## Sunday, 21 June 2015

### Intrinsic Value - Dividend Discount Model

This is a section which I thought I should add to the Understanding Financial Statements topic as after understanding the financial statements, the next thing that an investor would or should know is how to use this information to value businesses. Of course, there are also as many intrinsic values of businesses as there are people valuing the business as there is no hard and fast rule on intrisic value and the factors which have some of the greatest impact on calculation come from the perception of the investor, which can and will, vary from investor to investor.

This section will cover two popular methods, the Dividend Discount Model (DDM) and the Discounted Cash Flow Model (DCF Model). This has been split into 2 parts when writing as each model takes quite a lot of explanation as well as diagrams.

Dividend Discount Model (DDM)

(Image source: http://zewt.blogspot.sg/2007/09/tax-free-dividends.html)

This model basically takes the dividends that the company pays out to its investors as the way to value the company. By taking the dividends that the company pays out to its investor, which can be done on a per-share basis, and estimating the future dividends as well as the appropriate risk discount and time value of money to get the present value of those dividends. I'm guessing words such as risk discount and time value of money as well as how to estimate the future value of dividends seem confusing at this point but I will explain them now and you may want to re-read this paragraph after reading the explanations to get a better understanding.

So, the time value of money is also known as the risk-free rate, it is the rate of return that you can earn on your money while taking no risk. Though there's no risk-free instrument of investment, many people take the US Treasury Bond Rate as a proxy for the risk free rate, while in Singapore, we can take the Singapore Government Bonds, also known as Singapore Government Securities (SGS) as the risk free rate, At time of writing the 30-year rate is roughly 3%. This can be found by going to the SGS website by MAS and going under statistics. In that website you can also find more information on purchasing SGS as well as the issuance calender.

The risk discount, or the risk premium, is the return on investment that you would have to earn to compensate you for taking on the risk of the company. This is the amount above the risk-free rate that the company would have to pay in dividends to compensate you for the extra risk you take by investing with the company instead of taking the risk-free rate by the government. If the risk that you took is not realized, then you would get a higher dividend yield than you would by investing in "risk-free" government bonds, and vice-versa. But if the company suffers a dividend yield decline in line with your risk premium, you would make the risk-free rate. (This can be quite confusing, any question please ask in the comments section, there will be some pictures later to try and further explain this).

Then what about estimating future dividends? We can give an estimated percentage increase in the dividend, which we can compound using software such as Microsoft Excel to give us the estimated future dividends. To get the present value of future dividends, we have to take the total value of future dividends and discount (deduct) the risk discount and the time value of money. This would allow us to get a good idea of whether the investment in our opinion is better than taking the "risk-free" rate.

This shows how to calculate the present value of dividends in Excel, with the starting time being Year 0, cell highlighted shows how to calculate present value of dividend (Not an Excel expert here)

But, since company's have theoretically infinite life spans, how do we estimate the value of dividends 100 years from now? In this model, we don't there's a formula called the Gordon Growth Model, which would estimate the perpetual value of those dividends, but it needs the current value of dividends, the risk discount, the risk-free rate and the perpetual growth rate (the estimated growth rate for the future on to eternity). For the perpetual growth rate, it is usually easiest to take the average GDP growth rate of Singapore or whichever country you are investing in for maybe 20, maybe 30 years. The perpetual growth rate would have to be lower than the risk discount plus risk free rate for this model to work (or you would get a negative or undefined value).

Present Value = Present Dividends / (Risk Premium + Risk-Free Rate - Perpetual Growth Rate)

This would give an approximate of the present value of all the dividends in the company's infinite life span.

This is following the previous example, showing how the Gordon Growth Model is used. Cell highlighted shows the formula used for calculation

Just something extra.......

Please make sure you understand the above before going on to this, it would be very confusing if you move on without understanding how the DDM works.

So for this extra part I'm going to add in different stages (time-periods) of growth. For example, let's say I can predict the growth rate of the company to be 6% for the next 5 years but I'm not sure after that so I want to leave it at 3% for the perpetual growth rate.

Adding 2-stage growth to the DDM

In the example above, the growth rate for the stock has been amended to the short-term growth rate (5-year). This would allow the dividend to "grow" at the set rate for 5-years (the formula with the new short-term rate just has to be added for the number of years desired).

This can be done for multiple stages, though it would get extremely confusing. Anyway, this last segment closes up this part on DDM. The next section would be on the Discounted Cash Flow Model (DCF Model) (linked to the page) and is similar, it just uses Free Cash Flow as the basis for valuing a company instead of dividends.

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