Stock valuation: Two-stage Dividend Growth Model (Critical Review)

By Jackie, Researcher

Topic: Education

Area of discussion: Finance

Chapter: Valuation of Assets and Company (Stock valuation model)

The objective of this week’s research is to compare which method is more accurate, faster and consumes lesser time by comparing the table method and the formula method to calculate the two-stage dividend growth model. Step by step tutorial is provided below with clear explanation and workings.

Introduction

Ideally, many companies will usually experience above normal growth rates for a short period of time before settling in on a lower but stable perpetual growth rate. Thus, it would be inappropriate to calculate the stock’s intrinsic value based on the single-stage dividend growth model. Unlike single-stage dividend growth model, the two-stage dividend growth model formula is often not provided in exam.

Sample question

Compute the value of a share of common stock of a company whose most recent dividend was $2.50 and is expected to grow at 3 percent per year for the next 5 years, after which the dividend growth rate will increase to 6 percent per year indefinitely. Assume 10 percent required rate of return.

Therefore, by using the formula method, we can actually save a lot of time (especially during examinations as the time is limited). Besides, it is also more accurate as it minimizes the rounding effect as compared to the table method. Moreover, we can compute it much faster as we do not need to refer to Future Value Interest Factor (FVIF) table as well as Present Value Interest Factor (PVIF) table.

The table is available here for

Future Value Interest Factor (FVIF): http://arjun.net.np/calculators/fvif_table.php

Present Value Interest Factor (PVIF): http://arjun.net.np/calculators/pvif_table.php?beg=0

Notes:

The question above is extracted from Principles of Corporate II – FIN326, Session: May 2010, Tutorial 3 at Mr.Lim’s class in INTI College Subang Jaya, Malaysia.

Related links and additional readings:

Dividend growth models

http://financialplanningbodyofknowledge.com/index.php?title=Dividend_growth_models

Why a stock valuation process is important in Dividend Growth Model?

http://omniglot.com/onlineinfo/stock/Dividend_Growth_Model.html

Dividend discount model – stock valuation – formula – how to calculate –Subjectmoney.com

http://www.youtube.com/watch?v=1WPbqT0zjys

Are pie-charts evil or just misunderstood ?

OK - I admit it: when I see a pie-chart in business analytics, my blood pressure rises and, yes, I am apt to tell the analyst exactly what I think of the monstrous, hard to read, waste of space and ink they created.

I am most definitely NOT the first person to suggest that pie-charts are over used and close to useless.  Google 'Pie Charts are Evil' and see for yourself.  This is an area where career analysts tend to agree, yet, in practice, pie-charts are very, very heavily (ab)used.  In the hope that I can influence even a handful of people to create fewer of these eyesores I'm adding my voice to the argument.



Let's look at an example and see how it might develop.  I want to display share of sales for my company vs. the rest for the last month.  Something like this:

example 1

It's not very pretty is it ?  Perhaps if we made it 3D ?  (Just 3 clicks in Excel)

example 2

And "explode" it - that even sounds cool (4 more clicks).

example 3

Cool-er, but I want to see 'our' portion at the front so rotate it. (Another 4 clicks)

example 4

Now let's play with the 3D settings, surfaces and add a shadow (about 12 more clicks).

example 5

This is starting to look very cool !  It is a little hard though to see what the share is for 'Vendor G'.    Bit more than 25%?  Less than 33%? But, we can fix this!  With just 2 more clicks we have data labels.

example 6

Now that looks really cool and it's a... monstrous, hard to read, waste of space and ink .

Let me list the ways I find it offensive:

1. Graphical display is supposed to help us visualize data.  This display manages to visualize "Our share of sales last month was 28.8%" .  Just how much visualization do you need for that ? 
2. It turns out that we (humans not just analysts) are quite bad at estimating proportions from area.  This was an issue in the very first example.  And there is nothing to help us - pie charts have no scale to reference to so you're stuck estimating based on a few proportions you know well (halves, thirds, quarters).
3. Guessing the actual share got harder and harder as the chart got 'cooler'.  Going 3D, exploding the section and rotating so that we no longer had at least one part of our segment at 12 o' clock  all made it harder to read.
4. Adding shadow, highlights and texture probably did not do much harm, but it certainly did not help visualize our one and only fact. (Yes, I do know there are 2 numbers in the chart but as one is easily calculated from the other, essentially we have one useful piece of information)

 Expand this to multiple values and we can examine another issue.

example 7

Is it at all obvious to you which pie segment is related to which Vendor?  Note that I did not devise this color scheme for the example, it's the default that Excel provided when I added more data to the previous example.  If we are trying to spot categories by color they have got to be very high contrast and when we get to 8 different colors its very hard to tell some of them apart.  (The color blind could give up long before 8). In this case, I can figure it out from the thin orange segment which is clear to me.  The others are then charted (and labeled) in sequence so I can figure each one out.  But, does this not seem like an awful lot of work for your reader ?  

What if we add category labels to the pie segment too ? 

example 8

If you think this is an improvement, you should probably stop reading now and let's just agree to disagree.

By the way, those folks that did stop reading at the last sentence are so wrong !

Most of the blogs and articles I have read on this subject, quite a few, but probably less than 1% of the voluminous published material, spend a lot of time telling you why pie charts are wrong but less on suggesting alternatives.  Let's try and address that.

How about this as an alternative to example 8 ?

example 9

This just works.  A simple bar chart immediately fixes 2 of our issues.  

• We are no longer trying to estimate proportion from area (which we are bad at) but from length (where we are substantially better).  Even without the data labels you could make an intelligent guess as to actual values, more so if I added a few more grid-lines and scale labels.
• The category label is directly (and much more neatly) tied to its visualization.  No need for multiple colors, no trying to figure out which number relates to which category.

Perhaps its not as "cool-looking" and if you really wanted to, you could go 3D, switch out to pipes rather than bars and apply a texture or shadows.

example 10

Personally I don't think this adds any value for people who actually want to read and use it.  If you are publishing to people who don't want to read your material but may be impressed by the look of the graphic, perhaps it has a place ?

How about this as an alternative, a simple table.  Yes, its primitive, I know, but it really does work, try reading it.

example 11

  Or how about this, a "cooler" version using Excel's in-cell data bars?

example 12

Let's wrap this up by going back to our very first example.  We wanted to show share of sales for 'our' company.  On my screen (your's may well be different) this uses roughly a 2" x 3" space (5cm x 7.5 cm) to display only one useful number 28.8 %.  If that's all the data you have to display and you have such a space to fill, well, maybe, it's ok to use a pie chart.  But can't you display something a little more useful ? 

Example 13

 Same space, much more data and very importantly, much more useful.

So, back to the question at the top of this post.  Are pie charts evil or just misunderstood?  To my mind, they are 99.9% evil and misunderstood - if in doubt, don't use them.

IQ test [Updated, May 2012]

By Jackie, Researcher

Area of discussion: Intelligence Quotient [IQ]

Function of this discussion: To test our brain’s IQ

Requirement(s): Basic Mathematics’ skills involving area calculations

The objective of this post is to share an extremely tricky question related to IQ and see whether could we solve this question together. Besides, it allows us to share the conflicts or perhaps some weaknesses in Mathematics’ theories. By having different comments and opinions from different people will greatly help to solve this problem faster.

Introduction

Guest what? I saw this on my Facebook, and yet no one can give an accurate or reasonable explanation on why this could happen. So, I took this opportunity to share out to a larger crowd to see whether it could be solved or not?

My arguments:

I know there is a difference of 1 unit²between the first triangle and the second triangle, but I am going to tackle them separately as the confusion already exist if we tackle either one of them even without the existence of the other triangle.

(The triangle at the top)

According to Mathematics’ theory:

Area of a triangle 

= 0.5(length x height)

= 0.5(13x5)

= 32.5 units²

But this is different if we calculate it one-by-one, all the four shapes together:

Red: 0.5(8x3) = 12 units²

Orange: 7 units²

Dark green: 0.5(5x2) = 5 units²

Light green: 8 units²

Total : 32 units²

Why is there a difference of 0.5 unit²exist?

(The triangle at the bottom)

According to Mathematics’ theory:

Area of a triangle 

= 0.5(length x height) – 1                                                                      (note: minus one for the missing unit)

= 0.5(13x5) – 1

= 31.5 units²

But this is different if we calculate it one-by-one, all the four shapes together:

Red: 0.5(8x3) = 12 units²

Orange: 7 units²

Dark green: 0.5(5x2) = 5 units²

Light green: 8 units²

Total : 32 units²

Again, why is there a difference of 0.5 unit² exist?

I know some of you may argue that one of the triangles is concave, and the other is convex (or perhaps the triangles are bend at the hypotenuse, but this is not important anymore if we treat them as a separate IQ question. This is because the difference in calculation of 0.5 unit² already arises even if we did not compare the first triangle at the top with the other triangle at the bottom. Therefore, is the calculation wrong? Or is there a conflict between calculating one-by-one method and calculating by using Mathematics’ formula related to triangle?

Analytic tools "so easy a 10 year-old can use it"

If you search the web you'll find lots of analytic tools to support your business: tools to help with forecasting, inventory optimization, risk analysis, simulation for production lines and warehouses, production scheduling, supply-chain network design, vehicle loading, price-sensitivity modeling and planogram building - and that is very, very far from being an exhaustive list.

Some of these tools are bought as a service that includes expertise to prepare your data, do the modeling work for you and configure the system to meet your needs. These tools will be much more expensive than the 'roll your own' variety and the more frequently that expertise is required, the more you will pay.

If the business problem you are working on is relatively stable (meaning that the same issue comes up repeatedly and your business rules around how to solve it stay the same) such a system can have a long a fruitful life once set up. Vehicle loading applications are a good example - once configured to your needs they should need infrequent updates to work well.

Many analytic applications are more one-off in nature and if you use an expert to help you with every use it will cost you a substantial amount of money. So, do you really need all that expertise or is it simple enough that you can pick it up? Desktop analytic tools could help you deliver millions in savings and can be bought for a few thousand dollars. Many of them are marketed as being simple to use, and imply that you'll be able to pick it up as you go with, perhaps, a little training,

Let's look at an analogy - driving a car. Cars are very complicated things and yet almost every adult can drive one. Why would business analytic tools be any different? Cars are certainly complicated but I see no reason a 10 year old could not master driving one because they do not need to understand or master most of that complexity.

• Cars have been around for a long time and have seen billions, perhaps trillions of dollars invested to make them robust and hide almost all the complexity from the driver.
• Cars have relatively few controls that you need to understand to operate them: ignition, steering wheel, brake, accelerator, turn-signals, lights, mirrors, windscreen-wipers and gear selector. I know there are more gadgets but master these few (and hoping I missed nothing important) you can drive a car.
• You get instant feedback when you use these controls badly and that really helps you learn
• Most of us get a lot of practice driving a car and some of us are still quite bad at it :-)

In contrast most business users are ill-equipped to take on analytic tools where the complexity remains very apparent, there can be hundreds of options to choose from in building and executing your models and these must be understood to use the tool effectively.

Let's make a distinction here between getting a tool to work and getting it to work effectively. I've seen a lot of spreadsheet using Excel's Solver add-in which solves optimization models: you build a spreadsheet that models some aspect of your business then ask it to find the combination of input values that maximize your output (profit, sales or some such value). If you built a model with no errors and avoided a handful of functions that this optimizer can't handle it will run and most likely return an answer. It may even be able to guarantee (depending which algorithm it used) that this is the absolutely best answer available - the optimal solution to your model. Unfortunately, many of the models bear little resemblance to the real-world issue you are trying to optimize and consequently the optimal solution for the model is not particularly good (and certainly not optimal) in the real world.

There's one good example of an analytic application that really is "so easy a 10 year-old can use it" and it's not a business application at all. It came to prominence in the last few years and is now available in cars, on low-cost specialized devices, even on your phone - GPS navigation. Behind the scenes there is a large, accurate database of road networks and locations along these roads and an efficient routing algorithm (the analytic part) to find the shortest route between any 2 points The whole thing is wrapped into a well-designed user interface so that all this complexity is hidden from the user and we don't care because it just works, all of the time. Well, almost all of the time :-)

In my opinion, there are very, very few analytic tools that are truly accessible to business users without some configuration, packaging or guidance from an expert. If you are serious about solving a business issue that needs some analytic work, you need the tool and the mechanic to wield it.

Export chopsticks to China [Updated, May 2012]

By Jackie, Researcher

Type of business industry: Manufacturing

Product: Disposable chopsticks

Target market: China [major]; Japan & Korea [minor]

The objectives of this research are to identify which commodity can easily penetrate into China’s market successfully, the reasons behind it, the issues involved in this business activity, and demographic analysis of certain locations in order to get the sources of production.

Introduction

Nowadays everywhere around the globe, you can almost easily spot “made in China’s commodities”. With the population size of 1.3 billion, the Chinese almost manufactures everything and successfully penetrate into every country’s market with its golden formula: low labour cost. However, have you ever thought of some products that are needed by them of which other countries can manufacture it and sold to them? In short, what are those essential products that can penetrate into China’s market?

Answer: Chopstick

When I said this to my colleagues, 6 out of 6 roll on floor laughing and saying back to me, “Jackie, you are crazy”. Oh well, this basically indicates that most of the people are still not concern and aware of this type of business. I got this idea through reading National Geographic’s magazine few months ago and because the information given was restricted, I have to do my own research by searching other business journals and magazines as well. After months of analyzing it, I have successfully identified this type of business’ potential too.

Sushi King : "This chopsticks are made from natural wood and are not processed with any bleaching agent"

True, but strange!

Did you know that even now, China is importing chopstick from other countries? I know how you feel now [same as mine when I was first introduced to this matter]: strange. The first reason is simple and straight-forward. China uses 45 billion disposable wooden chopsticks a year, but the country has a very low lumber resource (CBS Evening News, 2011). Well, this point is arguable because chopsticks are not necessary have to be made using timber. Bamboos can be used as its substitute [and China is rich in bamboos]. Another strong reason is due to China’s National Logging Ban [issued in 1998] to preserve and conserve their natural forests from being over use. They actually observed and know that their forests were slowly degrading and deteriorating which are mainly resulted from unsuitable and unsustainable management strategies and methodologies. [See reference 1] 

A brief summary of real case study on Georgia’s Chopsticks Company:

Georgia Chopsticks Company manufactures roughly four millions of chopsticks daily and exports them to China and Japan. The main idea is China and Japan have insufficient wood to produce their own chopsticks, but Georgia has. The owner, Lee started the business when he heard that China has a moratorium on domestic tree cutting in order to protect its dwindling lumber resources. The abundant poplar and sweet gum trees in Georgia were found to be ideal for producing straight, pliable, and light coloured chopsticks. Each pair of chopstick is less than a penny to be made. Georgia Chopsticks is the only one, America’s chopsticks manufacturer in the United States. The owner is planning to produce 10 million chopsticks daily by the end of 2012.

Tee Kendrick, left, and Toriano Jenkins roll up chopped wood for further cutting.

Esteban Fabela peels away the bark from a steaming log.

Chopsticks are moved on a conveyor belt.

A worker loads boxes of chopsticks onto a shipping container.

Issues and threat to set-up such business

1. Law constraints

    For example, China’s National Logging Ban [issued in 1998] to preserve and conserve their natural   

    forests from being over use whereas some countries require tree loggers to apply ‘logging license’ before 

    logging process starts. Normally tree cutting restrictions apply. However, not all type of trees can be cut 

    down because some trees are protected species.

2. Type of wood used 

    Ideally, the wood should have pleasant colour, texture and appearance: milky white. Based on my 

    observation, although country like Malaysia has high quality timber [as it is located in equator line] but the 

    wood is not suitable to make chopsticks as the colour of those wood are usually darker as compared to 

    Georgia [Malaysia’s timber are usually used to make furniture and outdoor landscape design]. 

3. Plastic, bamboo, or metal chopsticks as substitute

 This is the most worrying threat to this industry. However, some chopsticks users have commented that 

 using plastic chopsticks to eat hot food will somehow triggers the plastic’s chemical reaction which is 

 harmful to our body, resulting in food poisoning. Meanwhile, using bamboo is quite troublesome as it is 

 mandatory to remove its stingers first, and hence extra steps are needed before turning them into 

 chopsticks. Finally, it is very unlikely that the Chinese, Japanese nor the Korean will use metal chopsticks 

 to eat their food. The reason is simple. It is heavier and it is a heat conductor; it will transfer the heat from 

 the food to the users' fingers.

4. Environment factor

 As the business goes on, it will require more and more trees to be cut down. Thus, this is not a 

 environmental friendly business. Besides, the present of non-government organization (NGO) as well as 

 environmental conservation and protection groups will pose additional threat too.

Business Potential

According to Economics’ theories, this type of business has an extremely bright future whereby you can actually see the Georgia Chopsticks Company being the only one chopsticks manufacturer in America. This is so called: monopoly. The demand for chopsticks will rise in the future due to the increase in demand mainly in China, Japan and Korea. Eating using chopsticks are part of their culture and tradition. It is clearly noticeable that disposable chopsticks are often used in restaurant like Sushi King, Teppanyaki, and Chinese restaurant as well. This is however; very seldom people will go into this type of business as the work is too tedious. 

Additional readings and references:

Challenging the national logging ban in China: An Experience of community-based natural forest management in Sichuan province.

http://www.fao.org/DOCREP/ARTICLE/WFC/XII/0098-C1.HTM

China’s large-scale afforestation projects, importing timber from west and central Africa, combating illegal logging, implementing new laws and customs monitoring.

http://www.illegal-logging.info/approach.php?a_id=28

Georgia’s Hottest Export: Chopsticks!

http://www.thedenverchannel.com/news/29932489/detail.html

Fox News Channel: GA Chopstick Company exporting products oversea to Asia.

http://www.youtube.com/watch?v=x68s3qwiUcY

[CBS Evening News with Scott Pelley] Mark Strassman reports on how South Georgia, with its lush forests of sweet gum trees, has built a factory manufacturing and selling chopsticks to China.

http://www.youtube.com/watch?v=-KmALZWHgbQ

US factory exports chopsticks to China.

http://www.youtube.com/watch?v=6lgYqWappfk&feature=related

Notes: Pictures courtesy from google search.

All information is accurate at the time of posting.