Unit 3 - Cashflow and Method of comparison

Prepared by
Dr. Vignesh V
Department of Structural Engineering
Sanjivani College of Engineering, Kopargaon.
EEST241-ENGINEERING ECONOMICS
UNIT III
CASH FLOW
Methods of comparison of alternatives – present worth method (Revenue dominated cash flow
diagram), Future worth method (Revenue dominated cash flow diagram, cost dominated cash
flow diagram), Annual equivalent method (Revenue dominated cash flow diagram, cost
dominated cash flow diagram), rate of return method, Examples in all the methods.
3.1 INTRODUCTION
The primary objective of the traditional Income Statement and Balance Sheet is to report to the
interested parties the operational performance and economic position of an enterprise. An
intelligent reader can gather sufficient idea about costs, revenues, profit/loss assets, liabilities and
owners equity from these statements. Under the Companies Act, a company is required to
include the figures of previous year in the financial accounts so that the interested parties may
compare individual figures for better understanding of the corporate performance and economic
position. The schedules attached to published account explain important items for the knowledge
of the concerning parties. The format of published accounts has been revised from time to time
with a view to providing more and more information to the shareholders, creditors and others.
Nobody can deny the usefulness of the traditional form of annual accounts which form an
important basis for making financial decisions.
No doubt the annual accounts in their traditional forms are very important but they suffer from
certain limitations. The serious limitation of a Balance Sheet is that it is a static document as it
shows the economic position at a point of time and fails to show fully the movements or changes
in the assets, liabilities and owners equity. From the financial accounts in their usual form, it is
not clear as to how the funds were generated and how they were utilized between the closing
dates of two Balance Sheets. In order to provide such information, another document known as
Statement of Changes in Financial Position is prepared. This document shows the changes in the
financial position between the closing dates of the Balance Sheets.
In this connection it is important to understand clearly the meaning of the word 'Fund' which is
used in three different senses. In a narrow sense, fund means each and the statement based on
this concept is known as Cash Flow Statement. In a broader sense, fund means all financial

Prepared by
Dr. Vignesh V
resources which flows through working capital accounts and fixed capital accounts and a fund
flow statement based on this concept is almost a new form of Balance Sheet. The APB
(Accounting Principles Board, U.S.A.) has recommended the preparation and presentation of

Prepared by
Dr. Vignesh V
statement of changes in financial position according to the broadest sense of the term 'Fund.'
However, the meaning of the 'Fund' in both the narrow as well as broader senses do not find
favor with many academicians and practitioners who prefer to consider Fund in the sense of
Working Capital i.e., Current assets minus Current liabilities. In this chapter, we shall illustrate
the preparation of statement of changes is financial position based on all the three concepts of
Fund.
Funds Flow Statement is known by different names such as: (i) Where Got Where Gone
Statement, (ii) Statement of sources and application of funds, (iii) Statement of changes in
working capital, (iv) Statement showing summary of financial operations, (v) Statement of
sources and application of working capital, (vi) Statement of changes in financial position, (vii)
Funds Flow statement, etc. It may be noted that there is no official name of the statement as its
preparation is still obligatory. Only few enlightened firms in India publish this statement for the
guidance of their members and creditors. However, it is advisable that the title of the statement
reflects the concept of fund on which it is based.

Prepared by
Dr. Vignesh V
3.2 CASH FLOW STATEMENT
We have seen the preparation of Funds Flow Statement which treated 'Fund’ in the sense of
working capital. The statement of changes in financial position can also be prepared on the basis
of the cash concept of the word 'Fund.' It is knows as Cash Flow Statement if Fund is considered
in the sense of cash.
The preparation of Cash Flow Statement is important to understand the paradoxical situation in
which a firm finds difficulty in honoring its short period business commitments despite the
existence of sufficient working capital as indicated by the Fund Flow Statement (working capital
basis). This happens when a large proportion of working capital is tied up in the form of
inventories and other working assets.
The Fund Flow Statement based on working capital concept does not take into account the
qualitative structure of working capital.
Cash is a peculiar component of working capital. It should be distinguished from other
components in any scheme of short-period financial planning. The Cash Flow Statement enables
a firm to know the availability of cash from different sources and the manner of its utilization.
A projected Cash Flow Statement tells the management about the case position at different
timings. The management can arrange for additional necessary cash in case cash outflow exceeds
the cash inflow in any particular period of time. Similarly surplus cash, if any, can be invested
for effective utilization of cash balances.
3.5 DIFFERENCE BETWEEN CASH FLOW ANALYSIS AND FUND FLOW
ANALYSIS
Following are the points of difference between Cash Flow Analysis and a Funds Flow Analysis.
1. A Cash Flow Statement is concerned only with the change in cash position while a Fund Flow
Analysis is concerned with change in working capital position between two balance sheet dates.
Cash is only one of the constituents of working capital besides several other constituents such as
inventories, accounts receivable, prepaid expenses.

Prepared by
Dr. Vignesh V
2. A Cash Flow Statement is merely a record of cash receipts and disbursements. Of course, it is
valuable in its own way but it fails to bring to light many important changes involving the
disposition of resources. While studying the sort-term solvency of a business one is interested
not only in cash balance but also in the assets which can be easily converted into cash.
3. Cash flow analysis is more useful to the management as a tool of financial analysis in short
period as compared to funds flow analysis. It has rightly been said that shorter the period covered
by the analysis, greater is the importance of cash flow analysis. For example, if it is to be found
out whether the business can meet its obligations maturing after 10 years from now, a good
estimate can be made about firm's capacity to meet its long-term obligations if changes in
working capital position on account of operations are observed. However, if the firm's capacity
to meet a liability maturing after one month is to be seen, the realistic approach would be to
consider the projected change in the cash position rather than an expected change in the working
capital position.
4. Cash is part of working capital and, therefore, an improvement in cash position results in
improvement in the funds position but the reverse is not true. In other words "inflow of cash"
results in "inflow of funds" but inflow of funds may not necessarily result in "inflow of cash"
Thus, a sound funds position does not necessarily mean a sound cash position but a sound cash
position generally means a sound funds position.
5. Another distinction between a cash flow analysis and a funds flow analysis can be made on the
basis of the techniques of their preparation. An increase in a current liability or decrease in a
current asset results in decrease in working capital and vice versa. While an increase in a current
liability or decrease in a current asset (other than cash) will result increase in cash and vice versa.
Some people, as stated before, use the term 'funds' in a very narrow sense of ,cash' only. In such
an even the two terms 'Funds' and 'Cash' will have synonymous meanings.

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3.6 PRESENT WORTH METHOD OF COMPARISON
In this method of comparison, the cash flows of each alternative will be reduced to time zero by
assuming an interest rate i. Then, depending on the type of decision, the best alternative will be
selected by comparing the present worth amounts of the alternatives.
The sign of various amounts at different points in time in a cash flow diagram is to be decided
based on the type of the decision problem.
In a cost dominated cash flow diagram, the costs (outflows) will be assigned with positive sign
and the profits, revenue, salvage value (all inflows), etc. will be assigned with negative sign.
In a revenue/profit-dominated cash flow diagram, the profit, revenue, salvage value (all inflows
to an organization) will be assigned with positive sign. The costs (outflows) will be assigned
with negative sign.
In case the decision is to select the alternative with the minimum cost, then the alternative with
the least present worth amount will be selected. On the other hand, if the decision is to select the
alternative with the maximum profit, then the alternative with the maximum present worth will
be selected.
3.6.1 REVENUE-DOMINATED CASH FLOW DIAGRAM
A generalized revenue-dominated cash flow diagram to demonstrate the present worth method of
comparison is

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Dr. Vignesh V
P represents an initial investment and Rj the net revenue at the end of the jth year. The interest
rate is i, compounded annually. S is the salvage value at the end of the nth year.
To find the present worth of the above cash flow diagram for a given interest rate, the formula is
PW(i) = – P + R1[1/(1 + i)1
] + R2[1/(1 + i)2
] + ... + Rj[1/(1 + i) j
] + Rn[1/(1 + i)n
] + S[1/(1 + i)n
]
In this formula, expenditure is assigned a negative sign and revenues are assigned a positive sign.
If we have some more alternatives which are to be compared with this alternative, then the
corresponding present worth amounts are to be computed and compared. Finally, the alternative
with the maximum present worth amount should be selected as the best alternative.
3.6.2 COST-DOMINATED CASH FLOW DIAGRAM
A generalized cost-dominated cash flow diagram to demonstrate the present worth method of
comparison is
P represents an initial investment, Cj the net cost of operation and maintenance at the end of the
jth year, and S the salvage value at the end of the nth year.
To compute the present worth amount of the above cash flow diagram for a given interest rate i,
we have the formula
PW(i) = P + C1[1/(1 + i)1
] + C2[1/(1 + i)2
] + ... + Cj[1/(1 + i) j
]+ Cn[1/(1 + i)n
] – S[1/(1 + i)n
]
In the above formula, the expenditure is assigned a positive sign and the revenue a negative sign.
corresponding present worth amounts are to be computed and compared. Finally, the alternative
with the minimum present worth amount should be selected as the best alternative.

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Dr. Vignesh V
3.9. FUTURE WORTH METHOD
In the future worth method of comparison of alternatives, the future worth of various alternatives
will be computed. Then, the alternative with the maximum future worth of net revenue or with
the minimum future worth of net cost will be selected as the best alternative for implementation.
A generalized revenue-dominated cash flow diagram to demonstrate the future worth method of
comparison is presented in
P represents an initial investment, Rj the net-revenue at the end of the jth year, and S the salvage
value at the end of the nth year.
The formula for the future worth of the above cash flow diagram for a given interest rate, i is
FW(i) = –P(1 + i)n
+ R1(1 + i)n–1
+ R2(1 + i)n–2
+ ... + Rj(1 + i)n–j
+ ... + Rn + S
In the above formula, the expenditure is assigned with negative sign and the revenues are
assigned with positive sign.
corresponding future worth amounts are to be computed and compared. Finally, the alternative
with the maximum future worth amount should be selected as the best alternative
A generalized cost-dominated cash flow diagram to demonstrate the future worth method of
comparison is given in

Prepared by
Dr. Vignesh V
The formula for the future worth of the above cash flow diagram for a given interest rate, i is
FW(i) = P(1 + i)n
+ C1(1 + i )n–1
+ C2(1 + i)n–2
+ ... + Cj(1 + i)n–j
+ ... + Cn – S
In this formula, the expenditures are assigned with positive sign and revenues with negative sign.
corresponding future worth amounts are to be computed and compared. Finally, the alternative
with the minimum future worth amount should be selected as the best alternative.
3.10. ANNUAL EQUIVALENT METHOD
In the annual equivalent method of comparison, first the annual equivalent cost or the revenue of
each alternative will be computed. Then the alternative with the maximum annual equivalent
revenue in the case of revenue-based comparison or with the minimum annual equivalent cost in
the case of cost based comparison will be selected as the best alternative.
A generalized revenue-dominated cash flow diagram to demonstrate the annual equivalent
method of comparison is presented in
P represents an initial investment, Rj the net revenue at the end of the jth year, and S the salvage
value at the end of the nth year.
The first step is to find the net present worth of the cash flow diagram using the following
expression for a given interest rate, i:
PW(i) = –P + R1/(1 + i)1
+ R2/(1 + i)2
+ ... + Rj/(1 + i) j
+ ... + Rn/(1 + i)n
+ S/(1 + i)n

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In the above formula, the expenditure is assigned with a negative sign and the revenues are
assigned with a positive sign.
In the second step, the annual equivalent revenue is computed using the following formula:
Where (A/P, i, n) is called equal payment series capital recovery factor.
corresponding annual equivalent revenues are to be computed and compared. Finally, the
alternative with the maximum annual equivalent revenue should be selected as the best
alternative.
A generalized cost-dominated cash flow diagram to demonstrate the annual equivalent method of
comparison is presented in
relation for a given interest rate, i.
PW(i) = P + C1/(1 + i)1
+ C2/(1 + i)2
+ ... + Cj/(1 + i) j
+ ... + Cn/(1 + i)n
– S/(1 + i)n
In the above formula, each expenditure is assigned with positive sign and the salvage value with

Prepared by
Dr. Vignesh V
negative sign. Then, in the second step, the annual equivalent cost is computed using the
following equation:
Where (A/P, i, n) is called as equal-payment series capital recovery factor.
As in the previous case, if we have some more alternatives which are to be compared with this
alternative, then the corresponding annual equivalent costs are to be computed and compared.
Finally, the alternative with the minimum annual equivalent cost should be selected as the best
alternative.
If we have some non-standard cash flow diagram, then we will have to follow the general
procedure for converting each and every transaction to time zero and then convert the net present
worth into an annual equivalent cost/revenue depending on the type of the cash flow diagram.
Such procedure is to be applied to all the alternatives and finally, the best alternative is to be
selected.
3.10.3 ALTERNATE APPROACH
Instead of first finding the present worth and then figuring out the annual equivalent
cost/revenue, an alternate method which is as explained below can be used. In each of the cases
presented in Sections 3.10.1 and 3.10.2, in the first step, one can find the future worth of the cash
flow diagram of each of the alternatives.
Then, in the second step, the annual equivalent cost/revenue can be obtained by using the
equation:
Where (A/F, i, n) is called equal-payment series sinking fund factor.

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3.11. RATE OF RETURN METHOD
The rate of return of a cash flow pattern is the interest rate at which the present worth of that cash
flow pattern reduces to zero. In this method of comparison, the rate of return for each alternative
is computed. Then the alternative which has the highest rate of return is selected as the best
alternative.
In this type of analysis, the expenditures are always assigned with a negative sign and the
revenues/inflows are assigned with a positive sign.
A generalized cash flow diagram to demonstrate the rate of return method of comparison is
presented in
In the above cash flow diagram, P represents an initial investment, Rj the net revenue at the end
of the jth year, and S the salvage value at the end of the nth year.
expression at a given interest rate, i.
PW(i) = – P + R1/(1 + i)1
+ R2/(1 + i)2
+ ... + Rj/(1 + i) j
+ ... + Rn/(1 + i)n
+ S/(1 + i)n
Now, the above function is to be evaluated for different values of i until the present worth
function reduces to zero, as shown in Fig.
In the figure, the present worth goes on decreasing when the interest rate is increased. The value
of i at which the present worth curve cuts the X-axis is the rate of return of the given
proposal/project. It will be very difficult to find the exact value of i at which the present worth
function reduces to zero.

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Dr. Vignesh V
So, one has to start with an intuitive value of i and check whether the present worth function is
positive. If so, increase the value of i until PW(i) becomes negative. Then, the rate of return is
determined by interpolation method in the range of values of i for which the sign of the present
worth function changes from positive to negative.

Unit 3 - Cashflow and Method of comparison

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