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					NPV Vs. IRR Methods
The NPV and IRR methods would in certain situations give the same accept-
reject decision. But they may also differ in the sense that the choice of an
asset under certain circumstances may be mutually contradictory. The
comparison of these methods, therefore, involves a discussion of
(1) the similarities between them, and
(2) their differences, as also the factors which are likely to cause such

NPV and IRR: Similarities
The two methods-IRR and NPV- would give consistent results in terms of
acceptance or rejection of investment proposals in certain situations.
Conventional Investment A conventional investment is one in which the
cash flow pattern is such that an initial investment (outlay or cash outflow)
is followed by a series of cash inflows. Thus, in the case of such
investments, cash outflows are confined to the initial period.
Independent Proposals The independent proposals refer to investments
the acceptance of which does not preclude the acceptance of others so
that all profitable proposals can be accepted and there are no constraints
in accepting all profitable projects.
The reason why both the methods are equivalent and support or reject a
proposal is simple. According to the NPV method, the decision rule is that a
project will be accepted if it has a positive NPV, that is, NPV exceeds zero. The
IRR method would support projects in whose case the IRR is more than the
required rate of return (r exceeds k). When the NPV = zero or the IRR = k, the
project may be accepted or rejected. The projects which have positive net
present values will also have an IRR higher than the required rate of return.
Thus, Fig. 1 portrays NPV as (i) positive; (ii) zero; and (iii) negative
corresponding to three situations (a) IRR > K; (b) IRR = K; (c) IRR < K.
Figure 1 shows the relationship between the NPV of a project and the
discount rate. If there is no K, or discount rate is zero (a very unreal situation),
NPV is maximum. As the value of K increases, the NPV starts declining. At 12
per cent rate of discount, the NPV is zero. This is the IRR also because by
definition it is that rate of discount which reduces the NPV to zero. Assuming
cost of capital to be 8 per cent, we find that NPV is positive by amount (a) and
the project is acceptable and so is it under IRR as its value is > K (0.12 > 0.08).
If we assume K to be 16 per cent, the project is unacceptable as the NPV is
negative by amount (b) and so is it under IRR as IRR < K (0.12 < 0.16). The two
approaches lead to identical results with regard to the accept-reject decision.


         Net present value


                             0                      8
                                          4                12   16   20
                                       Discount rate (K)


Figure 1 : NPV and Discount rate
NPV and IRR Methods: Differences
However, in certain situations they will give contradictory results such that if the
NPV method finds one proposal acceptable, IRR favours another. This is so in the
case of mutually exclusive investment projects. If there are alternative courses of
action, only one can be accepted. Such alternatives are mutually exclusive. The
mutual exclusiveness of the investment projects may be of two types: (i)
technical, and (ii) financial.
Technical Exclusiveness The term technical exclusiveness refers to alternatives
having different profitabilities and the selection of that alternative which is the
most profitable. Thus, in the case of a purchase or lease decision the more
profitable out of the two will be selected.
Financial Exclusiveness The mutual exclusiveness may also be financial. If there
are resource constraints, a firm will be forced to select that project which is the
most profitable rather than accept all projects which exceed a minimum
acceptable level (say, k). The exclusiveness due to limited funds is popularly
known as capital rationing.
The different ranking given by the NPV and IRR methods can be illustrated under
the following heads:
1.       Size-disparity problem;
2.       Time-disparity problem; and
3.       Unequal expected lives.
1. Size-disparity problem
Size disparity arises when the initial investment in mutually exclusive projects
is different.

Example 1
 Particulars                               Project A           Project B    Project B-A
Cash outlays                               (Rs 5,000)          (Rs 7,500)      (Rs 2,500)
Cash inflows at the end of year, 1              6,250               9,150           2,900
IRR (%)                                            25                  22              16
k                                                         10
NPV                                            681.25              817.35
Thus, the two methods rank the projects differently. Project A has a higher IRR (0.25)
than project B (0.22) but the NPV of project B (Rs 817.35) is more than that of A (Rs
681.25). The important question is which method, in such a situation, gives better
results? The answer should be related to the effect of the decision on the maximisation
of the shareholders’ wealth. The IRR method is not compatible with the goal of wealth
maximisation. It is concerned with the rate of return on investment or yield rather than
the total yield on the investment. In the above example, assuming 10 per cent to be the
required rate of return, the firm would be left with Rs 750 [Rs 6,250 – (Rs 5,000 + 0.10 ×
Rs 5,000)] after one year in case project A is accepted and Rs 900 [Rs 9,150 – (Rs 7,500) +
0.10 × Rs 7,500] in case project B is accepted. The NPV method suggests that project B is
better. This recommendation is consistent with the goal of the firm of maximising
shareholders’ wealth.
Incremental Approach
The conflict between the NPV and IRR in the above situation can be
resolved by modifying the IRR so that it is based on incremental analysis.
According to the incremental approach, when the IRR of two mutually
exclusive projects whose initial outlays are different exceeds the required
rate of return, the IRR of the incremental outlay of the project requiring a
bigger initial investment should be calculated. This involves the following
1)   Find out the differential cash flows between the two proposals.
2)   Calculate the IRR of the incremental cash flows.
3)   If the IRR of the differential cash flows exceeds the required rate of
     return, the project having greater investment outlays should be
     selected, otherwise it should be rejected.
In Example 1, the IRR of the differential cash outlay of Project B is 16 per
cent. The required rate of return is 10 per cent. Thus, project B is better
than project A in spite of the fact that IRR in the latter is lower because it
offers the benefits offered by project A plus a return in excess of the
required return on Rs 2,500, that is, differential cash outlays.

2. Time-disparity Problem
Time-disparity arises when the cash flow pattern of mutually exclusive projects is
Example 2
Year                                                              Cashflows
                                                     Project A                    Project B
0                                                  Rs 1,05,000                  Rs 1,05,000
1                                                       60,000                       15,000
2                                                       45,000                       30,000
3                                                       30,000                       45,000
4                                                       15,000                       75,000
IRR (%)                                                     20                           16
NPV (0.08)                                              23,970                       25,455
We find on the basis of a comparison of the internal rate of returns that project A is
better, but the NPV method suggests that project B is better. Since the cost of capital is 8
per cent, given the objective of the firm to maximise wealth, project B is definitely better.
Under the time-disparity problem it is the cost of capital which will determine the ranking
of projects. If we take k = 0.10, we shall find project A is better as its net present value
would be Rs 19,185 compared to Rs 18,435 of B. Its IRR is also more than that of B. Both
the methods give identical prescription. But it does not imply that the IRR is superior to
the NPV method, as the NPV is giving the same ranking as the IRR. In the event of
conflicting rankings, the firm should rely on the rankings given by the NPV method.

3. Projects With Unequal Lives
Another situation in which the IRR and NPV methods would give a conflicting
ranking to mutually exclusive projects is when the projects have different
expected lives. This is shown in Example 3.
Example 3
There are two projects A and B. A has a service life of one year, while B’s useful
life is five years. The initial cash outlay for both the projects may be assumed to
be Rs 20,000 each. The cash proceeds from project A (at the end of the first year)
amount to Rs 24,000. The cash generated by project B at the end of the fifth year
is likely to be Rs 40,200. Assume that the required rate of return is 10 per cent.
Compute the NPV and the IRR of the two projects.
                         IRR and NPV of Projects A and B
           Project                IRR (per cent)                  NPV
             A                          20                       Rs 1,816
             B                          15                        4,900
Obviously, the ranking given by the IRR and NPV methods is different. According
to the IRR method, the recommendation would favour project A while the NPV
method would support project B. The conflict in the ranking by the two methods in
such cases may be resolved by adopting a modified procedure. There are two
approaches to do this:
(1) Common time horizon approach
Common time horizon approach makes a comparison between projects that
extends over multiples of the lives of each.

Example 4
Particulars                                 Project A          Project B
Initial outlay                             Rs 10,000           Rs 20,000
Cash inflows after taxes
       Year-end        1                       8,000               8,000
                       2                       7,000               9,000
                       3                          Nil              7,000
                       4                          Nil              6,000
Service life (years)                               2
Required rate of return                                 0.10

                                       Project A
Year                Cash flows            PV factor           Total present value
0                      Rs 10,000            1.000                          (Rs 10,000)
1                           8,000           0.909                                 7,272
2                           7,000           0.826                                 5,782
3                       (10,000) a          0.826                               (8,260)
3                           8,000           0.751                                 6,008
4                           7,000           0.683                                 4,781
NPV                                                                               5,583
a Machine replaced at the end of year 2.
                                     Project B
Year            Cash flows               PV factor            Total present value
0                   Rs 20,000              1.000                              Rs 20,000
1                       8,000              0.909                                  7,272
2                       9,000              0.826                                  7,434
3                       7,000              0.751                                  5,257
4                       6,000              0.683                                  4,098
Net present value                                                                 4,061
Decision Project A should be preferred to project B because of its larger NPV. If we had
compared the two projects without incorporating the consequences of replacing the
machine at the end of year 2, the decision would have been the reverse, because the net
present value of project A then would be Rs 3,054 [Rs 7,272 + Rs 5,782 – Rs 10,000].
(2) Equivalent annual value, (EANPV)/cost approach (EAC).
The EANPV/EAC is a better approach. The EANPV is determined
dividing the NPV of cash flows of the project by the annuity factor
corresponding to the life of the project at the given cost of capital.
The EAC is obtained dividing the total PV of cash outflows by the
relevant annuity factor. While the maximisation of EANPV is the
decision-criterion in the case of revenue-expanding proposals, the
minimisation of EAC is the guiding criterion for cost reduction

Example 5 (Revenue-expanding Investment Proposal)
A firm is considering to buy one of the following two mutually exclusive
investment projects:
Project A: Buy a machine that requires an initial investment outlay of Rs
1,00,000 and will generate the CFAT of Rs 30,000 per year for 5 years.
Project B: Buy a machine that requires an initial investment outlay of Rs
1,25,000 and will generate the CFAT of Rs 27,000 per year for 8 years.
Which project should be undertaken by the firm? Assume 10 per cent as cost
of capital.
(i) Determination of NPV of Projects A and B
  Project      Years         CFAT PV factor (0.10)      Total PV        NPV
    A            1-5    Rs 30,000        3.791       Rs 1,13,730   Rs 13,730
    B            1-8       27,000        5.335          1,44,045      19,045

(ii) Determination of EANPV:
                                Net present value of the project
   EANPV                                                                                   (1)
             PV of annuity correspond ing to life of the project at given cost of capital

EANPV (A) = Rs 13,730/3.791 = Rs 3,621.74
EANPV (B) = Rs 19,045/5.335 = Rs 3,569.82
On the basis of NPV criterion, Project B is preferred. However, on the basis of
EANPV, project A becomes more desirable, with higher EANPV. In fact,
acceptance of project A would be a right decision.
Example 6
(Cost-reduction Investment Proposal) A firm is considering to instal a large
stamping machine. Two machines currently being marketed will do the job
satisfactorily. Machine A costs Rs 50,000 and will require cash running
expenses of Rs 15,000 per year. It has a useful life of 6 years and is expected to
yield Rs 2,000 salvage value at the end of its useful life. Machine B costs Rs
65,000 but cash running expenses are expected to be Rs 12,000. This machine
is expected to have a useful life of 10 years with salvage value of Rs 5,000.
Assume both the machines would be depreciated on straight line basis for tax
If the corporate tax rate is 35 per cent and cost of capital is 10 per cent, which
machine should be bought by the company?
                      Equivalent Annual Costs of Machines A and B
Particulars                    Costs                  PV        Adjusted PV
                               Machine A    Machine B factor    Machine A     Machine B
0 (Initial cost)                Rs 50,000   Rs 65,000   1.000    Rs 50,000      Rs 65,000
(Operating cost):
 1-6 years (A)                      6,950
 1-10 years (B)                        —        5,700   4.355     30,267.25
                                                        6.145     ________      35,026.50
                                                                  80,267.25   1,00,026.50
Less: Salvage value:
 6th year (A)                      2,000`               0.564      1,128.00            —
 10th year (B)                                  5,000   0.386            —          1,930
Present value of total costs                                      79,139.25     98,096.50
Divided by annuity PV
factor for 10 per cent
corresponding to the life of
the project (capital
recovery factor)                                                     4.355          6.145
Equivalent annual cost
(EAC)                                                               18,172      15,963.63
Recommendation Since Machine B has a lower equivalent annual cost, it is preferred
Working Notes
                        Determination of Operating Costs
Particulars                                                Machine A Machine B
Cash running cost                                          Rs 15,000   Rs 12,000
 Less: Tax shield @35 per cent (assuming profitable            5,250       4,200
 Less: Tax advantage on depreciation charged every year:
  Machine A (Rs 8000 × 0.35)                                   2,800             —
  Machine B (Rs 6,000 × 0.35)                                     —        2,100
Effective operating cash outflows                              6,950       5,700

Reinvestment Rate Assumption
The conflict between the NPV and IRR methods is mainly ascribed to the
different reinvestment rate assumptions of intermediate cash inflows
accruing from projects. The IRR method implicitly assumes that the cash
flows generated from the projects are subject to reinvestment at IRR. In
contrast, the reinvestment rate assumption under the NPV method is the
cost of capital. The assumption of the NPV method is conceptually superior
to that of the IRR as the former has the virtue of having a uniform rate
which can consistently be applied to all investment proposals.
The IRR can be modified (to overcome the deficiency of the reinvestment
rate assumption) assuming the cost of capital to be the reinvestment rate.
Implicit investment rate
Implicit investment rate is the rate at which interim cash flows can be

The superficiality of the reinvestment rate under the IRR method can be
demonstrated by comparing the following two investment projects.
Project               Initial investment                    Cash inflows
                                                   Year 1                Year 2
A                           Rs 100                Rs 200                    0
B                             100                    0                   Rs 400

Under the IRR method, both projects have a rate of return of 100 per cent. If Rs
100 were invested for one year at 100 per cent, it would grow to Rs 200, and if
invested for two years, to Rs 400. Since both the projects have the same IRR, the
firm should be indifferent regarding their acceptability, if only one of two projects
is to be picked up as both the projects are equally profitable. For this to be true, it
is necessary that Rs 200 received at the end of year 1 in case of project A should
be equal to Rs 400 at the end of year 2. In order to achieve this, it necessarily
follows that the firm must be able to reinvest the first year’s earnings at 100 per
cent. If not, it would be unable to transform Rs 200 at the end of the first year into
Rs 400 at the end of the second. And if it cannot transform Rs 200 into Rs 400 in a
year’s time, the two projects A and B cannot be ranked equal. There is no reason
to believe that a firm can find other investment opportunities at precisely the
required rate.
In contrast, the present value method does not pose any problem. Let us calculate
the present value of Example 7, assuming cost of capital (k) as 10 per cent.
Example 7
Year                       Project A                           Project B
           Cashflows       PV factor   Total PV    Cashflows PV factor Total PV
1               Rs 200         0.909 Rs 181.80             0          —            —
2                      0          —      ______       Rs 400      0.826 Rs 330.40
                                          181.80                           330.40
Less: Initial outlay                      100.00                           100.00
Net present value                          81.80                           230.40

The PV method indicates that project B is preferable to project A as its net
present value is greater. The reinvestment rate in the PV method seems more
realistic and reasonable. It assumes that earnings are reinvested at the same
rate as the market cost of capital.
However, the IRR can be modified assuming the cost of capital to be the
reinvestment rate. The intermediate cash inflows will be compounded by
using the cost of capital. The compounded sum so arrived at and the initial
cost outflows can be used as the basis of determining the IRR.
Thus, the assumption regarding the reinvestment rate of the cash inflows
generated at the intermediate stage is theoretically more correct in the case of
NPV as compared to the IRR.
Computational Problems
IRR method also suffers from computational problems. These may be
discussed with reference to two aspects.
Computation in Conventional Cash Flows
It has been shown while computing the IRR that the calculation of the
IRR involves a trial-and-error procedure as a result of which
complicated computation has to be done. In conventional proposals
having a constant cash inflow stream (i.e. annuity) the computation, is
not so tedious.
Computation in Non-conventional Flows
The problem of computation of IRR gets accentuated when cash flow
patterns are non-conventional. The complications in such cases are
a)   that the IRR is indeterminate, and
b)   there may be multiple IRRs

Indeterminate IRR
For the following pattern of cash flows of an investment proposal, the IRR
cannot be determined.
Example 8
        CO0     = Rs 1
        CFAT1        2
        CO2          2
Where subscripts 0, 1, 2 refer to respective time periods, CFAT = cash inflows,
CO = cash outflows
The required equation to solve the IRR is:
                            2               2
                    1                           , which leads to r 2  1
                         1  r 2       1  r 
Clearly, the value of IRR is intermediate. On the other hand, the NPV of this
project, given k as 10 per cent, can be easily ascertained. This would be
negative (Rs –0.834), as shown below:

Clearly, the value of IRR is intermediate. On the other hand, the NPV of this
project, given k as 10 per cent, can be easily ascertained. This would be
negative (Rs –0.834), as shown below:
      Year              Cash flows         PV factor         Total present
        0                 Rs (1)             1.000                  Rs 1.000
        1                  +2                0.909                     1.818
        2                  (2)               0.826                   (1.652)

Multiple Rates of IRR
Another serious computational deficiency of IRR method is that it can yield
multiple internal rates of return. This is illustrated in Example 9.

Example 9
Initial cost                           Year 0                    (Rs 20,000)
Net cash flow                            1                            90,000
Net cash flow                            2                          (80,000)

                                                    Rs 90,000  Rs 80,000 
           The required equation is : Rs 20,000              
                                                     1  r   1  r 2 
Let (1 + r) be = X and divide both sides of equation by Rs 10,000, 2 = [(9/X) –
(8/X)2] = 0
Multiplying by X 2, we can transform the equation into the quadratic form, 2X 2
– 9X + 8 = 0
Such an equation with a variable to the second power has 2 roots which can
be identified as:

                b  b 2  4ac
            X                                                       (2)
where    a = coefficient of the variable raised to the second power
         b = coefficient of the variable raised to the first power
         c = constant or coefficient of the variable raised to the zero power
Substituting the values for a, b, and c into the quadratic formula produces
value for X of 1.21. Since X = (1 + r), the internal rates for this project are 21.9
and 228 per cent.

Thus, the project yields a dual IRR. This kind of problem does not
arise when the NPV method is used. The problem with the IRR is that
if two rates of return make the present value of the project zero, (21.9
and 228 per cent respectively in our example), which rate should be
used for decision-making purposes?
To conclude the discussion relating to the comparison of NPV and
IRR methods, the two methods would give similar accept-reject
decisions in the case of independent conventional investments. They
would, however, rank mutually exclusive projects differently in the
case of the
1)   Size-disparity problem,
2)   Time-disparity problem, and
3)   Unequal service life of projects.
The ranking by the NPV decision criterion would be theoretically
correct as it is consistent with the goal of maximisation of
shareholders’ wealth.

Net Present Value Vs. Profitability Index
In most situations, the NPV and PI, as investment criteria, provide the same
accept and reject decision, because both the methods are closely related to
each other. Under the PI method, the investment proposal will be acceptable if
the PI is greater than one; it will be greater than one only when the proposal
has a positive net present value. Likewise, PI will be less than one when the
investment proposal has negative net present value under the NPV method.
However, while evaluating mutually exclusive investment proposals, these
methods may give different rankings.
Example 10
Year                                            Project A              Project B
0                                              (Rs 50,000)            (Rs 35,000)
1                                                   40,000                 30,000
2                                                   40,000                 30,000
Present value of cash inflow (0.10)                 69,440                 52,080
NPV                                                 19,440                 17,080
PI                                    69,440/50,000 = 1.39   52,080/35,000 = 1.49

Thus, project A is acceptable under the NPV method, while project B under
the PI method. Which project should the firm accept? The NPV technique is
superior and so project A should be accepted.
   Project Selection Under Capital
The capital rationing situation refers to the choice of investment proposals
under financial constraints in terms of a given size of capital expenditure
budget. The objective to select the combination of projects would be the
maximisation of the total NPV. The project selection under capital rationing
involves two stages:
(1) identification of the acceptable projects.
(2) selection of the combination of projects.
The acceptability of projects can be based either on profitability index or
IRR. The method of selecting investment projects under capital rationing
situation will depend upon whether the projects are indivisible or divisible.
In case the project is to be accepted/rejected in its entirety, it is called an
indivisible project; a divisible project, on the other hand, can be
accepted/rejected in part. These are illustrated in Examples 11 and 12
Example 11 (Divisible Project)
A company has Rs 7 crore available for investment. It has evaluated its options and
has found that only 4 investment projects given below have positive NPV. All these
investments are divisible. Advise the management which investment(s)/projects it
should select.
Project           Initial investment (Rs      NPV (Rs crore)             PI
X                            3.00                  0.60                 1.20
Y                          2.00                      0.50                 1.25
Z                          2.50                      1.50                 1.60
W                          6.00                      1.80                 1.30
         Ranking of the Projects in Descending Order of Profitability Index
Project and (rank)     Investment outlay      Profitability index     NPV (Rs crore)
                           (Rs crore)
Z (1)                         2.50                   1.60                  1.50
W (2)                         6.00                   1.30                  1.80
Y (3)                         2.00                   1.25                  0.50
X (4)                         3.00                   1.20                  0.60
Accept Project Z in full and W in part (Rs 4,50,000) as it will maximise the NPV.

Example 12 (Indivisible Project) A company working against a self-imposed
capital budgeting constraint of Rs 70 crore is trying to decide which of the
following investment proposals should be undertaken by it. All these
investment proposals are indivisible as well as independent. The list of
investments along with the investment required and the NPV of the projected
cash flows are given as below:
Project                    Initial investment (Rs       NPV (Rs crore)
A                                   10                        6
B                                   24                        18
C                                   32                        20
D                                   22                        30
E                                   18                        20
Which investment should be acquired by the company?
NPV from investments D, E and B is Rs 68 crore with Rs 64 crore utilised
leaving Rs 6 crore to be invested in some other investment outlet. No other
investment package would yield an NPV higher than this amount. The company
is advised to invest in D, E and B projects.
Trial and error process is an integral part of selecting optimal investment
packages/set in capital ratinoning situation. Consider Example 13.
Example 13 Sound Limited has a financial resource constraint of a maximum of Rs
65 lakh in the current year. It has evaluated a large number of investment projects
but has discarded all except those listed below. All the listed investment proposals
are independent. The selected list of investments provide investment outlays, gross
present value, NPV and present value index.
Project         Investment           NPV        Gross present         Present value
                     outlay                             value                index
A             Rs 21,85,000    Rs 15,07,500        Rs 36,92,500                 1.69
B                19,10,000       10,70,000           29,80,000                 1.56
C                15,50,000        2,15,000           17,65,000                 1.14
D                13,00,000        2,75,000           15,75,000                 1.21
E                11,45,000       15,80,000           27,25,000                 2.38
F                 9,40,000        4,25,000           13,65,000                 1.45
G                 6,75,000        6,20,000           12,95,000                 1.92
H                 5,35,000        3,90,000            9,25,000                 1.73
I                 4,65,000        6,10,000           10,75,000                 2.31
J                 4,30,000        4,77,500            9,07,500                 2.11
K                 4,10,000        2,95,000            7,05,000                 1.72
L                 3,50,000        3,05,000            6,55,000                 1.87
M                 2,75,000        1,07,500            3,82,500                 1.39
N                 2,45,000        2,05,000            4,50,000                 1.84
O                 1,90,000        3,00,000            4,90,000                 2.58
               1,26,05,000       83,82,500         2,09,87,500
Which investments should be acquired by Sound Limited?
Solution First, we should arrange the investment projects in descending order of
present value (PI) index. The optimal investment portfolio/set will be one which
yields the maximum NPV. The investment projects are accordingly listed below.
Project   PI      Investment outlays of              NPV of
                  Project          Cumulative        Project                Cumulative
O         2.58       Rs 1,90,000       Rs 1,90,000            Rs 3,00,000   Rs 3,00,000
E         2.38         11,45,000         13,35,000             15,80,000      18,80,000
I         2.31          4,65,000         18,00,000               6,10,000     24,90,000
J         2.11          4,30,000         22,30,000               4,77,500     29,67,500
G         1.92          6,75,000         29,05,000               6,20,000     35,87,500
L         1.87          3,50,000         32,55,000               3,05,000     38,92,500
N         1.84          2,45,000         35,00,000               2,05,000     40,97,500
H         1.73          5,35,000         40,35,000               3,90,000     44,87,500
K         1.72          4,10,000         44,45,000               2,95,000     47,82,500
A         1.69        21,85,000         66,30,0001             15,07,500             —
B         1.56        19,10,000          63,55,000             10,70,000     58,52,5002
F         1.45          9,40,000                                 4,25,000
M         1.39          2,75,000                                 1,07,500
D         1.21        13,00,000                                  2,75,000
C         1.14        15,50,000                                  2,15,000
1 Not feasible at this stage; cumulative investment outlays exceed Rs 65 lakh.
2 Investment outlay as well as NPV consist of projects (from O to H) plus project B.

In case the company is guided simply by the PI index, then it selects the first
nine projects (numbered from O through K) plus project B. This investment
package yields an NPV of Rs 58,52,500.

Project     Investment outlays of                NPV of
            Project (s)             Cumulative       Project (s)      Cumulative
O to H                    —      Rs 40,35,000                  —     Rs 44,87,500
A             Rs 21,85,000           62,20,000     Rs 15,07,500         59,95,000
M                  2,75,000          64,95,000            1,07,500      61,02,500
Such a substitution exercise involves a trial and error approach. Thus, the
optimal investment package consists of 10 projects (O, E, I, J, G, L, N, H, A and
M) requiring a total investment outlay of Rs 64.95 lakh, yielding a total NPV of
Rs 61,02,500.

Fallout of Capital Rationing
Capital rationing limits the amount to be spent on capital expenditure
decisions. The firm may impose such a limit primarily for two reasons: (i)
there may be a paucity of funds and(ii) corporate managers/owners may be
conservative and may not like to invest more than a specified/stated sum in
capital projects at one point of time; they may like to accept projects with a
greater margin of safety, measured by NPV.
Whatever might be the reasons for capital rationing, it usually results in an
investment policy that is less than optimal. The reason is that capital
rationing does not allow the business firm to accept all profitable investment
projects which could add to net present value and, thus, add to the wealth of
Another notable consequence is that capital rationing may lead to the
acceptance of several small investment projects (promising higher return per
rupee of investment) rather than a few large investment projects. Acceptance
of such a package of investment projects is likely to have a bearing on the
risk complexion of the business firm (perhaps it may decrease).
Finally, selection criterion of investment projects under capital rationing
(based on one-period analysis) does not reckon intermediate cash inflows
expected to be provided by an investment project.

Case 1
Avon Chemical Company Ltd is presently paying an outside firm Re 1 per gallon to
dispose of the waste material resulting from its manufacturing operations. At normal
operating capacity the waste is about 40,000 gallons per year.
After spending Rs 40,000 on research, the company discovered that the waste could be
sold for Rs 15 per gallon if it was processed further. Additional processing would,
however, require an investment of Rs 6,00,000 in new equipment, which would have an
estimated life of 5 years and no salvage value. Depreciation would be computed by the
reducing balance method @ 25 per cent. There are no other assets in the 25 per cent
Except for the costs incurred in advertising Rs 20,000 per year, no change in the
present selling and administrative expenses is expected if the new product is sold. The
details of additional processing costs are as follows: variable—Rs 5 per gallon of waste
put into process; fixed (excluding depreciation)—Rs 30,000 per year.
In costing the new product, general factory overheads will be allocated at the rate of Re
1 per gallon.
There will be no losses in processing, and it is assumed that all of the waste processed
in a given year will be sold in that very year. Waste that is not processed further will
have to be disposed off at the present rate of Re 1 per gallon. Estimates indicate that
30,000 gallons of the new product could be sold each year.
The management, confronted with the choice of disposing off the waste, or processing
it further and selling it, seeks your advice. Which alternative would you recommend?
Assume that the firm’s cost of capital is 15 per cent and it pays, on an average, 35 per
cent tax on its income.
Cash outflows:
Cost of additional investment                                           Rs 6,00,000
(i) Present value of cash inflows (excluding depreciation), t = 1 – 5
       Particulars                                                        Amount
Increase in sales revenue (30,000 × Rs 15)                              Rs 4,50,000
Cost saving: reduction in disposal costs (30,000 × Re 1)                    30,000
 Less: Incremental costs:                                                  4,80,000
  Variable (30,000 × Rs 5)                            Rs 1,50,000
  Fixed, manufacturing or processing                        30,000
  Advertising                                               20,000         2,00,000
Earnings before taxes                                                      2,80,000
 Less: Taxes                                                                98,000
CFAT                                                                       1,82,000
× PVIFA                                                                    (×)3.352
Total present value                                                        6,10,064
(ii) PV of tax shield due to depreciation
Year             Depreciation          Tax advantage      PV factor      Total PV
 1                 Rs 1,50,000              Rs 52,500         0.870     Rs 45,675
 2                     1,12,500                39,375         0.756        29,767
 3                       84,375                29,531         0.658        19,431
 4                       63,281                22,148         0.572        12,669
(iii) PV of tax advantage due to short-term capital loss: [0.35 × (Rs 1,89,844) ×
0.497] = Rs 33,023.
(iv) Determination of NPV
Gross present value [(i) + (ii) + (iii)]                              Rs 7,50,629
 Less: Cost of additional investment                                     6,00,000
NPV                                                                      1,50,629
Note: Rs 40,000 spent on research is irrelevant cost and so is the allocated
share of factory overheads.
Recommendation: Since the NPV is positive, the company is advised to
purchase new equipment.
Case 2
An educational institute is planning to install airconditioners for its new computer
centre. It has received proposals from 2 manufacturers. The first proposal is for the
installation of 6 window airconditioners @ Rs 25,000 each. The other is for the
installation of split airconditioners of an equal capacity costing Rs 2,00,000. The
useful life of window airconditioners is 6 years and that of split airconditioners is
10 years. The cash operating costs associated with each proposal are given below:
Year                                       Proposal 1                     Proposal 2
1                                           Rs 20,000                      Rs 18,000
2                                              20,000                         18,000
3                                              20,000                         18,000
4                                              25,000                         22,000
5                                              25,000                         22,000
6                                              25,000                         22,000
7                                                                             26,000
8                                                                             26,000
9                                                                             26,000
10                                                                            26,000
The salvage value of the window airconditioners at the end of 6 years is expected
to be Rs 10,000 and that of the split airconditioners Rs 15,000. Advise the
educational institute which proposal should be selected by it if its opportunity cost
of funds is 10 per cent.
Solution Equivalent Annual Cost
                                  Proposal 1
Particulars            Year                    Cost   PV factor (at           PV
Purchase cost          0              Rs 1,50,000            1.000    Rs 1,50,000
Operating costs        1                   20,000            0.909        18,180
                       2                   20,000            0.826        16,520
                       3                   20,000            0.751        15,020
                       4                   25,000            0.683        17,075
                       5                   25,000            0.621        15,525
                       6                   25,000            0.564        14,100
Salvage value          6                 (10,000)            0.564        (5,640)
Total PV                                                              Rs 2,40,780
Equivalent Annual Cost (EAC) = (Total present value of the project / PV of
annuity corresponding to the life of the project at the given cost of capital.
Rs 2,40,780/4.355 = Rs 55,288.17

                                  Proposal 2
Particulars         Year   Cost           PV factor (at 10%)     PV
Purchase cost       0       Rs 2,00,000                  1.000        Rs 2,00,000
Operating costs     1            18,000                  0.909             16,362
                    2            18,000                  0.826             14,868
                    3            18,000                  0.751             13,518
                    4            22,000                  0.683             15,026
                    5            22,000                  0.621             13,662
                    6            22,000                  0.564             12,408
                    7            26,000                  0.513             13,338
                    8            26,000                  0.467             12,142
                    9            26,000                  0.424              11,024
                    10           26,000                  0.386             10,036
Salvage Value       10         (15,000)                  0.386             (5,790)
Total PV                                                              Rs 3,38,174
Equivalent Annual Cost (EAC) = Rs 3,32,384/6.145 = Rs 55,032.38
Recommendation         The educational institution should        go     for     split
airconditioners as their equivalent annual cost is lower.

Case 3 Bhushan Organics supplies chemicals and dyes to various units in and
around NCR Delhi. The onsite delivery of chemicals and dyes every month is 2,000
units. The unit sale price is Rs 100. The cost per unit is Rs 50. It is using a tempo
which can carry a maximum of 80 units. The total distance covered in one trip is
400 kms. The cost of diesel in the NCR Delhi is Rs 25.5 per litre. The average
consumption of diesel is 8 kms per litre.
Due to increase in demand for dyes for industrial use, Bhushan Organics has an
opportunity to make and deliver 2,500 units per month. To cater to the increased
demand, the company is contemplating buying a mini truck with a capacity to carry
165 units. The required mini truck is available from Tata for Rs 14,00,000. The
tempo being currently used has a book value of Rs 6,00,000. It can be sold for Rs
4,00,000. The salary of the tempo driver is Rs 6,000 per month. If the mini truck is
acquired, Bhushan Organics would have to increase his monthly salary to Rs 8,000.
The consumption of diesel by the truck would average 5 kms per litre. The
maintenance cost of the mini truck would be Rs 8,500 compared to Rs 6,200
maintenance cost of the tempo. Bhushan Organics uses straight line method of
depreciation for tax purposes. The tempo has a remaining useful life of 5 years.
The mini could truck serve the need of the Bhushan Organics for the next 5 years.
The applicable tax rte is 35 per cent.
Ravindra Arora, the CEO of Bhushan Organics , has asked the CFO, Sunil Joshi, to
examine the financial viability of the proposal to replace the tempo by the mini truck
and make appropriate recommendation in this regard. Assume a required rate of
return of 14 per cent.
Solution: Financial Analysis of Replacement of Tempo by Mini Truck

(A) Incremental cashoutflow (t = 0)

Cost of mini truck                                      Rs 14,00,000

Less sale value of tempo                                    4,00,000

Less tax advantage on loss on sale of tempo:

Current book value                    Rs 6,00,000

Sale value                               4,00,000

Loss on sale                             2,00,000

Tax advantage                                 x 0.35        70,000 Rs 9,30,000

(B) Increment cash outflows (t = 1 – 5)
Incremental revenue1 (500 units x 12 months x Rs 100              6,00,000
Less incremental costs:
Cost of additional units2                       2,40,000
Diesel charges3                                 (15,300)
Maintenance cost4                                  2,300
Driver’s salary5                                  24,000
Depreciation6                                   1,60,000         4,71,000
Earnings before taxes                                             1,29,000
Less taxes (0.35)                                                  45,150
EAT                                                                83,850
Add depreciation                                                  1,60,000
CFAT (t = 1 – 5 years)                                            2,43,850
PVIFA5.14                                                          x 3.433
Total PV                                                                     8,37,137
NPV (B – A)                                                                  (92,863)
1 [ 500 units (2,500 units – 2,000 units) x 12 months x Rs 100]
2 (500 units x 12 x Rs 50)   3 Diesel charges

3 Diesel charges
                                                            Truck      Tempo
Mileage km/lit                                                  5               8
Kms per trip                                                  400         400
Trips/month (2,500 units ÷ 165 units per trip)                 15               -
               (2,000 units ÷ 80 units per trip) -               -         25
Kms annually (12 months x 15 x 400)                        72,000               -
               (12 months x 25 x 400)                            -    1,20,000
Diesel consumed (72,000 ÷ 5)                               14,400               -
           (1,20,000 ÷ 8)                                        -      15,000
Total cost (14,400 x Rs 25.5)                          Rs 3,67,700              -
          (15,000 x Rs 25.5)                                     - Rs 3,82,000
Savings in diesel cost (Rs 3,82,500 – Rs 3,67,200) =   (Rs 15,300)
4 Maintenance cost (Rs 7,500 – Rs 6,200)
5 Drivers salary [(Rs 8,000 – Rs 6,000) x 12 months)

6 Depreciation:
  Depreciation on truck (Rs 14,00,000 ÷ 5)              Rs 2,80,000
  Depreciation on tempo (Rs 6,00,000 ÷ 5)                  1,20,000
The proposal to acquire the mini truck and dispose off the tempo is
financially viable.   The CEO may approve it and initiate follow-up


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