Namaskar and welcome to this series of lectures
on Principles of Construction Management and
today we will talk about Economic Decision
Making in Construction Projects, largely concentrating
on ‘time value of money’. What we had
done last time was to understand that in a
construction project, the expenses, as far
as the contractor is concerned, are incurred
throughout the project - may it be in procurement
of material, hiring charges for equipment,
salaries of the people hired and so on. The
payment for those activities is received by
the contractor at different points in time
through running account bills.
This idea that expenses are being incurred
over a period of time and there is revenue
which is generated at different points in
time - this requires us to understand what
is called ‘time value of money’, and that
is what our focus in the discussion today
will be.
So now, to get started, the value of an investment
or project depends upon the amount of cash
flows expected from the project and timing
of these cash flows. This is what we were
trying to address when we said that for a
given project the payment can be made all
at once at the end of the project or in installments
as the project proceeds. What the timing of
these payments, is what determines what is
call the ‘cash flow’.
We must remember that cash flow for one party
and the cash flow for the other party can
be different. When I make a payment to someone,
it is an expense for me. It goes out from
my system, whereas, it becomes a receipt for
the other person who receives that payment.
Continuing the discussion here focuses on
using the concept of time value of money for
a better understanding of decision making
in construction projects.
So, what is ‘time value of money’? The
value of money changes with time, so what
is a hundred rupees today may not be hundred
rupees tomorrow. It would have gained some
money, if there was an interest application.
We are not, in this discussion, including
the concept of inflation at all, where the
value is actually getting eroded on account
of factors which are not governed by this
concept of interest. We are largely concentrating
on the concept of interest. Now, what is the
interest? Interest basically represents the
earning power of money, and, can be looked
upon as a premium paid to compensate the owner
for the foregoing the use of the loaned money.
So if I keep a hundred thousand rupees in
the bank, I get an interest of 3 percent,
4 percent, whatever is the prevailing rate,
because I forego the right to use that money
at that point in time. The bank, however,
gives me 3 percent or 4 percent of an interest
because with that money, it generates more
money by giving out a loan to different investors.
Now, they could charged 7 percent, 8 percent,
or 15 percent, whatever it is, by the bank.
Therefore, there exists a present value and
a future value for any investment. So, we
can talk in terms of present value, or, we
can talk in terms of future value. In the
discussion today, we would largely concentrate
on the concept from the point of view of present
value.
Now, let us look at cash-flow diagrams, which
are basically a visual representation of inflow
and outflow of funds - those that are either
received or spent during the project’s lifetime.
So what we are looking at – let’s say
this as an example - we plot on the x-axis,
which is this line here, time; and plot the
outflow of funds below this line here, and
the inflow of funds above this line. So, what
it is showing is that there is an outflow
of funds that occurs at points 0, 4 and 6,
and,inflow of funds occurs at points 1, 2,
3, 5 and 7 to the extent that the inflow is
2,00,000, 50,000, 3,00,000, 1,00,000, and
4,00,000 and the outflow is 10,00,000, 50,000,
and 1,50,000.
Now, please remember that we will follow the
same convention in terms of showing inflow
- which is revenue, and outflow - which is
expenditure, throughout this discussion today.
Now, obviously, if this outflow is occurring
here, and this inflow is occurring here, we
really need to understand the concept of interest,
and try to understand what is the present
value of this 2,00,000 or this 3,00,000 or
this 50,000, and so on. Similarly, we must
understand what is the present value, for
example, of this 50,000, or 1,50,000. On the
other hand, as I mentioned in a previous slide,
we can take all of these values here and try
to find out what is their value at a future
date and based on the present value or the
future value, we can determine whether this
cash-flow diagram or whether this investment
which has this kind of an inflow and outflow,
is acceptable to us or not.
So now, let’s move forward and try to understand
how do we do interest computations. So, basically,
two classifications that I have taken - one
is a single payment, where we talk in terms
of a compound amount factor and a present
worth factor, and there is a system of equal
payments, where we are talking about the compound
amount factor, the present worth factor, the
sinking fund deposit, the capital recovery
factor, and so on.
So these are very simple factors which can
be determined from first principles, but instead
of determining them from first principles
all the time, there are tables which are readily
made available to engineers, who can immediately
find a factor - a number by which a certain
income or an expenditure is multiplied to
get the present worth, and so on and so forth,
as we shall see in subsequent examples.
So now, coming to the single payment compound
factor. Let us not bother so much about the
nomenclature, but try to understand what is
the physics, and, what is the principle involved.
In this case here, what we are saying is,
that given a principal P, a rate of interest
i, for a period of n years, what is the final
amount that is accruing? This is something
which we know from our understanding of the
whole concept of compound interest and we
know that this is nothing but, (1+i)n. So,
in this course, how we will read this particular
situation is - what is the F given P, i and
n?
If we take an illustrative example, how much
does a deposit of INR 10,00,000 grow into,
in 5 years at a rate of 8 percent compounded
annually. If we use this formula, we find
the number to be INR 14,69,328. So, we now
have a factor which could be 1.469 or something
like that and this is what we multiplied by
this amount here to get this value. So, what
we have here is - P is known to be INR 10,00,000,
the interest or the rate of interest is known
to be 8 percent, the n is 5 years and we find
this growth in the investment made.
Similarly, a single payment present worth
factor represents what is the P if we want
an F for a given i and n. So, like last time,
this single payment present worth factor is
represented as 1 / (1+i)n, which is just the
reciprocal of the previous discussion and
the illustrative example which I can give
you is, what is the present value in INR or
the Indian rupees, of an asset which is expected
to have a worth of INR 20,00,000 after 10
years, assuming that the interest is compounded
annually at the rate of 10 percent.
If we do that and use this given formula,
we find the number to be 7,71,086. Basically
what we are saying is that, if we have this
amount of money here, it will grow to an amount
of money which is required at the end of a
given period of time if we assume a certain
rate of interest. So, in these two cases - in
one case, we have this value known to us and
we find this value, whereas, in the present
slide what we are showing is - we are given
this value and we are trying to find out how
much we should have in hand today so that,
it grows to that required amount of money
at a certain point in time later on.
So, now coming to those more distributed investments,
let’s talk about the equal payment compound
amount factor, which basically says that if
we keep depositing or setting aside an amount
A for a period of n years at a rate of interest
i, what would be the final F? So this is what
is the equation which turns out to be. We
are not deriving these equations. You can
derive those equations from first principles,
and I am leaving that part out. As an illustrative
example, let’s talk in terms of what is
the worth in rupees at the end of 10 years
for an ordinary annuity of INR 20,000 operated
at an annual compounding rate of 8 percent?
So what we are saying is that we will set
aside INR 20,000 every year for a period of
10 years, and, if the rate of interest is
8 percent, what would this final amount be?
So if we operate this equation, we find that
the amount is INR 2.89 lakhs. So if we look
at our investment directly, what we are doing
is we are investing 20,000 for 10 years which
is, basically, we are investing 2,00,000.
Now this 2 lakh is growing to 2.89 because
this 20,000 is earning an interest for 9 years,
the next 20,000 is earning an interest for
8 years, this one is for 7 years and so on,
and this total interest is 89,732.
So this is the way to look at an equal payment
compound amount factor. Continuing with our
discussion, there is an equal payment sinking
fund deposit factor and like I said, let’s
not bother about the nomenclature, what we
should understand is the principle involved.
How is the cash flow being modeled and how
to calculate the present value or the future
value of that particular investment? So, coming
to this factor here, what it says is that,
if we want a certain amount at the end, then
what amount should we be setting aside every
year for n years at a rate of interest of
i?
So that is what the question is, that how
much should be invested in a bank every year
to make a sum of INR 20,00,000 at the end
of 20 years assuming that the bank offers
an interest of 8 percent compounded annually.
If we do this, the answer is 43,705. If we
keep setting aside INR 43,705 for 20 years
and the rate of interest applicable is 8 percent
compounded annually, the amount payable to
us at the end will be INR 20,00,000 or 2 million
or 20 lakhs. This again is the same idea where
this first investment earns an interest for
19 years, the second investment earns for
18 years, third investment earns for 17 years
and so on, and the total interest that we
get is actually the difference of 43,705 multiplied
by 20 with respect to the 20 00,000 that we
are getting.
So we are investing surely a lesser amount
of money here. I’m leaving it to you compute
that and the final amount that we get. There
is another very interesting and a very important
factor, call the equal payment present worth
factor, which basically something like this,
that if we make this investment for n years
every year at a certain rate of interest,
what is the present worth of that entire investment?
So we would be investing an amount A over
a long period of time and the present worth
of all these A’s would be different, because
they would have different periods of time
where the locking is occurring and that can
be determined using this formula and as an
illustrative example, let’s say that what
is the present worth of an ordinary annuity
of INR 20,000 invested for a period of 10
years, being operated at an annual compounding
rate of 8 percent?
So if these were the conditions being applied,
the present worth of this investment is INR
1,34,260. Now please see the difference. We
are talking of the present worth being 1,34,260
for a total amount which is 20,000 and 10
years which would make it, let’s say, 2,00,000.
So the difference between 2 lakh and 1.34
lakhs is arising because that 1.34 is the
present worth of this entire investment, which
is being distributed over a period of 10 years.
I would also like to mention that for sufficiently
large n, the factor becomes 1/i, that is,
if the investment continues for a long period
of time, then the factor can be taken to be
1/i as a thumb rule.
Now, equal payment capital recovery factor
which is EPCRF - again not bothering about
the nomenclature, what we are talking about
is, given a P, what should be the A for n
years, at a rate of interest of i, and this
is the formula which comes out of this, and
the illustrative example would be - what should
be the annual installment for a period of
6 years that the lender has to fix to recover
a total amount of INR 200,000, at an operating
interest compounded annually for 4 percent?
So, if there is a INR 2,00,000 which is occurring
here, what should be the annual installment
which is to be taken. In this case, it turns
out to be INR 38,150.
So, what is being said is that for INR 2,00,000,
if it has to be recovered in a manner that
the rate of interest is 4 percent and the
period of recovery is 6 years, then the installment
should be INR 38,150. So, effectively, what
is being paid is 38,150 multiplied by 6 and
what was lent was 2,00,000. So the difference
between these two is effectively the interest
component. What I would like to leave you
as a thought would be that try to do it on
a spreadsheet and try to find out that if
there was a loan which was taken and an interest
at any rate accrues in the first year, or
the second year and so on and so forth, then,
if a certain amount of money is returned to
the lender, whether that money should be going
towards servicing the interest or it should
service the capital or it should be both.
So, depending on this exercise, there would
be some very interesting results that you
would see, and in fact, that is the kind of
thought process which we have when we talk
in terms of soft loans, banks try to induce
people to take loans by playing with this
distribution of the servicing. So, what I
am leaving to you to find out is as far as
how this particular 38,150 is concerned, whether
it is going towards the payment of the interests
or whether it is going towards the payment
of the capital - those are things which I
am leaving out from the discussion at present
because of the simple reason that this is
not a course in economics. We are trying to
just show you different parts of a construction
management course, where we are trying to
explain to you or get you interested in what
it entails to be a construction manager.
So, going forward, let us talk of economic
decision making now. Construction management
involves cost comparisons between different
alternatives and this very commonly happens
when we are trying to buy an equipment and
we have options which have different capital
costs and they may have different maintenance
costs. As an illustrative example, consider
two options of equipment, let us say A and
B, where A has a high initial cost and low
yearly maintenance, but B has a low initial
cost but high annual maintenance.
So what we are looking at, as far as option
A is concerned, this outflow is very high,
but subsequently this is lower. Whereas, in
case of B, if this was A, B - this is lower,
but these are, let’s say, higher. So, how
do we compare this option with this option?
This can easily be done if we follow some
of the principles that we have discussed so
far.
Now, this slide lists some of the common decision
making criteria -the Payback Period, the Return
on Investment, Discounted Payback, Net Present
Value, Internal Rate of Return, Equivalent
Annual Charge, and the cost-benefit ratio.
These two do not consider the time value of
money, but these four consider the time value
of money. In our discussion today, we would
not touch upon the Return on Investment, the
Equivalent Annual Charge and cost-benefit
ratio, but we will talk about other things.
So the first thing that we need to talk about
is the Payback Period. Now, it is the period
at which the investor gets the investment
back and as we mentioned in the previous slide,
this does not consider the time value of money,
and therefore, out of the various alternatives,
a project or an investment with shorter payback
period is preferable. What we are saying is
that if we make an investment today and we
keep getting something out of this, at what
point in time - this is our time axis - at
what point in time, this amount here becomes
equal to the sum of these amounts here. So,
that is my Payback Period and since we are
not talking of the time value of money, we
can simply, algebraically sum these revenues.
So as an example, let us consider two alternatives
- A and B, the initial investments for both
projects is estimated to be INR 50,000. Option
A is estimated to give INR 10,000 in the first
year, INR 20,000 in the second year and INR
15,000 in the next four years, whereas, Option
B gives you INR 10,000 for all the six years.
Which is a better alternative?
So for that, we simply draw the cash-flow
diagram for A, which is 50,000 of an investment,
10,000, 20,000, 15,000, 15,000, 15,000 and
15,000. Whereas, for option B, it is 10,000
for all the six years. So what is the period,
in which this 50000 is being recovered in
the two cases? The payback period for A is
3 years and 4 months because 3 years gives
you a recovery of 10 and 15, i.e.- 25, and
20 that is 45, and all that you need to recover
is 5,000 out of this 15,000. Assuming that
it is happening linearly, it is one-third
of that year, which is 4 months. In the case
of B, the situation is simple. It’s 10,000
for every year and therefore, the payback
period is 5 years. Which of them is better?
Project A is preferable than B as the payback
period for A is lower than that of B.
Now let’s talk in terms of a Discounted
Payback Period. It is similar to the Payback
Period except that it considers the time value
of money and that is something which I am
leaving out of the discussion today, I am
not taking it up for solution. I’ll leave
it to you to find out the payback periods,
assuming that the discount rate is 10 percent.
Now let’s talk about the Net Present Value
- the NPV. Now this is the sum of all cash
flows discounted to the present, using the
concept of time value of money. So let us
try to see what happens. What we are doing
is, for all the CFt - the CFt is the cash
flow at year t, n is the life of the project,
k is the interest rate - for all the CFt that
occurs, we bring all of this down to a value
at present. That is what I said that in this
discussion today, we would concentrate on
the present value. We can do the same exercise
for the future value as well, but once we
understand how to do it for the present value,
we can easily do it for the future value as
well.
So now, NPV, mathematically, is represented
like this –
And if the NPV is greater than 0, then the
project creates a value to the investor and
usually alternatives can be assessed based
on their NPV. And let’s try to understand
the importance of time value of money in cash
flows.
.
Let us take an illustrative example where
there is a table which shows you the different
cash flow parameters. It gives you a cash
flow of minus 200 initially and then a positive
cash flow for 7 years and for the eighth year
the cash flow is a +37 and what we are asked
to do is to calculate the payback period and
the NPV of cash flow at an interest of 15
percent throughout. We have to find out whether
the project is worth executing or not. We
have to basically find out what is the NPV,
whether it is greater than zero or less than
zero, and by how much and so on and so forth.
If we translate this information given in
the table to a cash flow diagram, this is
what we are looking at. We are look at 200,000
going out and 35 coming in for 7 years and
37 coming in the 8th year.
With this, if you simply calculate the payback
value, without considering the time value
of money and that is what is the definition
of the payback period, we find that the period
is 5 years and 9 months. So, in 5 years and
9 months, this plus something would total
to 200.
Now, moving to the next part of the problem,
which is to calculate the NPV using the time
value of money at the rate of 15 percent,
for this diagram, we have these discounted
factors for each year.
So each of these numbers here gets multiplied
by these factors - that these factors are
reducing as time goes on, because these amounts
of money are available to us for longer periods
of time. If we sum up all these numbers here,
we get the net NPV which turns out to be –43,610
and since it is negative, the project is not
recommended. Now this is not recommended at
a rate of 15 percent. If this rate of interest
was to change, how will the situation change?
And that is something we can always do as
a simple exercise. So having done this exercise
at 15 percent,
what I am asking you to do is to carry out
the exercise of computing the NPV at 10 percent
and 5 percent. You will find that the NPV,
obviously, changes. Try to see how it changes
and then plot the variation of the net present
worth - the NPV - with the rate of interest
that you have used, and what you will be able
to determine what is called the Internal Rate
of Return, which is IRR.
Now, let us see what IRR is. It is the discount
rate at which the NPV of the cash flow is
zero. Effectively what it means is, we are
looking at a situation - if NPV is plotted
against the discount rate, there will be a
point of intersection like this, and that
is what will be the IRR or the internal rate
of return, and that is what I am asking you
to plot and see. Once you plot the example
for 15 percent, 10 percent and 5 percent,
I think you should be able to find out the
internal rate of return for the example that
we are working on. Please note that an alternative
with a higher IRR is preferred for an investment.
Now if we talk in terms of how to make a choice
between alternatives using NPV, let us try
to look at an example where there are two
brands of equipment A and B, whose cost is
different.. There is an initial investment
of INR 7,00,000 in one case and INR 4,00,000
in another and the annual maintenance cost
of these two equipment are given here for
A and B. A has a maintenance cost of INR 3,00,000
every year, whereas, B has the maintenance
cost of INR 5,00,000. Which of these equipments
should be chosen?
So if we look at the cash flow diagram for
A, this is the representation. Similarly,
for B, the representation is given like this
and using this equation that we already talked
about, the Net Present Value for A is INR
14.77 lakhs, whereas, for B, it is INR 16.95
lakhs. So, given these two NPVs, the NPV of
A is lower and therefore, A is preferred.
This is how we have used the time value of
money and the Net Present Value kind of concepts
to find out which of the alternatives makes
more sense.
However, till now, we have taken examples
in a manner that they had equal lives. So,
for example, what we are talking about just
now was, in both cases, we are talking of
3 years was the service life of the equipment.
But there is always the possibility that the
alternatives may not have equal lives, they
may not have equal maintenance cost at different
points in time, but those are things which
we can incorporate in our thought process
fairly easily and evaluating alternatives
with unequal lives - in most situations the
alternatives do not have equal lives and to
be fair with the ranking process of alternatives,
the lives should be modified such that they
become equivalent because that is the only
way to be able to make a fair comparison.
The two commonly used approaches are common
multiple method and a study period method.
What these approaches really mean is that
in the common multiple method the least common
multiple of life periods of alternatives is
chosen as the co-terminus life period. So,
what we are saying for example, is the following:
if there is an equipment which has a service
life of 3 years and another one which has
a service life of 4 years, we can say that
over a period of 12 years we will need 4 replacements
for this, and 3 replacements for this, and
then try to do the exercise that we have carried
out just now and we will have an answer to
our question as to whether equipment A or
B should be preferred. So, what happens in
the study period method is given here and
with this we come to an end of our discussion
today.
The references, like one by K N Jha, F K Crundwell
and H Kerzner would probably help you understand
the concepts that we have gone over.With this
we come to an end of the discussion.
Thank you.
