prefer x to y, then you should also prefer a z% chance to win x to a z% chance to win y. We can calculate the ‘expected value’ or ‘expected utility’ of any decision based on all the possible payoffs that could happen weighted by their respective probabilities of happening, which will output a weighted average expected value (e.g. a bet with a 70% chance of winning £10 and a 30% chance of losing £5 = (0.7 * 10) + (0.3 * –5) = £5.50). A negative number will mean a gamble that isn’t worth it, and a positive number will mean a gamble that could be worthwhile – depending on the ‘opportunity cost’, which is your next best alternative option (e.g. putting the money instead into a bank savings account for the interest or purchasing safe government bonds). Taking into account the opportunity cost is important because although doing plan A can be better than doing nothing at all, it might not be better than doing plan B. And when your money (or time or other resources) is being invested in plan A, it cannot be invested in plan B at the same time i.e. you must give up one option to do the other, or you cannot do both simultaneously.
This is how we should rationally make decisions, but we barely always do. Of course in the real world, we don’t always have accurate information for all the possible payoffs and their probabilities of happening in order to make reliable expected value calculations, and given the timeframe and resources we may have before we must make a decision, we’ll have to make do with estimates and these estimates could prove to be way off. But if we do have the information then we must use it to work out the expected values of our choices; and even if we don’t have the information, we should try to seek it and make our best estimate, and not beat ourselves up if, with the bias of hindsight, in the future things don’t turn out as expected despite us making our best estimate with the information we had at the time we had to make our decision.
When making financial investments or thinking about going into a business, calculating the net present value (NPV) is the rational way of working out whether a project is worth doing or not (the ‘time value of money’ – or discounting future cash flows to present value, taking into consideration the present costs of the investment too) – this calculation takes into account the way that receiving £1 today is worth more to you than receiving £1 tomorrow, because the sooner you receive money, the sooner you could invest it elsewhere for a return (e.g. have it in your own bank account to accrue interest); the same logic applies to paying £1 tomorrow is worth more to you than paying £1 today, when payments are interest-free (albeit buying stuff on interest-free credit might lull people into buying things they cannot afford even in the future). Again, if a project or option has a negative NPV then do not accept it (i.e. it doesn’t beat the opportunity cost), and if it has a positive NPV then accept the project or option that offers the highest positive NPV.
As a related but side note, unless one has a prior agreement (a futures contract or option), we obviously pay today’s price when buying something today. So when an entrepreneur values their own company to an investor at a value they think it’s going to be worth some time tomorrow for an investment today, they are being totally naïve! The present value is what we should pay unless we wish to buy at a premium.
Only take into account the marginal cash flows (the amount of cash one needs to generate if one sells another £1 of goods/services), and do take into account the marginal costs, incidental effects or externalities that arise if a particular project is undertaken compared to if it is not undertaken too (e.g. the cannibalisation of existing business, economies of scale or complimentary effects). Are ‘fixed costs’ always fixed or are there incremental marginal costs if a new project is undertaken? You’ll also need to consider the after tax cash flows, ensure cash flows are recorded for the right time (e.g. when you receive money for a job may not be the exact same day you do that job), and be consistent in the treatment of inflation (nominal versus real/adjusted-for-inflation figures).
It’s also important to forget about ‘sunk costs’ (i.e. how much you’ve invested into something up until now) – there’s nothing you can do about them now; bygones are bygones. Always only think about doing what’s best for today onwards, or the net present value or utility (e.g. don’t go to that concert you know for sure you won’t enjoy just because you’ve already paid for the ticket (even if you cannot sell it on or get a refund), since you could instead spend that time doing something you know you’ll enjoy). Think about the opportunity costs again – don’t think assets can’t be doing other things because they can (e.g. renting it out, or selling it and reinvesting the cash) and don’t forget that spending time on one activity usually means taking time away from doing something else i.e. nothing truly comes for free!
So investors shouldn’t really be thinking in terms of how much they’d paid for a security and how much it is worth now, but only in terms of how much it is worth now and how much they think it’s going to be worth in the future. Yet too many investors still base their ‘keep or sell’ decisions on ‘I paid x for it a year ago and now it’s worth y’ and sell if they’re up and keep if they’re down.
Now emotional or otherwise psychological values do matter in many contexts, so it’s not just about the money (e.g. the emotional value of doing something that is personally more enriching and meaningful than outright pays financially the most, or the emotional value of keeping a pet even though the pet is costing a fluffy lot – woof woof). Determining these values is of course personal – but even so, these emotional values cannot be considered infinite or truly priceless in the real world (e.g. it’s not sensible to go bankrupt over keeping a pet, not least because it won’t be good for the animal’s welfare too if one cannot afford to keep him/her healthy).
Note that emotions are not irrational per se – they’re only irrational if they’re disproportionate to the expected values (gains or costs). For example, it’d actually be irrational to not fear a train moving towards you while you’re standing on the track, proportional to the distance away and speed of this train (I suppose depending on how much you value your own life, which I hope is a lot); or it’d be irrational to romantically love someone who keeps on letting you down and cheating on you. Unfortunately, there are a lot of occasions where and when our emotions and behaviours are irrational (e.g. fearing truly harmless insects, blanket racist stereotypes, discounting far future costs entirely, such as environmental costs or one’s future health).
I fathom that some of the above sounds like opaque jargon to some of you(!) I recommend taking an introductory finance MOOC to help you become smarter with your money (free course options are often available). I expect it’ll be worth your investment of time!