The value of any asset is nothing but the present value of all cash flows that the asset would generate in future. The asset could be anything that generates a net cash inflow

– a business

– an investment property

– a plot of land

– a loan earning interest income (where we are the lender)

– a patent earning royalty income…

– Or even our residential home (if we have purchased it without a mortgage, then our owned home protects us from future cash outflows in terms of rent)

Let me take a shot at explaining this in a simple way such that even my teenager would be able to understand…

Let’s take the simple example of a bank account. Let’s say we have a bank deposit account where we put in some money…but we have forgotten the password of the account as well as the amount that we had put in. However we know that we receive $500 in interest every year and the interest rate is 5% (well it used to be at some point of time in the past). This immediately tells me that the amount of money in the bank = $500 / (5%) or 500/0.05 = $10,000

What we did here is a simple calculation of finding the capital amount (value of the amount in the bank) using the cash flow (the yearly interest payment)…If we want to use some finance jargon what we did here is actually called ‘capitalizing the cash flow’ using a discount rate which in this particular case is the interest rate….in other words we ‘discounted’ all the future cash flows (interest incomes) with the interest rate (discount rate) to figure out what is the value of the bank account today. We will discuss the concept of ‘discount rate’ further below

Let’s now take the simple example of a rental property that generates a rent of $1000 every month (net of all expenses). For us to be able to derive the value of the property, we would need to know the discount rate….in real estate parlance it is also known as the ‘Cap rate’ or capitalization rate. Going forward we will denote the annual discount rate as R and all the cash flows as C (assuming that the cash flows stays same). T stands for the time period (here it is monthly)

C = $1000/month

Let’s assume R = 6% per annum. Here as we are dealing with monthly cash flows we need to work out the equivalent monthly discount rate, which is 6%/12 = 0.5%.

Let us denote this discount rate for the time periods (in this instance monthly) as ‘r’. ( r=0.5%). [Note: in any situation where the frequency for a particular cashflow is yearly, then R=r]

Now if we draw a timeline, for all the cash-flows, it will look like the one below:

T= Month 1 (T1) Month 2 (T2) Month 3 (T3) .……………………

C= $1000(C1) $1000(C2) $1000(C3) …………………….

Here the present value of the property (V) = C1/(1+r) + C2/(1+r)^2 + C3/(1+r)^3 + C4/(1+r)^4 +……….

The above equation that extends indefinitely can be simplified (using some high school math….explained later for those who are curious) as

V = C/r

Now as you can see, it is a simple equation that uses the cash-flow of each period and the discount rate for the period and calculates the value of the asset. Here the assumption is that the cash-flow does not change.

So the value of the rental property = $1000/0.5% = 1000/0.005 = $200,000

*At this point it would be relevant to mention the ‘discount rate’ is nothing but the opportunity cost of your capital….it is the rate of return that a similar investment can provide. Now there are academic methods deriving the discount rate (using the concepts of CAPM, Beta etc)…in the early days I learnt these concepts and carried them in my mind long enough for me to be very embarrassed about. To cut a long story short…..these theories that are still taught in most academic courses/business schools are nothing but meaningless nonsense. The idea of ‘Beta’ equates ‘volatility of a stock price’ with ‘Risk’…you talk to any successful investor and they will tell you that there cannot be anything further from truth. Volatility is actually a great thing and it allows us investors to purchase great assets at favourable prices when lot of people are feeling scared about holding them…..So you can safely repeat after me ‘VOLATILITY IS NOT SAME AS RISK’ and you will have the support of the investing gurus like Buffett, Munger, Klarman, Greenblatt et al.*

So in the above example, where our rental property is generating a rent of $1000. If however in general the rental yield in the real estate market is 8% (discount rate or cap rate) instead of 6%, then the monthly discount rate = 8%/12 = 0.66%

Value of the property = $1000/(0.0066) = $150,000….so as the discount rate goes up, the value of the asset goes down because the future cash flows get ‘discounted’ by a higher denominator.

However if there is some growth in the cash flows (like what typically happens in most good businesses), and if the yearly growth in the cashflow is denoted by ‘g’….Which means C2 = C1 X (1+g)…..C3 = C2 X (1+g) etc etc.

then this simple equation becomes :

V = C/(r-g) This equation is also known as the Gordon’s Growth Model

So now imagine there is a business that you own some shares in. The business will pay a dividend (cash flow) of $200 a year from now…and the dividend is expected to increase by 3% every year for ever. Let’s assume that the opportunity cost of your investment = 10% (which means you can expect to receive a 10%/annum return on other similar investments).

So the intrinsic value of your share of holdings in the business can be calculated as:

V = $200 / (10% – 3%) = $200 / 0.07 ~ $2,857

Hope you get the idea of how value is calculated…..the same concept is often easily represented by a ratio like Price/earnings or other commonly used multiple….which is basically the other side of the same coin.

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For those of my readers who are mathematically curious…..

The no-growth scenario (C1=C2=C3……)

V = C/(1+r) + C/(1+r)^2 + C/(1+r)^3 + C/(1+r)^4 +……….

Or V = 1/(1+r) X [C + (C/(1+r) + C/(1+r)^2+……….)]

The expression inside the (..) is same as V….so the entire equation can be written as

V=1/(1+r) X [C + V]

Or V*(1+r) = C + V

Or V + V*r – V = C

Or V*r = C

Or V = C/r

The Growth (g) scenario:

(V) = C1/(1+r) + C2/(1+r)^2 + C3/(1+r)^3 + C4/(1+r)^4 +……….

To simplify the equation:

Let’s replace C1 with C

C2 = C X (1+g)

C3 = C X (1+g)^2

So V = C/(1+r) + C*(1+g)/(1+r)^2 + C*(1+g)^2/(1+r)^3 + C*(1+g)^3/(1+r)^4 +……….

Or V = 1/(1+r) X [C + C*(1+g)/(1+r) + C*(1+g)^2/(1+r)^2 + C*(1+g)^3/(1+r)^3 +……….]

Or V = 1/(1+r) X [C + (1+g)*{C/(1+r) + C*(1+g)/(1+r)^2 + C*(1+g)^2/(1+r)^3 + C*(1+g)^3/(1+r)^4 +……….}]

Or V = 1/(1+r) X [C + (1+g)* V]……We just replaced the expression inside { …} with V as it is exactly same

Or V*(1+r) = C + (1+g) * V

Or V*(1+r) – V*(1+g)= C

Or V * (r – g) = C

Or V = C / (r – g)…….Gordon’s Growth Model Formula

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