How to value an asset (Ch 1)
The value of an asset can be arrived at simply by thinking of the following; The value of an asset is the cash flows derived from that asset, over its useful life, discounted for the time value of money, and the uncertainty related to receiving those cash flows.
Let’s break that down further:
An Asset: In this case, anything that is producing money (As we will see later, it doesn’t necessarily need to produce money, but this is a simplistic definition). Think for example of a cow that produces milk that you sell for money, or a car that you drive for Uber which helps you to get paid for rides.
Cash Flow: We can think of cash flows as the coming in or going out of money. Think for example every time you collect money for the milk you sell from your cow, or every time a passenger pays Uber (and Uber pays you) for a ride. (Again, all examples are “coming in”/positive cash flows, but the opposite can be true, paying for the grass to feed your cow and paying for gas for your car would both be examples of “coming out”/negative cash flows)
Useful Life: You can simply think of this as the duration of time that your asset will be able to produce money. Think for instance about how long your cow will be able to live (or its milk-producing life), or how long your car will be able to run, therefore giving you the ability to give rides to passengers and earn money. If your car will be able to run for 10 years, and in those 10 years it gives you the ability to pick up passengers and earn money, then your car’s useful life is 10 years.
Time Value of Money: Time Value of Money is a financial concept that embodies the fact that having things now is better than having things later (there is a mathematical formula to support this, which we will get to later). In essence, because of uncertainty, having $100 (or any amount of money) today is better than having $100 a year from now.
Discounting: In this context, discounting simply means that we have to account for the concept of time value of money as it relates to our cash flows, meaning - through a mathematical formula - we have to find what the value of a given cash flow in a given future year is worth today.
Now, to more easily grasp the concept, we can think about the value of an asset as being derived from three key things.
Value of an asset; (1) Cash Flows, (2) Uncertainty, (3) Time Value of Money.
(2) and (3) are pretty much summed up in the above section - except for the math.
(1) Can be expanded a bit further. 4 key variables affect cash flows; Timing, Duration, Magnitude, and Growth.
(Bear with me here, we will get to the math last and exemplify everything with the pertinent formulas)
Timing: Timing addresses the question of “When will I get the money”. In simple terms, as explained above, with everything else equal, receiving money earlier is better than receiving money later. $100 today is worth more than $100 dollars a month from now.
Duration: Duration aims to answer the question “How long will I receive money for?”. In simple terms, everything else equal, receiving money for a longer period of time is better than receiving money for a shorter period of time. If you and me both have a cow, and our cows produce milk that we can both sell for $1,000 a year, if my cow lives for 20 years and yours for 10, I am better off as my cash flow stream has a longer duration.
Magnitude: Magnitude will answer the question of “How much money will I get”. In simple terms, you would rather have more money given to you at any point in time, than less. Think - everything else equal - if two competing uber passengers offer you either $6 or $8 for a ride, you’d rather take the $8 passenger.
Growth: Magnitude will answer the question “How much can I expect my cash flow stream to grow”. Simply meaning, are you expecting that as time passes, the cash you are receiving will increase in magnitude. Here, instead of thinking of the actual cash value, we are thinking about the rate at which cash is growing from x to period y. Think, if you are a milk producer, and school milk packaging company offers you a contract that says they will pay you $100 every month + a 1% growth rate per month, and you have another offer (everything else equal) that will pay you $100 month + 5% annual growth rate, you would rather take the first option.
Uncertainty will affect each of those 4 cash flow variables when thinking about any cash flow stream (other than the risk-free rate, i.e. us treasuries), we assume that there is some degree of uncertainty as to the occurrence of our cash flows. (The beauty of finance is that if markets work properly, we are rewarded for the added uncertainty!)
For our purposes, we can simply think of uncertainty as adding layers of complexity to our ability to accurately forecast an exact value or scenario for any of our 4 variables.
For instance, think of timing, imagine you have $100 that will be paid to you every year, for 4 years, using a - very - simple framework of mind (everything else equal), you are more confident (or certain) that you will get paid the $100 dollars in year 1 than you are in year 4. This doesn’t mean you won’t get paid in year 4, it just means that the likelihood that you’ll be able to accurately predict that you will get paid is less in year 4 than it is in year 1.
The concept stands true for the other variables. In thinking of the magnitude, the further you are into the future, the less accurate your forecasts will be, so a better framework of thought are ranges, rather than single-point estimates. For example, better than “We will get paid $5 in year 4”, a better framework of thought is “it is likely that our payment in year 4 will be in the $3-$6 range”.
As a - general - rule of thumb, the further you are forecasting into the future, the more uncertainty you will have.
Finally! The math.
Time Value of Money is the concept that a dollar today is worth more than a dollar in the future. Why? Because of two concepts you will here a lot if you delve into finance, compounding and discounting.
Compounding: Compounding simply means the ability of something to make gains (progress, etc…) on top of gains. This will cause what we call exponential growth, growth will accelerate the more that time passes (because gains will be pilling up on top of previous periods of gains).
The formula we use in finance to think of compounding is the Future Value formula.
Future value = Present Value * (1 + Rate)^number of periods
Here is an exercise to understand compounding a bit better:
Say you have two choices, starting with $100 you can either (1) earn 10% a year for 3 years, compounded. Or (2) earn 10% a year for 3 years, non-compounded.
On the compound option, your return will be the following;
In Year 1:
$100 * (1 + 10%) = $110
In Year 2:
$110 * (1 + 10%) = $121
In Year 3:
$121 * (1 + 10%) = $133.1
$133.1 is your final value at year 3.
On the non-compound option, your return will be the following:
In Year 1:
$100 * (1 + 10%) = $110
In Year 2:
$100 * (1 + 10%) = $110
In Year 3:
$100 * (1 + 10%) = $110
$130 will be your final value (your initial $100 that are kept constant through 3 years + $10 dollar in return every year for 3 years).
In 3 years, and at a 10% its a small difference, but try it out over many many years and you are sure to be astonished! The difference in our example is that you are making your 10% return on top of the 10% return you made already, meaning in year 2 you are making 10% on $110 (In option 1) as opposed to 10% on $100 (In option 2).
By the way, we can simplify the math in option 1 to be:
Value at Year 3
$100 * (1 + 10%)^3 = $133.1
Discounting: Discounting is quite literally the opposite of compounding (we are literally re-arranging the formula to solve for present value), here we are basically tapping into the economics concept of opportunity cost if we can earn a certain rate of return on our money (10% in our previous example for instance), what should we pay today for something in the future.
(This is the process we use when valuing an asset)
If my math is correct, if we try to value what we should pay for a $133.1 cash flow 3 years into the future, the formula should tell us it is $100. Let’s try it out:
Future Value formula:
Future value = Present Value * (1 + Rate)^number of periods
Solving for present value:
Present Value = Future value / ((1 + Rate)^number of periods)
Inputting our numbers:
$133.1 / (1 + 10%)^3 = $100
Voilà!
(A note: When valuing an asset, you will have to discount each cash flow for every given period separately!)
As promised, using the math, here are some examples of our 4 concepts with time value of money at play.