Saturday, November 22, 2008

How to Value Equities - The Discounted Cash Flow (Dividends) way! - Example:SingPost

A reader asked us to write about valuing equities using the Discounted Cash Flow method sometime back. It has been long overdued...sorry dude or duddette...we have been busy analysing some stuff of late. Before you read on, we would like to mention that this method entails a lot, a lot and we mean a lot of assumptions and it is highly theorectical. Garbage in- garbage out. Why do you think Research Reports target prices are nearly always way off target? Anyway, its the thought process that counts and not the final target price. Who knows, when thinking through the may actually gain insights on the stock you are researching. So its not useless..this model.

There are many forms of DCF analysis and we will be looking at discounting dividends. This is most appropriate for valuing stable companies (for example in a mature industry) and those that have a consistent payout of dividends . (Please note that there are other types such as discounting Operating Free Cash flow or discounting Free Cash flow ).We will be using SingPost as an example. See below for the yearly dividends they give out. We started from year 2006.

Based on the table above, it is logical to assume that they will be giving out at least S$0.0625 in dividends every year from 2009 and beyond. So here comes the DCF formula. Its looks ugly but its actually quite easy. SGDividends will walk you through.

Figure 1

The foundation of this formula is that the value of a asset ( stock in this case) is the present value of its expected future cash flows ( dividends in this case). In the above formula, it is taking all the dividends up to infinity years ahead and bringing it back to the present value, now. People then compare this present value now with the current stock price to see if its cheap or not. The dividends for a company could grow in time, therefore, the variable g takes into account the dividends growth.
As SGDividends is all about making complicated things even easier than easy. We are going to derive a formula which will be easier than easy to use. The derivation is below in figure 2, but you can skip this part amd jump to the final formula in Figure 3.

Figure 2

You can read up on the sum of infinity through thislink. From the above maths in figure 2, we derive the following formula in figure 3 from the equation in figure 1. Isn't it much easier to use now?
Figure 3

So let's put all this mumbo-jumbo in practice, shall we?

For Singpost:
Dividends for current period ( or most recent period) , Do= S$0.0625.
As it is in a mature industry, assuming dividends is growing slowly at a rate, g = 2%.

Let's assume your required rate of return, K = 6% ( We use 6% just to follow the rate from DBS preferential shares. It can be anything you wish because its YOUR required rate of return.Most people would then choose as high a rate of return as possible as more is better right?Then its wrong. You should consider your required rate of return as the rate of return of the next best investment which you think you can get. So if you thought DBS preference shares at 6% is one of the best around or it makes you happy, then use it as a benchmark to input the K.)

Value of stock = [0.0625(1+0.06)] / ( 0.06 - 0.02) = $1.65625

Price currently as of 21 Nov 2008 as listed on SGX = $0.76.

Don't go rushing to buy this stock yet as we have said before there are many assumptions. Firstly, there is no guarantee that Singpost will continue giving out dividends or dividends will grow. There is no guarantee that Singpost will last forever, it might go bankrupt like Ferrochina ( you think so?). If Singpost decides to be crazy and start giving out more dividends than is manageable to its survival as a company, then of cos using the model doesn't work as it will not last and the current value you calculate will be too big and wrong. It is theoretical and also you will realise that this is not appropriate for all companies, since some companies don't give out dividends.

Important: The objective of the articles in this blog is to set you thinking about the company before you invest your hard-earned money. Do not invest solely based on this article. Unlike House or Instituitional Analysts who have to maintain relations with corporations due to investment banking relations, generating commissions,e.t.c, SGDividends say things as it is, factually. Unlike Analyst who have to be "uptight" and "cheem", we make it simplified and cheapskate. -The Vigilante Investor, SGDividends Team


  1. Hey Guys, how about using Microsoft Equations to do ur equations? Look nicer :)

  2. Hey dude,

    We dont have Microsoft Equations installed.
    Is our handwriting so bad....hmm? Kinda untidy..but a doctor's handwriting is worse and they are prescribing medicine..!

  3. How did you arrive at the DCF formula?

    I already spotted a mistake. You sum the value to infinity.

    First term = Do
    Common ratio = (1+g)/(1+k)

    Value = Sum to infinity = first term / (1 - common ratio)

    = Do/[1 - (1+g)/(1+k)]

    = Do/ [ (1+k-1-g) / (1+k) ]

    = Do[ (1+k) / (1+g)]

    According to your formula, this should be the value and not Do/ (k - g)! Even if your original assumption is correct, your value will be wrong.

  4. Hi Digital,

    Thanks for pointing out the mistake. We will change it.

    However, the final formula should be [Do (1+k)] / (k-g)

    Thats the problem with being cheapskates like money to get an editor!

    Thanks again Digital!

  5. Hehe, I made a mistake too. Your value should be = Do[(1+k)/(k-g)]

  6. I think this formula is flawed. What if k = g , then the value will be infinite? That means with just 1 share, I can own the entire world. Can't be true right?

  7. Hi Digital,

    Yes if k=g then it will be infinity. Infinity value for a stock feels wrong. We agree.

    However, when we think about it, if k = g , either means our required rate of return is very low ( let's say this person really don't know about investments and he/she thinks putting in POSB banks 0.25% is really good already) or g is high to meet our k, therefore, infinity might mean that this is a definite stock for you ( you and not the rest of the investors as k is your required rate of return).

    Its really theoretical Digital. In fact, if the denominator is negative, then the value of the stock becomes negative. Thats just how analysts use to value the stocks you still trust them?

  8. Erm, your "new" formula is also wrong

    The constant growth model is actually

    V = Div/(k - g)

    where D = D0 (1 + g)

    Your dividend stream cannot grow by the required return...



    PS - I think we can safely assume that analysts are "smart" enough to know that if k-g is negative, the model cannot be used

    And typically if g > k, the high-growth company will not be paying dividends anyway as it needs cash to fuel its growth (think dotcom companies)...

  9. the last post got the basic DDM right: the Div used should be that of next period (since valuing FUTURE cash flow)

    there are certainly limitations for DDM. e.g. if (k-g) becomes very small, V increases dramatically. so equation not applicable when k n g are very close to each other.

    as with all models, input data assumptions very important. if not garbage in, garbage out.

    always good to compare ur results with that obtained using another valuation mtds: absolute (e.g. FCFF, FCFE. there's also multi-stage models avail) n relative (e.g PE, PB, PS).

    if ur assumptions r correct, results should be close (not exactly same, but at least in the same ballpark. also, expect greater valuation differences btwn absolute n relative valuation mtds)

  10. hi Anony, one stand alone valuation method is perfect. Garbage in garbarge out and it's always better to use many more to reconfirm..the more one researches before investing....the risk gets lower due to one's due diligence =)

    Thanks for reading =)


  11. I like to calculate it based the few assumptions:

    1. No growth in dividends
    2. Min dividends that singpost is going to give, which is 0.05 cts per yr.
    3. Required returns of 6%

    Based on your formula, I'll get:

    [0.05(1+0.06)]/(0.06) = $0.88

    Let's apply an 'error' correction, in case our assumptions go wrong. Let's apply 30% error, meaning I'll take 70% of the calculated value:

    70% of 0.88 = $0.62

    (at this price, the dividend yield of singpost becomes 8%, based on 0.05 payout - and this represents the min yield unless singpost goes bellyup)

    Checking the charts, the lowest it ever went to in recent history is 0.605 on 29th Jan 2009. I think it good to look at singpost again at this price.

  12. Erratum: should be 5 cts per year, not 0.05 cents in assumption (2)

  13. Hi La Papillion,

    Very conservative figures you have used...even including a 30 % discount!

    A very good dividend play our opinion ..not capital play..even they admit it in their propectus, quote"
    domestic mail volume in Singapore has continued to increase in recent years, potential future growth in
    traditional mail services is limited in Singapore by the size of the Singapore domestic mail market and the threat
    of electronic substitution. Therefore, key elements of our mail strategy are reducing costs and achieving growth
    through developing value-added services and international expansion."unquote..

    Very strong Free Cash Flow...hmm maybe we will consider buying it.. =)

    SGDividends Team

  14. SGDiv,

    Hey, didn't we read this all the time - take care of the downside and the upside will take care of itself? haha :)

    I didn't mention this in the previous comments. Even though the yield looks good, there are others which seem better. I don't really like the debts that singpost is holding. Besides, the business isn't that fantastic seriously. While I do not think that the liberalisation of the postal market will harm singpost much (their competitor have some problems accessing hdb and condo mailboxes), it's the overall less reliance on hard mailing that makes it worrying.

    A word on such models...I did a discounted FCF modelling for singpost for a period of 10 yrs. Churns out a price of $1.20 for singpost. Well, that is after I bought it at 1.18. Grr.... Anyway, the pt is that if you want to purchase, I can make the necessary assumptions in the model to make it a 'value' buy :) Really GIGO - garbage in garbage out.

    Maybe you can look at this two: Challenger and vicom :)

  15. Hi LP,

    took a quick look at challenger..Don't really like its business model...Basically, they are heaviily dependent on walk in customers with government contracts, corporate contracts and Electronic signage taking the back seat. This is the demand part.

    From the supply part...looks like they have large supplers like HP ,IBM...looks like they do not have any supplier power.

    From the competition part..Best Denki, Courts, Harvey...wah too much competition...

    Electronics depreciate damn fast....on the inventory part..its a hassle...

    Challenger no no...haha for us....

  16. Hi Sgdiv,

    I have the same sentiments about challenger. But there's a pro by the name of dydx (a grahamian investor) who had it. The dividend yield is fantastic, the last time I looked.

    You know grahamians don't bother too much with the business aspects, more on buying it cheap relative to value without holding for long.

    When I have some time in hand, I'll do some articles on it, can share with you

  17. Hi La papillion...

    We are very "kiasee" and paranoid..haha everything also must look lah....

    Anyway..challenger dividends is not really consistent and the top 3 shareholders are insiders ( directors) who together hold 76% of the company.......... know dividends....

    Sure..thanks lets share if we have any ideas :)


  18. Your Figure 3 is still wrong

    You have future dividend growing by k (the required return?!)

    Of course unless you mean to say that g = k, but the formula won't work if g = k...


  19. Hi Anony,

    The formula is based on Geometic progression formula ( A level maths) where sum to infinity = first term/ ( 1 - common ratio).

    first term = D0

    Common ratio = (1+g)/(1+K).

    Plug these values into the formula and u get the formula is figure 3.

    Yes, if K=g, it will result in the denominiator being 0. The formula will be invalid since anything divided by zero is invalid. This is the limitation of the model.

    Maybe u get share the formula which u think is more right? Would be eager to learn =)


  20. I find that the best indication of how undervalued a stock is is the price to sales ratio or what is commonly referred to as market cap.

    Simply stated. If a company does 1 billion in annual sales but it has a market cap of 100 million dollars than the price to sales ratio is ten to one. In other words the market is valuing a company that does 1 billion dollars in annual sales at just 100 million dollars. But what does this mean. It means everything if you are a classic value investor.

    Here is a perfect example of why the price to sales ratio is so very important if you are a value investor in stocks. If our 1 billion dollar company is breaking even that is they are not making a profit nor losing money. Lets say the company has 250 millon dollars in long term debt and 80 million dollars in cash. We will say they are in the food business they make a wide aray of food products. Maybe the company did a buyout of another company a few years ago that did not work out as well as expected. So thats why the company is having trouble making a profit but things now seem to be moving in the right direction. If I purchase shares in the company for say 10 dollars. And over a five year period the company improves their earnings performance to the point where their now earning say 60 million dollars on sales of one billion two hundred million dollars. Thats a profit margain of 5%. If the stock were to now trade at twenty times earnings that would now mean that the price of the stock would be at 120 dollars a share or another way to put it the marketcap is now one billion two hundred million instead of 100 million.

    The problem for me is not that this investment method is not effective it works great. I purchased seaboard stock back in 2000. I think it was for 190 dollars a share around that. I following the exact method I describe above. I sold my shares about five years later for 2500 dollars yes thats correct 2500 dollars or more than twelve times what I paid for the shares. Seaboard was profitable when I bought it and profitable when I sold it. The stock was just a great undervalued stock that was overlooked by investors.

    Like I was saying before the problem is not with this investment method. Its that stocks like seaboard are very rare indeed theirs just not a whole lot of quality companies out their selling a very low price to sales ratios. Another issue that I have been having is when a company of decent quality trades at a very low price to sales ratio its not long before a private equity firm or the family of a family owned company takes notice and usually makes a low bid for the shares and takes the company private preventing me from realizing the enormous gains that mght have been possible had I not been forced to sell my shares out to a party that was making a very unfairly low offer for the shares of the company.

    Another thing to keep in mind when it comes to value stocks that have a low price to sales ratio that could give the buyer a tremendous advantage is this.

    I mentioned a little earlier that are food company had 80 million dollars of cash on their balance sheet now if the company choose to they could buy back a large chunk of their stock maybe 30 million dollars worth of the shares outstanding it would only cost them 30 million dollars they still would have 50 million dollars of cash left on their balance sheet. This means that under the positive earnings outlook for a company the stock price could even be much higher than 120 dollars a share. If the company were to retire a large percentage of their exsisting shares in a stock buyback.


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