Determining intrinsic value per share of a stocks (Part 2 of 2) - A company is worth the present value of all its future cashflows?

I shall now follow through the discussion on how to calculate the present value of a company's future free cashflows. Before I continue my discussion, please be cautioned to take my sharing with a pinch of salt. This is because I am by no means a qualified accountant or analyst. I am just an average retail investor doing my own research into investing methodologies and principles from reading investment literature and attending investment seminars. However, I believe in constant learning and correcting my mistakes so as to become a better investor with time. One has to start off somewhere to fall and pick oneself up and fall again and repeat the whole process of falling and picking oneself up constantly in order to grow no matter in which areas of life, not just in investing.

An old traditional method - Looking at present value of future cashflows to determine investment value

Early economists more than 60 years ago like Irving Fisher and John Burr Williams proposed that the value of a stock is equal to the present value of its future cashflows. In my earlier post, we have seen how free cashflows are important to a company as it is the freed up cash that can be taken out of a company yearly without harming its business. Portions of free cashflows can be reinvested into a business, paid out to shareholders as dividends or be used in share buy backs to increase the % ownership of each shareholder.

There is a need to calculate the present value of future free cashflows a company is projected to generate. This is because the future cashflows investors would expect to receive is worth less than the current free cashflows. Two reasons abound regarding why future cashflows is worth lesser than current cashflows. Firstly, money we receive today can be invested immediately to start generating returns, but we cannot invest future money until we receive them. This is also called the opportunity cost of receiving money in future compared to receiving money today. Money at hand always has better immediate investment value than future money as it can be put into investing straight away to start compounding returns. Secondly, there is a risk an investor may not receive a company's future projected cashflows, and there is a need to compensate this risk taken, also called the risk premium.

Risk premium also depends on the nature of the business, whether its free cashflows is consistently stable or unstable. A company where its free cashflows keeps fluctuating through the years with no stability makes it difficult to predict its future cashflows with certainty, thus such company carries a higher risk premium.

Due to opportunity cost of receiving money in future compared to now and also risk premium, there is a need to discount the future cashflows a company is projected to generate by a discount. The higher the opportunity cost and risk premium an investor has to absorb, the higher will be the discount on a company's future cashflows to calculate the present value of the future projected cashflows.

As such, this simple idea of discounting a company's projected future cashflows to a present value is called the discounted cashflow (DCF) model for valuing a company's intrinsic value.

No investing methodology is perfect and an investor has to understand the possible limitations of every methodology. DCF assumes that a company's intrinsic value depends solely on the present value of future cashflows it is projected to generate. So, this method places importance on valuing a company based on free cashflows. If an investor is convinced a company's value is tied strongly to the amount of free cashflows it can generate for a period of time and he is willing to only pay for a company's free cashflows, then this method will make absolute sense for him. If an investor is not convinced by DCF model, it maybe better for him to adopt other ways of valuing a company (e.g. looking at P/E ratio).

Mathematical calculations behind Discounted Cashflow (DCF) model

It is not my wish to bother with complex calculations when doing investment. After reading some literature on Warren Buffett's investing wisdom, I remember one quote from this master investor which mentioned that investing is not a simple exercise, neither is it meant to be a complex exercise requiring intense mathematical calculations that it is not attainable by many without a relevant degree of certification. So, a high IQ investor with ability to crunch complex data and financial figures may not necessarily make a better investor than one with some basic financial and investing knowledge. As more variables and factors are considered in assessing an investment, it may not necessarily make an investment sound as an investor has a chance of misjuding each variable being considered. So, the more variables being considered in assessing an investment means more chances of misjuding the investment.

Thus, I will try to keep the discussion of the DCF model simple. My hope is not to provide a rigourous discusssion over this model but rather to bring out only simple appreciation on the required calculations and later to discuss this model's usefulness and limitations based on the context of its required calculations.

CFn = Free cashflow generated for nth year (e.g. CF1 means free cashflow generated for first year),

r = discount rate (depends on opportunity cost and risk premium)

Step 1: We have to forecast the free cashflow (FCF) a company can generate for next 10 years. For simplicity (since I am not an analyst trying to be as accurate as possible; anyway I don't think analysts can be perfectly accurate or else they would have make millions themselves in forecasting a company's future prospects so perfectly if they are really able to do so), I forecast a stable company should grow its free cashflows over 10 years at a pre-determined fixed compounded annual growth rate (CAGR). The compounded annual growth rate to use is rather subjective depending on individual investor. I use the same compounded annual growth rate based on a company's past cashflows.

For calculations of future cashflows for 10 years at my pre-determined annual growth rate, I use the formula Future cashflow = Present cashflow X (1+ r/100)^n, where r is the compounded annual growth rate and n is the number of years.

E.g. Company A's current cashflow is $100. It can grow at 10% compounded annual growth rate. At first year, company A can generate cashflow CF1 of $100 X (1+10/100)^1 = $110. At second year, it can generate cashflow CF2 of $100 X (1+10/100)^2 = $121. The calculation goes on until the 10th year.

Step 2: After forecasting all the future cashflows, we have to discount each cashflow by a discount rate to account for the opportunity cost and risk premium. Again, determining an appropriate discount rate is subjective. An investor can consider the yield he will receive on an alternative risk free investment (e.g. government bonds) had he not considered this current investment which is being assessed. Let's assume Singapore government bonds over a 10 years maturity period provide yields around 3 to 6% annually. So, an investor can have a discount rate of at least 3% over here. An investor can consider a higher discount rate than 3% (say 12%) if he perceived the company is risky and he should be compensated at higher discount rate on the future cashflows to calculate the present value of these future cashflows. So, a more conservative investor considers a higher discount rate when discounting future cashflows to their present value.

Step 3: Now, we have worked out the sum of all discounted cashflows for 10 years period (based on steps 1 and 2 plugging in the various values like current cashflow of a company, its cashflow compounded annual growth rate and its discount rate). We still need to determine discounted perpetuity value. Discounted perpetuity value is necessary to account for present value of a company's projected cashflows beyond 10 years. It is not feasible to compute all discounted future cashflows to infinity number of years, so a discounted perpetuity value estimates the present value of future cashflows far beyond 10 years.

(I will not present the calculations for discounted perpetuity value since my intention is not to provide a rigourous discussion on the mathematical calculations behind DCF model)

Step 4: Calculate total discounted cashflows (DCF) by adding 10 discounted cashflows for 10 years to the discounted perpetuity value. (Refer to DCF formula above)

Step 5: Calculate intrinsic value per share by dividing total discounted cashflows (DCF) by total number of shares outstanding for a company.

Discussion points on DCF model for determining intrinsic value per share of a stocks:-

1. There are at least two important variables affecting the calculations of discounted cashflows (the forecasting of future cashflows and the discount rate applied to discount the future cashflows to their present values).

2. It is by no means easy to forecast future cashflows. The compounded annual growth rate (CAGR) to use for determining future cashflows is subjective. An investor who is optimistic about a company's future cashflows can use a high CAGR to determine future stream of cashflows. Similarly, a conservative investor can use a lower CAGR. It depends on the investor's assessment of the company's future abililty to generate cashflows.

3. The discount rate an investor chooses can also be subjective. A conservative investor may use a high discount rate to discount the future cashflows to their present value. This is to account for the opportunity cost and risk premium he thinks he has to absorb when investing in the company. The discount rate may go as high as 15% to 20% up to the comfort level of an investor.

Conclusion:- DCF model is not a sure-win magic formula for determining intrinsic value per share of a stocks.

Different investors using the same DCF  model may still arrive at different intrinsic value per share for the same stocks depending on the CAGR they use to determine the future cashflows and the discount rate they use to discount future cashflows to their present value.

As such, DCF model is just one of many tools available for determining intrinsic value per share of company stocks. Valuation by DCF model may not be totally exact science, but it is partly an art since there is no absolute perfect forecast of future cashflows and no one perfect discount rate to be taken in the calculations of discounted cashflows. 

Thus, as with any other valuation tools, DCF model serves only as a guide and is not an absolute way to determine intrinsic value per share. No one can really peg a true intrinsic value to a company. Intrinsic value does change with time also. Therefore, an investor should always seeks to invest at a margin of safety below calculated intrinsic value per share to account for any misjudgment of the intrinsic value of a company. 

More discussions on using DCF model to determine intrinsic value per share for stocks in my portfolio, and I will also seek to discuss some mistakes I have commited by investing at higher than intrinsic value per share for some stocks in my portfolio in later post.