I gave this talk in February 1994. I thought it is still useful...
Assuming that the $100 interest income that you take out every year is not subject to any form of tax, you are effectively getting a return of 10% every year for five years out of the $1,000 you put in; do not forget, though, you are also getting your $1,000 back at the end of the period.
Whatever cash coming in less whatever cash going out over a fixed period is the NET CASH FLOW for the period which, for planning purposes, is usually one year. Though not exactly correct, net cash flows can also be derived as follows:
Less : Loan repayment
Equals : Net cash flow
If you prefer to leave income taxes out (which is not unreasonable since government can change tax rates and incentives from time to time), the IRR you work out is that of a before-tax one. Next is your investment horizon. It is of course your intention to make your business a going concern. There is really no question of your winding it up after a predetermined period. But let’s be realistic. If you were investing in a snooker parlour, a business where every Tom, Dick and Harry can go into, you would certainly want to make your money fast and be happy to call it quits after just a couple of years. However, if you venture into a steel mill, you are unlikely able to see any profit for the first three years. You would also hope that the state-of-the-art plant you invest in will probably remain efficient for the next ten to fifteen years. Ditto if you go into large scale cultivation of oil palms which take about three years to mature and a couple more years to reach their peak yields. For the steel mill or the palm oil business, your financial people would have to project a 20-30 year cash flow table to plan your capital needs, especially during the gestation period, and be comfortable with the level of cash flows once the project is on stream. From this cash flow, you can calculate the IRR, and see what its NPV is – if you already have a hurdle rate in mind – and estimate the payback period. You would obviously want a high IRR, a robust positive NPV and a payback period that is as short as possible. For very high risk undertakings, such as oil and gas explorations, anything less than 40% over the field life might not be tenable to one; however, most people are happy if see IRRs of 15% after-tax or so.
__________
$5.2 million
$2.31 million
$2.60 million
I have for the sake of clarity illustrated the concept with a simple example. There is really more to it than meets the eye. For instance, your project may take a year or two to complete. You may not have to come up with all capital you need to put up in one go. To be consistent, the installments have also to be discounted according to the period they are put in to conform to this “time-value” concept of money.
Internal
Rate of Return (IRR) is a term that is often heard in executive suites and
boardrooms. The general perception is that the mathematics involved is too
complex or forbidding and the task should best be left to one of those
bright-eyed MBAs in the office. One result is that many decision-makers do not
quite go beyond the figure to form conclusions, as if IRRs are absolute indicators
of financial viability in project investments. What does it really mean?
The
concept is actually quite simple. And IRR has many limitations.
Let
me try to explain it in the plainest manner.
Say,
you have $1,000 and are looking for a good place to grow your money. The
easiest and most risk-free way is to put the money in a neighbourhood bank to
earn interest. Banks used to pay reasonable interests on deposits, but not now.
Many are paying close to zero these days! But for illustration sake, let’s
assume a certain Goodie Bank is prepared to pay you an interest rate of 10% per
annum. After one year, your balance should show $1,100. Let’s assume this
scenario: (a) at the end of the year, you decided to withdraw the $100 interest
you had earned to spend and started the new year with a balance of $1,000 in
your savings book again, (b) the bank gives you the same interest rate for the
next four years, and (c) you also repeat the process of withdrawing $100 at the
end of every year for the next four years, and (d) at the end of the fifth
year, you close the account and take back your $1,000 together with the
interest of $100 that is due to you.
Beginning
Balance ($)
|
Ending Balance ($)
|
Withdrawal
($)
|
|
Year
1
|
1,000
|
1,100
|
100
|
Year
2
|
1,000
|
1,100
|
100
|
Year
3
|
1,000
|
1,100
|
100
|
Year
4
|
1,000
|
1,100
|
100
|
Year
5
|
1,000
|
1,100
|
1,100
|
Assuming that the $100 interest income that you take out every year is not subject to any form of tax, you are effectively getting a return of 10% every year for five years out of the $1,000 you put in; do not forget, though, you are also getting your $1,000 back at the end of the period.
This
10% is an IRR in its simplest form.
Is the 10% return good for you? Foremost in your mind, I suppose, is the question
of inflation. True, the $1,000 you get back five years later does not have the
same purchasing power as it now has. Even the $100 you take out at the end of
every year also seems to be getting “smaller and smaller”. In a real life
situation, bank interest rates also fluctuate from time to time. In the 1970s
and 1980s, more-than-10%-a-year rates were the order of the day; now you are
lucky to get 1 or 2% a year!
We
are now enjoying a period of relatively low inflation, if the people compiling
the CPIs are to be believed. The rate obviously also does not stay static. In
the above example, with adjustment for inflation, the real IRR to your $1,000 investment
for five years is much less than 10%.
In
the corporate world, IRR is commonly used, sometimes very indiscriminately so, to
measure the viability of a project. To be meaningful, it has to be expressed in
a manner such as this: The project yields an IRR of 21.3% over an 8-year period
– meaning, two elements must be present: a percentage and a time frame. There
must also be other qualifications. But let us not get carried away with too
many technicalities first.
IRR
can be defined as the expected average yearly rate of return you will get for
your investment over a given period of time, taking into account that a dollar
you receive tomorrow is different in value from the dollar you receive today.
Associated
with IRR is the term “discounted cash flow”. Let me try to illustrate with an
example.
Let’s
say someone comes to you with a seemingly interesting proposal: A project that
calls for a total investment of $10 million:
Fixed Assets $6 million
Working Capital $4 million
Unless
you do not believe in bank borrowings, you normally would go to a bank to raise
a loan to help finance part of the capital requirement for this project. (Debt
actually improves your Return on Equity – provided the cost of your debt is
lower than the Return on Total Assets; mathematically expressed, ROE = RTA +
D/E [RTA – CoD].) You will also want suppliers to extend credit to your
purchases of supplies, raw materials, services etc to reduce your working
capital needs. However, if you borrow from banks, you will have to make
provisions for the payment of interests and repayment of principal on a regular
basis. Mind you, the banks are not a very forgiving lot. If you make a profit,
you also have to pay taxes. You have also to set aside a good sum every year to
“rejuvenate” your fixed assets. In accounting jargon, you say this is a “depreciation”
or “amortization” provision. There is actually no cash flowing in and out of
this provision, though.
Whatever cash coming in less whatever cash going out over a fixed period is the NET CASH FLOW for the period which, for planning purposes, is usually one year. Though not exactly correct, net cash flows can also be derived as follows:
Profit from operations
Add :
DepreciationLess : Loan repayment
Equals : Net cash flow
If you prefer to leave income taxes out (which is not unreasonable since government can change tax rates and incentives from time to time), the IRR you work out is that of a before-tax one. Next is your investment horizon. It is of course your intention to make your business a going concern. There is really no question of your winding it up after a predetermined period. But let’s be realistic. If you were investing in a snooker parlour, a business where every Tom, Dick and Harry can go into, you would certainly want to make your money fast and be happy to call it quits after just a couple of years. However, if you venture into a steel mill, you are unlikely able to see any profit for the first three years. You would also hope that the state-of-the-art plant you invest in will probably remain efficient for the next ten to fifteen years. Ditto if you go into large scale cultivation of oil palms which take about three years to mature and a couple more years to reach their peak yields. For the steel mill or the palm oil business, your financial people would have to project a 20-30 year cash flow table to plan your capital needs, especially during the gestation period, and be comfortable with the level of cash flows once the project is on stream. From this cash flow, you can calculate the IRR, and see what its NPV is – if you already have a hurdle rate in mind – and estimate the payback period. You would obviously want a high IRR, a robust positive NPV and a payback period that is as short as possible. For very high risk undertakings, such as oil and gas explorations, anything less than 40% over the field life might not be tenable to one; however, most people are happy if see IRRs of 15% after-tax or so.
Let’s
go back to the $10 million project. Let’s assume that you plan for a 12-year
investment horizon and your accountant suggests that you finance the project
with an equity capital, viz., money from your own pocket, of $7 million and
raise the rest from a supportive bank. In corporate finance, you say you are
going for a 30-70 debt-to-equity ratio. Your accountant lays out the following
net cash flow projection for you:
End
of Year
|
Surplus/Deficit)
$ million
|
1
|
(1.5)
|
2
|
0.2
|
3
|
1.5
|
4
|
1.5
|
5
|
1.5
|
6
|
1.5
|
7
|
2.9
|
8
|
2.0
|
9
|
2.0
|
10
|
2.0
|
11
|
2.0
|
12
|
2.0
|
You
will want to attach some value to your fixed assets at the end of your investment
horizon. Let’s say you reckon they can fetch 20% of their original cost at the
end of the day. You must also not forget that you have also had some net
working capital in the business by then. We call these the residual or terminal
values:
Fixed Assets, 20% of M$6 million $1.2 million
Working Capital $4.0 million__________
$5.2 million
Now
let me introduce the concept of “discounting”. $1.00 put in a bank today will
become $1.10 if the bank pays an interest of 10% per annum. Conversely, $1.00
received a year from now is only worth $1.00/1.10 or about $0.91 today. If you
apply this principle to “bring” all the future yearly net cash flows to their
“present” value, you will see the following:
Period
|
Net Cash Flow
$ million
|
“Present” Value
$ million
|
1
|
(0.5)
|
-1.5/1.1
=-1.36
|
2
|
0.2
|
0.2/(1.1x1.1)
or 0.2/(1.1)2
=0.17
|
3
|
1.5
|
1.5/(1.1x1.1x1.1)
or 1.5/(1.1)3
=1.13
|
4
|
1.5
|
Repeat
Process
|
5
|
1.5
|
Ditto
|
6
|
1.5
|
Ditto
|
7
|
2.0
|
Ditto
|
8
|
2.0
|
Ditto
|
9
|
2.0
|
Ditto
|
10
|
2.0
|
2.0/(1.1)10
=0.77
|
11
|
2.0
|
2.0/(1.1)11
=0.70
|
12
|
2.0
|
2.0/(1.1)12
=0.64
|
You
will find that the factor used is simply:
1/(1.1)n
or (1.1)-n where
n is the period in question.
The
process of bringing these future yearly net cash flows to the present time is
called “discounting”. If you sum up the present values of these yearly cash
flows for the twelve years, you will get:
$7.65 million.
By
the same token, the terminal or residual value of $5.2 million has also to be
discounted by dividing it with a factor of (1.1)12, which gives
$1.66 million
This
figure has also to be included, making the Net Present Value a total of
$9.31 million.
Compared
this total with the amount of equity capital you propose to put in, which is $7
million, you see a surplus of
$2.31 million
Obviously,
the project yields an averagely more than 10% per year.
Now,
if you repeat the exercise by using a factor of 1.2, i.e., you discount the
future yearly cash flows by 20%, you will find that the sum of these two
present values, i.e.,
$4.40 million
is
not sufficient to cover the $7 million you propose to put in as equity
capital. You have a negative NET PRESENT VALUE situation of:
$2.60 million
An
obvious conclusion from the last exercise is that your investment cannot give
you an average yearly rate of return of 20%. If that is your expectation, which
may be your “hurdle” rate, then the project is, on a prima facie basis, a NO-GO
for you.
The
actual average yearly rate of return must therefore be somewhere between 10%
and 20%. The rate which gives you a net present value of ZERO, i.e., the
summation of all the cash flows – both in and out – “discounted” appropriately,
is the internal rate of return of your investment in the project. You can try
12%, 14%, 15.5%, so on and so forth. But the work is simply too laborious.
There are ready tables in financial management textbooks to help you with the
discounting, but they normally come in whole numbers, nothing fractional ones
like 1.5%. For those who are more mathematically inclined, you can use graphs
to determine the rate. However, with the advent of Excel, all you need is to
type =IRR(Cell A:Cell Z) and out comes the answer! The internal rate of return
of this project over 12 years based on a debt-to-equity of 30-70 is
13.7%
I have for the sake of clarity illustrated the concept with a simple example. There is really more to it than meets the eye. For instance, your project may take a year or two to complete. You may not have to come up with all capital you need to put up in one go. To be consistent, the installments have also to be discounted according to the period they are put in to conform to this “time-value” concept of money.
The
mechanics of working out IRRs is really a figure crunching exercise. Your
assumptions must be able to live up to scrutiny; otherwise, it is simply a
garbage-in-garbage-out exercise. Projects done devoid of business understanding
and entrepreneurial foresights are not worth the paper on which they are
written on. However, it has also to be accepted that no one can really foretell
what will become of things in the next three to five years, let alone twelve to
fifteen years! We can only rely on prevailing knowledge and sentiments to
project prices and costs. How many cash flow projections have lived up to their
authors’ forecasts? Few really! You may have the capacity, but would you be
able to achieve the level of volume objectives you have in mind for the next so
many years? Can you predict what your competitors will do? What about the
impact of currency fluctuations? Can duties and taxes remain static for the
next five to ten years? Your bank may revise its asking rate. Your product can
also become obsolete, so on and so forth.
You
may also decide to sell your business to a listed company which offers a
premium that you cannot rationally refuse. Or you may want to take the business
public yourself. Try taking a look at your work years later, if you know what I
mean!
It
is therefore also quite irrelevant to calculate IRRs to three or four decimal
places.
I
always caution the blind use of this investment appraisal tool. Remember the
rubber glove frenzy in the mid-1980s? So many investors got carried away by a
high, yet seemingly realistic, internal rate of return in the wake of a very
strong demand for rubber gloves. By all account, cost of product was low; analyst
would also tell you this: “You can’t go wrong with this project, IRR is
fantastic. I have also done a sensitivity test. Even if I bring down the price
by 10% and push the cost up by 10%, we still get an IRR of 60%.” Ditto on
people who go into projects based on conventional wisdom or people who embark
on businesses or products the business cycle for which are already well past
the take-off phase. They will surely go wrong. (If everybody is doing
discounted cash flows based on the same set of conventional assumptions, how
can the conclusions be different? What many analysts failed to realize is, once
the “glut” stage is reached, prices can go down by 50% and cost up by 50%, all
within a year or two! No wonder so many always get their fingers burnt.)
In
the world we live in today, IRR as a sacrosanct viability indicator is really
suspect. But IRRs do have their usefulness.
Where of when?
Comparative
analysis is one area where IRR is helpful.
Say
you have three investment options in terms of plant configurations. There are
all subject to the same external and internal environmental variables. For this
illustration, we assume their capital cost is the same - $100,000 – but their
net cash flow estimates are different, and the investments have negligible
residual value at the end of Year 6:
Option A
M$’000
|
Option B
M$’000
|
Option C
M$’000
|
|
Original
investment:
|
100
|
100
|
100
|
Net
cash flow:
|
|||
Year 1
|
40
|
25
|
10
|
Year 2
|
38
|
25
|
30
|
Year 3
|
26
|
25
|
30
|
Year 4
|
18
|
25
|
30
|
Year 5
|
16
|
25
|
30
|
Year 6
|
12
|
25
|
20
|
Total
|
150
|
150
|
150
|
IRR
under the situation can help you to evaluate the three options in a more
objective manner. Their IRRs over a six-year period are as follows:
Option A
|
Option B
|
Option C
|
16.9%
|
13.0%
|
12.1%
|
Although
the original investments are the same for the three options and cash flows over
the six years also all add up to $150,000 in absolute terms, the choice is very
clear.
IRR
is a useful quantitative method to appraise investments, but it is NOT a
be-all-and-end-all one. It should be used in conjunction with a few others.
![\mbox{MIRR}=\sqrt[n]{\frac{FV(\text{positive cash flows, reinvestment rate})}{-PV(\text{negative cash flows, finance rate})}}-1](file:///C:/Users/user/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png)
,
Modified
Internal Rate of Return
Some argue that IRR is flawed. Firstly, it assumes that interim positive
cash flows are being continuously reinvested at the same rate of return that the
project is generating them. This may not be realistic. A more realistic rate,
say the firm’s cost of weighted average cost of capital, should instead be
used. Secondly, cash flows in the initial years are usually negative. To
correct these two, a version called the Modified Internal Rate of Return is
also used. The formula is:
,
For example, if an investment gives the following cash flow projection:
|
Period
|
0
|
1
|
2
|
3
|
4
|
5
|
|
Cash Flow
|
-4,000
|
-1,000
|
3,000
|
3,500
|
3,500
|
4,000
|
then, the “r” from the following IRR formula, will yield 37.5%
To calculate the MIRR, we have to know our financing cost and to assume
our reinvestment rate. Let’s say they are respectively 10% and 12%. The formula
above will give us a rate of 27.5%, which is significantly lower than its IRR
of 37.5%.
But MIRR, like IRR, is also not a be all, end all formula in investment
analyses.
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