Download Valuation - Ohio University College of Business

Valuing
The Basics of Valuing ...................................................................
Valuation Under Uncertainty ........................................................
Valuation of an Equity Investment................................................
Valuation of an Acquisition Candidate ..........................................
Appendix 1. Present Value Tables
Future Value Table
Appendix 2. Apartment Building Spreadsheets
Appendix 3. Answers to various problems presented during the module
Appendix 4. Present value concepts and problems
Answers to problems
Appendix 5. Additional Equity Valuation Concepts/Considerations
The information contained in other valuation techniques
Price Earnings Ratio
PEG ratio
EVA and MVA
Technical Analysis
Sources of Information
Information Sources
1
During this module you are going to investigate the process of determining the monetary value of
something. We will do this investigation in four stages. The first will be an introduction to the basic
concepts which are used in the valuation process. We will then apply these concepts to three situations.
The first of these will involve the basic valuing of an asset, in this case an apartment building. The
second case will involve the valuation process of a company’s common stock. The third situation will
involve the process of one company buying another company. In order to keep this interesting for the
reader and the writer, much of the work will focus on tools you can use to enhance your personal net
worth.
For the purposes of this module it is assumed that the reader the basic elements of :
what is contained in an income statement (P&L),
what some of the more common noncash items like depreciation and amortization represent,
the basic elements of a balance sheet.
Section 1. The Basics of Valuing:
The basics of investing will be presented in a number of considerations with associated discussions
and explanations/proofs. (With the hope that the presented explanations/proofs turn these into theorems
or axioms).
First we will present you with what is the most important consideration and the basis of the rest of this
model;
The Financial Worth of anything is equal
to the present value of its future cash flows.
Note the use of the words financial worth. This module will consider quantitative financial analysis
only. We will mention some nonfinancial considerations as we go, but only in passing. This is not
meant to belittle their possible impact on your decision. When personally considering an investment, it
may be the nonfinancial aspects which are really the most important. Consider your evaluation of the
purchase of your home. Future cash flows inflows generated by the home probably played little or no
part in your decision.
Consideration 1. When valuing any possible investments, what is really being valued is the cash flow
from that investment. Investing is truly an art. An art which is based on the ability of one to project
cash flows and then determine the value of those cash flows. Without some competencies in this art, the
rest of this module, while technically correct, will be of little value. We will discuss some basic
elements of the art the next section and will suggest some readings in this area in Section 3.
Once one has a handle on the cash flows then it is simply a matter of determining the current
worth of those cash flow to come up with a value of the asset to you. With these projected cash flows in
hand, you can turn the question to;
How much would I need to put in the bank today, if the bank paid X% to be able
to withdraw these projected cash flows at the time they are estimated to occur?
X% is the return, stated as a percentage of the amount the investment is generating. One decides this
number based on the risk of the investment and the returns of other available investments.
2
If the cash flows are certain, then the only thing that can change the value of an investment
is a change in the required rate of return of the investors.
Consider:
How much would you pay for annual payments of $100 per year, starting in one year, and which
would continue forever and which had no risk?
Cash flow
The answer is in the formula Required Rate of Return.
Thus if your required rate of return is 10%, then you would pay $1,000 for the right to receive $100 per
year forever, ($ 100/.10). It might bother some of you that we have not provided for the return of your
original investment. This is really not a consideration, but to ease your mind, consider that should you
need your original capital back, you could sell the right to someone else who wanted a 10% rate of
return. For the purpose of this example, we are assuming that the rate of return you require is equal to
what the market will generate. Later in the module we will drop that assumption.
If this contract sold in the open market, what could cause the value of the contract to change?
Ans: The only thing that could change the market value of the contract would be
a change of the required rate of return.
Example:
If you bought the contract for $1,000 and if interest rates changed from 10% to 8%, what difference
would that make in the market value of your contract?
Ans:
$100
X
$100
.08
= 8%
=X
X = $1,250.00
so the value of your investment has increased by $250.
How much would the market value of the contract be if the interest rates increased to 12%?
100/.12 = ($833.33)
(and the above explains why the value of bonds goes up and down with changes in the interest rate).
To review, if the cash flow of an investment is known for certain, the only thing that can
rationally change the value of the investment is a change in the interest rates. (The use of the word
rationally is purposeful-we will address irrational behavior of markets later in the module).
If you are comfortable with what we have done thus far we will proceed. If you want to go over this
section again, or you want some review problems to solidify your knowledge in this area, we are
preparing an Appendix with more explanations and problems.
3
Now let us change the problem
How much would you pay for the certain cash flow of $100 per year for
the next three years if the cash flows started in exactly one year?
What is you required rate of return?
Let’s continue to use 10%
So the cash flows would look like
(X is the amount of the investment)
X
$100
$100
$100
|--------------------|--------------------|--------------------|
Y1
Y2
Y3
This problem is solved by reworking the question to
“How much would you need to put in the bank today
so that you could withdraw $100 per year for three
years and at the end of the third year, get back your
original investment?”
Before we can answer this question, we need to know what the required rate of return is. How do we
determine this? It is a product of the perceived risk of not receiving the payments and the risk free rate
of return. The risk free rate of return over time has proven to generally be 3% plus the rate of inflation).
We continue to assume risk free cash flows (maybe Federal treasury bills). Oh, by the way, interest is
always stated on an annual basis. To continue, we will use the 10% interest rate (required rate of return).
Now we will turn the question into three separate questions as there are three uneven cash flows
involved.
Q1
How much do you need to put in the bank so that at the end of one year you can draw out $100.
Bank pays interest annually at 10%.
Q2 How much do you need to put in the bank so that at the end of two years you can draw out $100.
Bank pays interest annually at 10%.
Q3 How much do you need to put in the bank so that at the end of three years you can draw out $100.
Bank pays interest annually at 10%.
The formula to determine how much you need to deposit in order to receive a certain sum is:
Present Value =Future Value/(1+i)n
The Present Value is the amount you need to deposit. The Future Value is how much it will be worth at
the end of n periods.
(We use n to represent periods as opposed to years in the formula in order to account for possible
differences in compounding. For instance, if the bank compounded twice a year, then the above formula
would be:
4
Amount to deposit = 100 X (1+.05)2 = 90.703
The lower amount is needed because the interest for the first six months earns interest itself during the
second six months.)
In our case then, the formula for the first year is:
Amount to deposit = 100/(1+.10)1 = 90.909
Now back to our problem.
We have calculated that we need to deposit $90.91 to be able to withdraw $100 in one year with
the bank paying interest at 10% compounded annually. How much do we need to deposit so that we can
withdraw $100 in two years, bank pays interest at 10% compounded annually?
Q1
PV = 100 /(1.10)2
= 100/1.21
= $82.645
For the third year,
Q2
PV = 100/(1.10)3
= 100/(1.331)
= $75.132.
Now let us put the three answers together:
Q3
Year 1 = 90.909
Year 2 = 82.645
Year 3 = 75.131
248.685
So we have determined that if you put $248.68 in a bank paying interest at 10%, compounded annually,
you will be able to withdraw $100 for each of the next three years, starting in one year, and at the end of
the three years, you will have exactly nothing left in the bank. Let’s prove it.
Deposit $248.68 in the bank. At the end of the first year you have earned interest at 10% or
$24.87. So you now have $273.55 (248.68+24.87) in the bank. You draw out $100. Your balance is
now 173.55. This is left in the bank for one year and earns interest at 10%. For the second year you
earn interest of $17.36. At the end of the second year, just before the second withdrawal, you have
$190.91 (173.55+17.36) in the bank. You withdraw $100 leaving you $90.91 in the bank. This earns
9.09 for the third year. At the end of the third year, just before the final withdrawal you have exactly
$100 in the bank. After you make your final withdrawal, you will have nothing left.
Looked at another way
interest .10 X 248.68 =
24.87
.10 X 173.55 =
17.36 .10 X 90.91 =
9.09
Deposit $248.68----------------------------------|---------------------------------|---------------------------------|
Year 1 248.68
Year 2
173.55
Year 2
90.91
Interest
24.87
Interest
17.36
Interest
9.09
273.56
190.91
100.00
Withdrawal 100.00
Withdrawal 100.00
Withdrawal 100.00
Bal end of yr. 173.55
Bal end of yr.
90.91
Bal end of yr.
-0-
5
************************************************************************************
Another way of looking at this is through an amortization schedule (actually a reverse amortization schedule)
Interest
Earned
Principal
Withdrawal
Balance
Y0 Beg Bal
$248.68
Y1
24.87
100.00 173.55
Y2
17.36
100.00 90.91
Y3
9.09
100.00
-0************************************************************************************
Present value tables. The generic results of the formula, 1/(1+i)n can be found in any present value table.
The best online table I have found is at http://www.ebs.hw.ac.uk/MBA/studentservice/05/FITA101.HTML.
This is a site of the Edinburgh Business School. I have also included one in Appendix 1. So if you wanted
to find the present value of $100, in one year, 10% interest, you go to the 10% column, go to row 1 (for one
year) and you find the value .909. You multiply that number times the future value you want to receive,
$100, and that gets you the present value, or the amount you need to deposit today to have the $100 in one
year.
Annuities. Because all the payments are the same, $100 in our example, you do not need to do each year
separately. You can just add up the present values (.9091+ .8624 + .7513) and multiply your result (2.487)
times the payment (100). (248.70). A series of payments which is the same is termed an annuity.
Underneath the present value table on your sheet, you will see the phrase “Present Value of an Ordinary
Annuity of $1". This table is a running subtotal of the present values. So line two in the annuity table is
simply line one and two of the present value table. To solve our problem we can use the annuity table since
all the payments are the same. We go to the 10% column and then go down to row 3. The figure there is
2.487. We multiply the 2.487 times the $100 payment and we get $248.70. (We are off two cents due to
rounding). I have included a present value of annuities table in Appendix 1.
Again, Appendix 4 has a lot more information and problems concerning present values.
To review, again
If the cash flow of an investment is known for certain, the only thing that can rationally change the
value of the investment is a change in the required interest rate. (The use of the word rationally is
purposeful-we will address irrational behavior of markets later in the module).
(I am emphasizing this so much now because later its truth becomes a little masked and people want to
abandon it for other more “truer truths”. I am consistently amazed that students tell me the value of a stock
is the cash flows plus what they expect to sell the stock for. They do not comprehend that the only thing
that can change the value (what they expect to sell the stock for) is real or estimated changes in the cash
flows. Please consider this last carefully before you proceed.)
The previous section was a very quick review of present value concepts. If you are not comfortable with the
formulas or the calculations, or the reasoning behind any of this, please go to Appendix 4 for a review of
present value concepts.
Section 2. Valuation under uncertainty
Suppose you saw the following ad in your Sunday morning paper:
For Sale Apartment Building
6
30 Units
Average Rent was $600 per unit, per month for the year 2000
2 years old
Price __________
Upon investigation you found that it would require little or no work on your part. There was a rental agency
which would keep the books, rent apartments, do evictions and other administrative tasks for 10% of the
rent. Your investigation showed that the apartments stayed about 90% occupied and that occupancy rate
was likely to continue. Additionally, the rental agency told you that you can expect rents to increase about
5% per year for the next three years (2001, 2002, 2003) because the building is new. After that, rent will
raise at the inflation rate, currently 2% per year. The repairs and maintenance costs are about $800 per
month for the first three years and then will rise with the level of inflation along with the other expenses.
You can expect the building to last for 30 years. At the end of 30 years the building will be worth about
what it will cost to demolish it. The land should be worth about $100,000 based on your estimates of
inflation and the real estate prices between now and then.
Assume it is Jan 1, 2001- what is the price you would pay?
How would you value such a potential investment? We are no longer in the arena of the certain. We start
with the assumption that you want an apartment building. (Remember Andrew Carnegie’s admonishment
that when one hears that elephants are on sale two for the quarter, that this is a deal only if you are in the
market for elephants and have a quarter. (A paraphrased quote).
Note that there is no price mentioned in the above ad. That is the way it should be.
Consideration #2. In all investments, you must first determine the value before you consider the price!
We must now make some estimations as to the cash flows possible from the apartment building. We will
begin by building an income statement (a P & L).
Step 1. Estimate the Cash Flows
We must estimate the revenues as best we can. All estimations of revenues and expenses should be
as exact as possible. There is always a general tendency to be conservative in estimations of the revenue and
expenses. This conservatism can cost you many a good deal as you do not know when you get to the end
the impact of each of your “conservative” estimations. Adjustments for softness or “looseness” in the
estimations should be made all at once, not as you do each individual part of the consideration of the
investment.
If we cannot get a handle on the revenues or the significant expenses associated with an investment,
we must walk away!
One thing you must constantly guard against is becoming emotionally involved with an investment. As we
spend more and more time considering a possible investment, we tend to become less objective and more on
the side of making the investment. This is a sure road to ruin over the long run. Some of the greatest
money made in investing is that saved by not making an investment.
or in the words of a forgotten old sage:
Consideration #3 Never love something that cannot love you back.
We estimate the revenues for the first three years as follows:
2001 = 1.05 X (.9 X 30 X 600 X 12) = 204,120
2002 = 1.05 X 204,120
= 214,326
7
2003 = 1.05 X 214,326
= 225,042
(2001 is the occupancy rate (.9) times the number of units (30) times the rent per unit (600) times the
number of months (12). This total is multiplied times 1.05 which will automatically include the 5% rent
increase for the year. The other two years are simply calculated using the prior year times 105%).
Revenues after this are simply increased at the 2% inflation rate.
We estimate the expenses as follows:
The rental agency fee will be 10% of revenues (per the ad)
The repairs and maintenance for each of the first three years will be $9,600. (800 X 12).
We will also get a tax deduction for the depreciation we will be allowed to deduct each year from our tax
return. This amount is, of course, based on the selling price which is what we are attempting to determine.
At this point, it is best to either ignore that number or to use a crude estimate for the first pass and then
refine the estimate when we begin to zero in on an appropriate purchase price. For our present calculations,
we will ignore the depreciation.
So for the first three years we now have:
Rents
Expenses
Management fee (10%)
Repairs & Maintenance
Total Expenses
Net Cash Flow
2001
204,120
2002
214,326
2003
225,042
20,412
9,600
30,012
174,108
21,433
9,600
31,033
183,293
22,504
9,600
32,104
192,938
Step #2. Determine the Required Rate of Return
Now that we have some sort of a handle on the investments possible outcomes-revenues and
expenses, we must determine how much of a return we will require from this investment. This
determination is a result of considering:
Amount of work we will be required to do in connection with the investment,
How sure you are of the projections you have made,
The return of risk-free investments,
Your tolerance for risk (sleep at night cost)
Opportunity costs,
Inflation factors
What percentage of your capital this investment will tie up
And so on, and so on
If one attempted to precisely calculate each of the above, one would probably find oneself in
mathematical gridlock which would never give an answer in time for an investment. It is easier to
categorize investment into Low Risk, Medium Risk, and High Risk. With the definition of risk being your
objective and subjective consideration of all the forces at work, such as those listed above. So, given our
categorization, we assign Required Rates of Return for each category. This is not a trivial process. It does
require a lot of estimations and some guesswork, but in it lies the secret to your wealth, so attack the
8
problem with due consideration. It is possible that you could build a model which would give numbers and
weightings to each of the above factors, but I am not sure that such would not be a product of “estimates of
estimates” and one which would give us unmerited comfort because it generated an “answer”
mathematically. Instead, we consider the relevant variables and our subjective weighting of each and decide
for us:
Low Risk must return at least 10%
Medium Risk must return at least 16%
High Risk must return at least 24%.
The above are mine. Yours will be different because different things are important to you.
These are on our continuum also, meaning that they simply define some parameters of our playing
field.
|---------------------|------------------------------|-------------------------------------|--------------------------5%
10%
15%
24%
60%
Gov
Low
Medium
High
Higher
Sec
Risk
Risk
Risk
Risk
( Pure
(Gambling?)
Once you look at these, you might be tempted to say that it is foolish to invest in anything other than
the high risk because that will give you the highest return. That is not true. You value opportunities using a
discount rate of 24% because you suspect that there is a strong chance that many of your estimates are off.
Thus the high discount rate is meant to cover a lot of possible shortfalls in our projections.1
For the apartment building, we have decided that the appropriate return would be 20%.
Step 3. Valuing the Project
By applying the present value techniques we have learned, we find that the present value of these cash flows
is found by going to the present value table in Appendix 1 or at
(http://www.ebs.hw.ac.uk/MBA/studentservice/05/FITA101.HTML), and getting the figures for each year
at 20% (.8333, .6944, .5787).
The present value of the first three cash flows, then is:
Net Cash Flow
Present value factor
Present value
174,108
.8333
145,084
183,293
192,938
.6944
.5787
127,279
111,653
These total to $384,016.
What does the above figure represent?
It represents what we would pay for the building to earn 20% if the building were going to last
exactly three years and then disappear. Put another way, this is the amount you would need to put in the
1
Obviously there could also be surprises on the positive side also, but you will find that in investing
situations, most surprises are negative in their impact.
9
bank today, bank paying interest at 20% annually, if you wanted to draw out $174,108 in one year,
$183,293 in two years, $192,938 in three years and have a zero balance in the account at the end of the third
year.
Note that we are assuming all cash flows happen at the end of the year. Practically,
of course, this does not happen-cash is going in and out throughout the year. The
assumption of year end cash flow is necessary to make the calculations. It actually
causes very little disturbance to the answers. If we are using a 20% discount and
the cash flows happen evenly during the year, the true discount rate would be a bit
higher.
Terminal Value
Obviously by applying the present value factors to the first three years cash flows, we have
addressed the beginnings of the valuation. We have another 27 years of cash flow to value. We value the
remaining 27 years using the processes developed in the first part of this module.
First we must determine our required rate of return. This will be a product of current interest rates,
inflation rates and how sure we are of our projections. So if we generally are able to earn 10% on our
investments, but we feel that this investment has some elements of risk, both in the future of the apartment
business and our estimations of the revenues and expenses, maybe we will require a 20% rate of return.
Note that I have assumed you are just a passive investor. To the extent that you will need
to put in time for this investment, you should adjust your cash flow to reflect payments to
yourself.
Now we can construct an annuity to determine the value of the last twenty seven years of the property.
First, we know the cash flow for the third year is $192,938. We know that this number will grow at 2%, the
rate of inflation, until the building is demolished in 27 years. If inflation is going to provide us with 2% per
year, then the amount the investment needs to return to us drops to 18%. (Consider that last sentence very
carefully, it is true and your understanding of it is crucial to the rest of the arguments).
So we now proceed with the question
How much do we need to put in the bank so that we can draw out
$192,938 per year for the next 27 years if the bank pays interest at
18%?
Go to the annuity table (Appendix 1) and look up 27 years at 18%. The figure you find is 5.4919. Now take
this number times the 192,938 and you get 1,059,596.20. This is the value of the cash receipts for 27 years
at 18%.
Note that this is the value three years from now.
Huh? Well you have the cash flows and their present values for each of the next three years,
Net Cash Flow
Present value factor
Present value
174,108
.8333
145,084
183,293
192,938
.6944
.5787
127,279
111,653
total
384.016
the value we calculated above $1,059,596 is the present value of the remaining 27 cash flows which start in
Year 4. Therefore this number is the present value at the end of year three! To make it the present value
10
now, we must go to the PV tables, 3 years , 20%, and we find the factor .5787. We multiply this times the
1,059,596 and get 613,188.
A first pass value of the building to us is, then
Present Value of first three years cash flow
Present Value of remaining 27 years
$384,016
613,188
$997,204
If our estimations as to the expenses and revenues are right, then should we get the building for less than
$997,204, we would be earning more than 20%. To the extent we pay more than the 997,204, we would be
earning less than 20%.
It is possible to figure out exactly what rate of return we are earning if we buy it
for a certain price. This calculation is known as the Internal Rate of Return. The
calculation is made using trial and error. For now, you should look this up in a
text book, eventually, it will be Appendix D.
This type of analysis, of course lends itself to a spreadsheet program of some sort. I have included in
Appendix B the problem done in such a manner. Also, included in the appendix is the spreadsheet with the
formulas exhibited in place of the numbers so you can check your/my logic.
You will note in the spreadsheet that I have a place for salvage value. This is the amount you could sell the
investment for when you are done with it. It is usually simply a guess. You would multiply this amount by
the present value factor for the number of years it would be before you sold and at the required rate of return.
Because receipt of the salvage value is usually so far away, the present value factor is very small and its
impact is negligible. In the present case, if there was a salvage value it would be multiplied times .0042
thirty years at 20%).
Now, before we go on, let’s check your understanding- do the following problem:
You have seen an ad for a used Mercedes in the Athens Messenger. The car is
for sale for $25,000. You believe you could make a buck by renting the car out.
You figure you could rent the car to the semi-rich on a daily basis for three years.
You think you could rent the car for $100 per day for the first year and $80 per
day the second year and $60 per day for the third year. You expect that the car
will be rented out about 70% of the time for each year. At the end of the third
year, you figure you can sell the car for $20,000. You estimate that the repairs
and maintenance on the car will be about $1,000 for the first year, $2,000 the
second year and $3,000 the third year. Licenses and fees will run $2,000 per year
for all three years. You will pay a rental company 10% of the gross rents you
receive each year to take care of all the paper work and the renting of the car to
the students. How much can you pay for the car today and make 20% on your
investment?
11
The answer is worked for you in Appendix 3
Another one
You are planning on buying a bus to rent out. You figure you can rent it out for $300 per day for the
first three years and then the rent will raise by 2% per year for seven more years. You plan to sell the
bus at the end of the ten years for $20,000. Expenses of operation are: pay to rental agent, 20% of
gross rents, repairs and maintenance, $1,000 per year and insurance, $1,200 per year. The R&M
expense and the insurance will remain the same for the next three years and then rise at the inflation
rate. You think the bus will be rented out 80% of the time. How much can you pay for the bus if you
want to earn 20%?
The answer is worked for you in Appendix 3
Section 3. Valuation of an Equity Investment
Biases Revealed.
As this is being written in April of 2001, markets have begun to return to rationality. This
makes this section easier to write and, hopefully, easier for you to understand. We have had numerous
years of what I consider irrational valuations of stocks. I need to say these things because I am going
to present what I believe is the only truly rational method to evaluate the shares of a company. Over
the long run, this method will make you money and will allow you to sleep at night. I play it
extremely aggressively in the money I manage. By extremely aggressively, I mean that I play both the
short side and the long side of the market.
Let’s go back to Universal Rule #1.
The Financial Worth of anything is equal to
the present value of its future cash flows.
From this rule comes the axiom that a share of stock is equal to the present value of its future
cash flows. Please note that there is a period at the end of that sentence. This axiom books no
“except”, “but” or other qualification, adjustment or modification!
What is a cash flow, EPS or Dividend?
We need to digress a bit and define what we mean by cash flow. Many very good finance texts
define the value of a security as equal to the present value of its dividends. In my opinion, this makes
the valuation process much harder than it needs to be. One must not only forecast earnings, but
forecast a dividend policy. We will use Earnings Per Share (EPS) as a surrogate for cash flow 2. We
2
We will assume that noncash charges such as depreciation are surrogates for cash outflows for
replacement of equipment and such. This argument does not work for amortization and probably that
12
believe this is a superior valuation method. We also tend to favor companies that are not yet paying
dividends. Why? First, if we get dividends, we must pay tax on them before reinvesting. Thus a
company who pays us a $100 dividend will cause us to pay the government approximately $30 of that
dividend in taxes. Thus we only have $70 to reinvest. If the company doesn’t pay the dividend and
invests the money instead, our full $100 is put to work for us. The argument is frequently made that a
bird in the hand is worth two in the bush-how do we know the company will ever give us the $100 if it
reinvests it itself. Our rejoinder to that is that we never ever invest in managements we don’t trust!
Our second argument for favoring companies that do not pay dividends is that they are probably
reinvesting my money at a rate higher than I could get. The company is reinvesting in itself or in
areas that will return ultimately more than I could do individually (remember I am working with after
tax money if I get a dividend.
Cynical Note. We are not so naive as to believe the textbook line that
Corporate Management’s primary goal is to increase shareholder
Wealth. Human beings are much more complex than that and do not seem
to be naturally altruistic. If we were to generalize, we have found that
the corporate managers goal seems generally to be to increase the corporate
manager wealth and power. There are exceptions. However, when we analyze a
company, we spend a lot of time analyzing the management and trying to
see how aligned their goals might be with making us money. Options are
promoted as a tool to align management goals with those of shareholders.
That argument has some problems because the risk factors and the time frame
of one holding expirable options is different than that of a shareholder.
Note on the use of surrogates: When one can’t measure something directly, but can measure
something that tracks something the hard to measure, then the thing that can be measured is called a
proxy or surrogate for the thing that can’t be measured or is extremely difficult to measure. For
instance, we are using EPS as a proxy for cash flow per share in this section. Warren Buffet3, Peter
Lynch and other notable investors use the fact that a company is buying back its own shares in the
market as a proxy or surrogate for shareholder friendly management. One must be very careful of the
use of surrogates where they are not applicable. For instance, it has been common for analysts to talk
about such things as “hits per page” or “price to sales” as if those terms had real meaning in the
assessment of a companies earnings. Cynically, it has been my experience that when such
substitutions are made, one finds little or no earnings in the company. Growth in sales or clicks or
anything means nothing unless such growth can be directly tied to growth in earnings per share.
Step 1 in the valuation
How much would you pay for the common stock of a company which is
earning $3,000,000 per year?
number should be added back to earnings. We do not do that for the purposes of this learning module,
as we assume this number for most companies is immaterial.
3
Warren Buffet is Chairman of Berkshire Hathaway. He is the second wealthiest person, as of this
writing, after Bill Gates, in the United States. He has made his money basically by investing in
companies. A study of his investment style reveals a methodology very similar to that outlined in this
module.
13
Obviously we need more information. Even if the company has discovered a cure for cancer and
earnings will grow at 1,000% for the next ten years, unless you are thinking about buying the whole
company, a move which we will discuss in the next section, you need to know at a minimum how
many shares are outstanding.
So let’s say the company we are looking at has 1,000,000 shares outstanding. What else do
you need to know? What are the projected earnings in the future (we are abandoning our cure for
cancer for a more realistic company!)
We are dealing in this section with the objective valuation of a security. However that
valuation is based on numbers which are estimates. To the extent that you are better than anyone else
at coming up with the estimates, you will be better than anybody else at making money from the
security. (Or avoiding losing money by passing on the investment.) Warren Buffet never invested in
anything he did not understand. He totally avoided the tech area for this reason. Understanding a
business, is of course a perquisite to being able to forecast the future of that business. Consider that as
you look for investment opportunities. You will probably be best served to look at companies in an
industry you understand.
The art of estimation of earnings is really beyond the charge of this module. I steer the student
toward such works as One Up On Wall Street, by Peter Lynch as an excellent starting point for such
an investigation. There are many services on the Internet which will provide you with earnings
estimates. (Putting “earning estimates” in Yahoo Search came with 3,170 web sites!) You must
investigate each of these to determine their reliability. Or, better yet, you should come up with your
own estimations and compare that with the published sources. Then, and this is the critical step,
reconcile the differences between your estimates and those of the “experts”.
So let’s assume that you have come up with the following estimates for the next three years:
20x1
20x2
20x3
3,500,000
4,400,000
5,000,000
we now break this into EPS by dividing each of the numbers by the shares outstanding4, so we have:
20x1
20x2
20x3
3.50
4.40
5.00.
Next we need to estimate what the company will earn for eternity starting in year 4. While this seems
like a daunting task, it is really not if we start with year 3 earnings.
Remember when we did:
How much would you for annual payments of $100 per year, starting in one year, and which
would continue forever?
Cash flow
The answer is in the formula:
Required Rate of Return.
Combined with the way we handled the last 27 years of the apartment building (Rate of Return Inflation Rate).
4
Actually we would be using the weighted average number of shares outstanding. For most companies,
the difference between the weighted average and the shares outstanding at year end is insignificant.
14
Before we can do the calculations we need to do, we must determine our required rate of return. This
is a product of two considerations:
How sure are you of your estimations?
What are the returns available to you in other investment opportunities?
For the first questions, we will raise our required rate of return if we think our estimations may be soft.
This gives us a margin for error just as we had in the apartment building estimations.
The second question is a bit trickier and must be considered carefully. When you are considering and
investment, you must compare its potential return will all other alternatives available to you. This
means that if you are considering investing in Ford Motor Car Company, you evaluate that estimated
return will all other stocks available to invest in, all other real estate investment available, the federally
insured rate that the local bank will pay on savings accounts, the possible return by betting it all on a
football game this weekend. The probably of success and related probable return of each of these
actions must be weighted before the investment decision is made. Also one must weigh how the
investment will affect his or her job or sleep. And on and on.
Lets assume that we have decided that a 20% rate of return is what we require for this particular
investment. Now what is the rate of growth we can expect from our possible investment target after
the third year? A good historical average would be between six and ten percent. Let’s say we are
comfortable with 7%. That means we think the company can generate a 7% growth rate from year 4
to the foreseeable future. This means that the company is going to internally generate 7% of our
required return each year. So the terminal value of the stock is the EPS for year 20.3/ (required rate of
return - growth rate of company).
Here = $5.00 / (.20-.07)
= 38.46
remember that figure is at the end of year 3. We will have to now figure its present valueSo the value of our stock is:
Year 1
= .8330 X 3.50 = $2.92
Year 2
= .6944 X 4.40 = 3.06
Year 3
= .5787 X 5.00 = 2.89
Term Value
Year 3 = .5787 X 38.46 = 22.26
Value of Stock to us
$21.13
15
Let’s retest the concepts: here are 5 companies with their earnings projections and the required rate of
return. Please value each of the companies: (I have also included columns for items we will discuss in
Appendix 5, the P/E and the PEG ratios)
Earnings
Estimated
Required
Last 12
Est Earnings
Growth
Rate
months
P/E
Year 1 Year 2
Year 3
Yr 3 on
of Return PEG
IBM
4.44
4.90
5.49
6.20
10%
JS
2.24
2.29
3.32
3.64
8.56
CIEN
0.42
0.73
1.16
1.51
10
CROS
3.29
3.85
4.32
4.97
9.50
PALM
0.08
0.03
0.04
0.05
12
Value these companies based on the above. My valuations are included in Appendix 3.
Acquisition Candidate
Realizing that as many as 60% of the mergers and acquisitions of companies (need cite here)
end in failure, we enter this area of valuation with much trepidation. We are going to assume that the
purchase of a business for strategic reasons has already been decided upon. In the next section we will
deal with the purchase of a company simply for investment purposes. We will assume that you have
done an appropriate impact analysis of the merger/acquisition and know as well as possible the
financial impact of the proposed alignment.
Step 1. Determine the financial impact of the aquistion.