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Lesson 13
Chapter 4
Capital Budgeting
Unit 2
LLoonngg--tteerrmm iinnvveessttmmeenntt ddeecciissiioonnss
After studying this lesson, you should be able to:
Describe and be able to use the IRR technique for evaluating capital
investments.
Understand the acceptance criteria for IRR. Explain some potential difficulties of several methods.
Compare IRR with NPV.
Understand and explain the use and role of capital rationing.
INTERNAL RATE OF RETURN (IRR)
The other important discounted cash flow technique of evaluation of capital budgetingproposals is known as IRR technique. The IRR of a proposal is defined as the discount
rate, which produces a zero NPV i. e., the IRR is the discount rate which will quite the
present value of cash inflows with the present value of cash outflow. The IRR is also
known as Marginal Rate of Return orTime Adjusted Rate of Return. Like the NPV, the
IRR is also based on the discounting technique. In the IRR technique, the future cash
inflows are discounted in such a way that their total present value is just equal to the
present value of total cash outflows. The time-schedule of occurrence of the future cash
flows is known but the rate of discount is not. Rather this discount rate is ascertained, by
the trial and error procedure. This rate of discount so calculated, which equates the
present value of future cash inflows with the present value of outflows, is known as the
IRR.
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Calculation:
Symbolically, the IRR is equal to the value of 'r' in the Equation
COo =nn
n
r
WCSV
r
CF
r
CF
R
CF
r
CF
or
CFo
)1()1()1()1()1()1(2
2
2
2
2
1
+
++
+
+
+
+
+
+
+
+
+
Where COO = cash outflow at time 0,
CFi = cash inflow at different point of time,
N = life of the project, andr = rate of discount (yet to be calculated)
SV&WC = salvage value and working capital at the end of the n years
The above Equation can also be written as
CO0 = nii
n
i r
WCSV
ri
CF
)1()(1 +
++
+=
Or o = 01 )1()(
COr
WCSV
ri nii
n
i
+
++
+=
CF
It may be noted in the Equation that this equation to be solved to ascertain the
value of 'r'. Unfortunately, the value of 'r' can only be ascertained by the trial and error
procedure together with linear interpolation.
Successive application of different discount rates to all cash flows must be made
until a close approximation of a zero NPV is found. With some experience, an analyst
will find that usually no more than two trials are necessary, because the first result will
show the direction of any refinement needed. A positive NPV indicates the need for a
higher discount rate, while a negative NPV calls for lowering the discount rate.
The specific procedure to find out the value of r implies finding out the net present
value of the proposal at two different assumed values of 'r' within which the IRR is
expected to lie. Thereafter, the two rates are interpolated to make the net present value
equal to zero.
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The detailed procedure for the calculation of IRR can be explained in two different
situations i. e.,
(i) When future cash flows are equal and take a form of annuity, and
(ii) When future cash flows are unequal. Both the situations have been taken up as
follows:
Case A: When future cash flows are equal:
A firm is evaluating a proposal costing Rs. 1,00,000 and having annual inflows of Rs.
25,000 Occurring at the end of each of next six years: There is no salvage value. The IRR
of the proposal may be calculated as follows:
Step 1:
Make an approximation of the IRR on the basis of cash flows data. A rough approxima-
tion may be made with reference to the payback period. The payback period in the given
case is 4 years. Now, search for a value nearest to 4 in the 6th year row of the PVAF
table. The closest figures are given in rate 12% (4.111) and the rate 13% (3.998). This
means that the IRR of the proposal is expected to lie between 12% and 13%.
Step 2:In order to make a precise estimate of the IRR, find out the NPV of the project for both
these rates as follows:
At 12%, NPV = (Rs. 25,000 x PVAF (12%, 6y) - Rs.l,00,000
=(Rs.25,000 x 4.111}-Rs.l,00,000
= Rs.2,775.
At 13%, NPV = (Rs. 25,000 x, PVAF (I3%, 6y) - Rs.l,00,000
= (Rs.25,000 x 3.998}-Rs 1,00,000
= Rs. -50.
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Step 3:
Find out the exact IRR by interpolating between 12% and 13%. It may be noted that IRR
is the rate of discount at which the NPV is zero. At 12%, the NPV is Rs. 2,775 and at
13% the NPV is Rs. -50. Therefore, the rate at which the NPV is zero will be higher than
12% but less than 13%. By interpolating difference of 1 %(13% - 12%), over NPV
difference of Rs. 2,825 [Rs: 2,775 -(-50)],
IRR = 12% +950,99775,02,1
000,00,1775,02,1
= 12.98%
So, the IRR of the project is 12.98%. The IRR can also be ascertained by starting
from 13%.
In such as case, the IRR is
IRR= 13% -950,99775,02,1
950,99000,00,1
= 12.98%
Case B: When future flows are not equal:
In case when the project is expected to generate an uneven stream of cash flows, the
calculation of the IRR is complicated. In order to minimize the number of calculations,
IRR can be calculated as follows.
I will explain this with the help of an example.
Example
Suppose a firm is evaluating a proposal costing Rs. 1,60,000 and expected to generate
cash inflows of Rs. 40,000, Rs. 60,000, Rs. 50,000, Rs. 50,000 and Rs. 40,000 at the end
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of each of next 5 years respectively. There is no salvage value thereafter. In this case,
there is an uneven stream of cash inflows and the IRR can be approximated as follows.
Step 1:
Find out the average annual cash inflow to get a Fake annuity.
Year
1
2
3
4
5
Cash inflows
(Rs.) CF
40,000
60,000
50,000
50,000
40,000
Total 2,40,000
= 2,40,000 /5 = Rs. 48,000.
Step 2:
Divide the initial outlay with the average cash inflows 1,60,000/48,000 = 3.33 yrs
Step 3:
Now, search for a value nearest to 3.33 in 5 years row of the PVAF table. The closest
figures given in table are at 15% (3.352) and at 16% (3.274). This means that the IRR of
the proposal is expected to lie between 15% and 16%.
Step 4:
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Find out the NPV of the proposal for both of these approximate rates as follows.
Year
1
2
3
4
5
Cash inflow
40,000
60,000
50,000
50,000
40,000
PVF (16%,5y)
.862
.743
.641
.552
.476
PVF (15%,5Y)
.870
.756
.658
.572
.497
PV (16%)
34,480
44,580
32,050
27,600
19,040
1,57,750
PV (15%)
34,800
45,360
32,900
28,600
19,880
1,61,540
At 16%, NPV = Rs. 1,57,750 - Rs. 1,60,000
= Rs. -2,250
At 15%, NPV = Rs. 1,61, 540-Rs. 1,60,000
=Rs.l, 540.
Step 5:
Find out the exact IRR by interpolating between 15% and 16%. At 15% the NPV is Rs.
1,540 and at 16% the NPY is Rs. -2,250. Therefore, the rate at which NPV is zero will be
more than 15%-but less than 16%. By interpolating the difference of 1% (i.e. 16% -
15%rover the NPV difference of Rs. 3,790 [i.e. Rs_ 2,250 - (- 1,540)],
IRR= 15% +750,57,1540,61,1
000,60,1540,61,
1
= 15.40%
So, the IRR of the project is 15.40%. The IRR can also be ascertained by starting from
16%. In such a case, the IRR is
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IRR = 16% -750,57,1540,61,1
750,57,1000,60,
1
= 15.40%
The Decision Rule:
In order to make a decision on the basis of IRR technique; the firm has to determine, in
the first instance, its own required rate of return. This rate, k, is also known as the cut-off
rate or the hurdle rate. A particular proposal may be accepted if its IRR, r, is more than
the minimum rate i. e., k, otherwise rejected. However, if the IRR is just equal to the
minimum rate, k, then the firm may be indifferent. In case of ranking of mutually
exclusive proposals, the proposal with the highest IRR is given the top priority while the
project with the lowest IRR is given the lowest priority. Proposals whose IRR is less than
the minimum required rate, k, may altogether be rejected.
This decision rule is based on the fact that the NPV of the project is zero if its
cash flows are discounted at the minimum' required rate i. e., k. If the proposal can give a
return higher than this minimum required rate, then it is expected to contribute to the
wealth of the shareholders. It may be noted however, that the IRR, r, of the proposal is
internal to the project while the minimum required rate, k, is external to the project.
The Critical Evaluation:
Besides the NPV technique, the IRR technique is the other important discounted cash
flow technique of evaluation of capital budgeting proposals. The IRR technique has been
compared with the NPV technique at a later stage.
However, the merits of the IRR technique can be summarized as follows:
i. The IRR technique takes into account the time value of money and the cash flows
occurring at different point of time are adjusted for time value of money to make
them comparable.
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ii. It is a profit-oriented concept and helps selecting those proposals which are
expected to earn more than the minimum required rate of return. So, the IRR
technique helps achieving the objective of maximization of shareholders wealth.
iii. The IRR of a proposal is expressed as a percentage and is compared with the cut-
off rate, which is also expressed as a percentage. Thus, the IRR has an appeal for
those who want to analyze proposal in terms of its percentage return.
iv. Like NPV technique, the IRR technique is also based on the consideration of all
the cash flows occurring at any time. The salvage value, the working capital used
and released etc. are also considered.
v. The IRR technique is based on the cash flows rather than the accounting profit.
Thus, it can be stated that the IRR technique possesses all the ingredients of a sound
evaluation technique. Still it has, on the other hand, some draw backs, as follows:
a) As far as the calculation of IRR is concerned, it involves a tedious and
complicated trial and error procedure.
b) An important drawback of the IRR technique is that it makes an implied
assumption that the future cash inflows of a proposal are reinvested at a rate equal
to the IRR. Say, in case of mutually exclusive proposals, say A and B having IRR
of 18% and 16%, the IRR technique makes an implied assumption that the future
cash inflows of project A will be reinvested at 18% while the cash inflows of
project B will be reinvested at 16%. It is imaginary to think that the same firm
will have different reinvestment opportunities depending upon the proposal
accepted.
c) Since, the IRR is a scaled measure, it tends to be biased towards the smaller
projects which are much more likely to yield high percentage returns over the
larger projects.
Example
A company is considering a new project for which the investment data are as
follows:
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Capital outlay Rs 2,00,000
Depreciation 20% p.a.
Forecasted annual income before charging depreciation, but after all other charges
are as follows:
Year 1 Rs 1,00,000
2 1,00,000
3 80,000
4 80,000
5 40,000
4,00,000
On the basis of the available data, set out calculation, illustrating and comparing the
following methods of evaluating the return:
(a) Payback method.
(b) Rate of return on original investment, and
(c) IRR.
Solution:
Since there is no tax, the annual income before depreciation and after other charges is
equivalent to Cash flows (CF).
(a) Capital outlay of Rs.2,00,000 is recovered in the first two years, Rs. 1,00,000
(year 1) + Rs 1,00,000 (year 2), therefore, the payback period is two years.
(b) Rate of return on original investment:
Year CF (Rs) Depreciation (Rs) Net income (Rs)
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1
2
3
4
5
1,00,000
1,00,000
80,000
80,000
40,000
40,000
40,000
40,000
40,000
40,000
60,000
60,000
40,000
40,000
2,00,000
Average Income = Rs. 2,00,000/5 = Rs. 40,000
Average incomeRate of Return =
Original investmentx 100
Rs 40,000=
Rs 2,00,000x 100 = 20%
(c) Calculation of IRR:
Total CF Rs 4,00,000Average CF =
No. of years=
5= 80,000
Cash outflows Rs 2,00,000PB value =
Average CF=
Rs 80,000= 2.5 years
Factors closest to PB value of 2.5 corresponding to 5 years (life of the project) are 2.532
(28%) and 2.436 (30%). Since the actual cash flow stream is higher in initial years than
average cash flows, higher discount rate of 33% may also be tried along with 30%.
Year CF (Rs.) PVF at Total PV (Rs.)
30% 33% 30% 33%
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1
2
3
4
5
1,00,000
1,00,000
80,000
80,000
40,000
0.769
0.592
0.455
0.350
0.269
0.752
0.565
0.425
0.320
0.240
76,900
59,200
36,400
28,000
10,760
75,200
56,500
34,000
25,000
9,600
2,11,260 2,00,900
The IRR of a project is the rate of discount at which the NPV is 0. Since the NPV
at 33% is Rs. 900 only (i.e., Rs. 2,00,900 Rs. 2,00,000), the IRR is 33% (approx).
Example
A firm whose cost of capital is 10% is considering two mutually exclusive projects X and
Y, the details of which are:
Year Project X Project Y
Cost 0 Rs. 70,000 Rs. 70,000
Cash inflows 1 10,000 50,000
2 20,000 40,000
3 30,000 20,000
4 45,000 10,000
5 60,000 10,000
Compute
i. Net Present Value at 10%,
ii. Profitability Index, and
iii. Internal Rate of Return for the two projects.
Solution
Calculation of NPV:
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CF (Rs.) PVF (10%,n) Total PV (Rs.)Year
1
2
3
4
5
X
10,000
20,000
30,000
45,000
60,000
Y
50,000
40,000
20,000
10,000
10,000
0.909
0.826
0.751
0.683
0.621
X
9,090
16,520
22,530
30,735
37,260
Y
45,450
33,040
15,020
6,830
6,210
Total PV
Less cash outflow
NPV
PI = (PV of inflows/PV of outflows)
1,16,135
70,000
46,135
1.659
1,06,550
70,000
36,550
1.522
Calculation of IRR:
Initial cash outlaysPayback value =
Average cash inflows
Rs 70,000Payback value =
Rs 33,000= 2.121
Rs 70,000Payback value =
Rs 26,000= = 2.692
The PVAF table indicates that for project X, the PV Factor closest to 2.121 against 5
years is 2.143 at 37% and Project Y, the PV factor closest to 2.692 is 2.689 at 25%. In the
case of Project X, since CF in the initial years are considerable smaller than the average
cash flows, the IRR is likely to be much smaller than 37%. In the case of Project Y, CF in
the initial years are considerably larger than the average cash flows, the IRR is likely to
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be much higher than 25 %. So, Project X may be tried at 27% and 28% and the Project Y
may be tried at 36% and 37%
Project X
Year CF (Rs.) PVF at Total PV (Rs.)
1
2
3
4
5
10,000
20,000
30,000
45,000
60,000
27%
0.787
0.620
0.488
0.384
0.303
28%
0.781
0.610
0.477
0.373
0.291
27%
7,870
12,400
14,640
17,280
18,180
28%
75,200
56,500
34,000
25,000
9,600
70,370 68,565
Since the NPV is Rs. 370 (i.e., Rs. 70,370 70,000) only, at 27%, the IRR is 27%
approx.
Year CF (Rs.) PVF at Total PV (Rs.)
1
2
3
4
5
50,000
40,000
20,000
10,000
10,000
36%
0.735
0.541
0.398
0.292
0.215
37%
0.730
0.533
0.389
0.284
0.207
36%
36,750
21,640
7,690
2,920
2,150
37%
36,500
21,320
7,780
2,840
2,070
71,420 70,510
Since the NPV @ 37% is Rs. 510 (i.e., 70,510 70,000) only, the IRR is likely to be
slightly more than 37% the results of the above calculations may be summarized as
follows:
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Project X Project Y
NPV 46,
PI 1.659 1.522
IRR 27% 37%
Example
A Company is considering the replacement of its existing machine, which is obsolete and
unable to meet the rapidly rising demand for its product. The company is faced with two
alternatives:
(i) To buy Machine A which is similar to the existing machine or
(ii) To go in for Machine B which is more expensive and has much greater
capacity.
The cash flow at the present level of operations under the two alternatives are as follows:
Cash flows (in lacs of Rs.) at the end of year:
0 1 2 3 4 5
Machine A -25 5 20 14 14
Machine B -40 10 14 16 17 15
The companys cost of capital is 10%. The finance manager tries to evaluate the
machines by calculating the following:
1. Net Present Value;
2. Profitability Index;
3. Payback period; and
4. Discounted Payback period.
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PV of cash inflow = 37.35 53.58
PV of Cash outflow 25.00 40.00
= 1.494 1.339
Calculation of Pay Back Period:
Cash inflows Cumulative cash inflowsYear
0
1
2
3
4
5
Machine A
-25
5
20
14
14
Machine B
-40
10
14
16
17
15
Machine A
-
-
5
25
39
53
Machine B
-
10
24
40
57
72
In both cases, the Pay Back Period is 3 Years.
Calculation of Discounted Payback Period:
Cash inflows Cumulative cash inflowsYear
0
1
2
3
4
5
Machine A
-25.00
4.15
15.00
9.52
8.68
Machine B
-40.00
9.10
11.62
12.00
11.56
9.30
Machine A
4.15
19.15
28.67
37.35
Machine B
9.10
20.72
32.72
44.28
53.58
Machine A Machine B
Outflow -25.00 -40.00
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In 3 years Pay back were 19.15 32.72
Unrecouped outflow 5.85 7.28
In 4the year Net Present value 9.52 11.56
5.85 7.28
Thus Pay back = 3 + = 3 +
9.52 11.56
= 3.614 years = 3.629 years
Conclusion:
1. NPV
2. Profitability Index
3. Payback Period
4. Discounted Payback
Machine A
12.35
1.494
3 years
3.164 years
Machine B
13.58
1.339
3 years
3.629 years
Choice
B
A
Indifferent
A
Because of rising demand of Companys product, Machine B should be the choice
as it has higher capacity and its NPV is also higher.
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NNooww iiss tthhee ttiimmee ttoo tteesstt yyoouurr uunnddeerrssttaannddiinngg::
MULTIPLE CHOICE QUESTIONS
1) The relevant cash flows of a capital budgeting project are:
(a) The total cash flows of the company.
(b) The added net income associated with the new project.
(c) The incremental after-tax cash flows that occur, given the decision to proceed
with the new project.
(d) The incremental added outflows, which occur if we proceed with the project.
2) Cash flows that have preceded the decision to proceed with the project or that
have been connected to be:
(a) Sunk.
(b) Irrelevant.
(c) Prior.
(d) Important in the evaluation of the project.
3) Which of the following is not generally included in the initial outlay of a capital
budgeting project?
(a) Funds for added net working capital
(b) The sale of the old facility the new project is replacing
(c) The sale of the new facility at the end of its useful life
(d) The cost of installation of the new facility
4) Morton Corp. is considering additional production facilities and expects inventory to
increase by Rs4 million, accounts receivable by Rs3 million, and accounts payable by
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Rs2 million. If other working capital accounts stay the same, what amount of added net
working capital should be considered as part of the initial outlay of this project?
(a) Rs9 million
(b) Rs5 million
(c) Rs7 million
(d) Rs1 million
5) While depreciation is not an operating cash flow, it is relevant in a capital budgeting
evaluation of operating cash flows because:
(a) Depreciation impacts the pre-tax operating cash flows but not the after-tax cash
flows.
(b) Depreciation, a non-cash expense, impacts the pre-tax operating cash flows, the
taxes paid, and the after-tax cash flows.
(c) Depreciation influences operating income before depreciation.
(d) A large amount of depreciation impresses investors and favorably impacts the
stock price of the company.
6) An added annual depreciation amount of Rs 60,000 associated with a project under
evaluation will increase operating cash flows by ______ for a company with a 40% tax
rate.
(a) Rs 60,000
(b) Rs 24,000
(c) Rs 36,000
(d) Not enough information is available.
7) A company is considering replacing extrusion equipment on its production line. The
old equipment can be sold for Rs 80,000 and has a book value of Rs 70,000. If it has a
40% tax rate, what is the total incremental cash flow related to selling the old equipment?
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(a) Rs 80,000
(b) Rs70, 000
(c) Rs 84, 000
(d) Rs 76, 000
8) Thomas Corp. is considering the purchase of a new machine that will generate an
additional Rs 100,000 in revenue and cost savings of Rs 20,000 per year. The first year
depreciation on the machine is Rs30,000. What are the after-tax operating cash flows for
the first year? Thomas has a tax rate of 40%.
(a) Rs 90, 000
(b) Rs 84, 000
(c) Rs 54, 000
(d) Rs 120, 000
9) In a capital budgeting project evaluation, the financing costs are considered when:
(a) Estimating the annual operating cash flows.
(b) Estimating the discount rate used in the NPV method.
(c) Estimating the initial outlay.
(d) Estimating the final terminal value payoff.
10) Morgan Corp. is studying the incremental cash flows of a pending replacement
investment. In Year 1, the new investment will increase cash revenues by Rs 40,000 per
year and reduce cash labor expenses by Rs 20,000. The added MACRS depreciation
expense is Rs 15, 000 and Morgan Corp. has a 40% tax rate. What is the incremental
after-tax cash flow for Year 1?
(a) Rs 15, 000
(b) Rs 45, 000
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(c) Rs 60, 000
(d) Rs 42, 000
Now we will move on to TRUE/FALSE exercises
1. The Raymond Company will spend Rs 25,000 to study the feasibility of building a
retail store at the junction of two interstate highways. If the store is built, the constructioncosts will be Rs1.5 million. The incremental start-up cost is Rs1.525 million.
(a) True(b) False
2. Initial costs for a project often include an investment in net working capital.
(a) True
(b) False
3. An increase in accounts payable is a cash outflow that is included in the net
working capital requirement for a project.
(a) True
(b) False
4. A tax decrease is a positive cash inflow.
(a) True(b) False
5. Lane International currently has depreciation expenses of Rs 953,000 a year. They
are considering building a new Rs5 million building that would be depreciated straight-
line over 30 years. The marginal tax rate of the firm is 35%. The new building would
provide an incremental positive cash flow from depreciation every year in the amount ofRs 58, 333.
(a) True(b) False
6. Fancy Shoes For You is considering adding a new line of ladies shoes called Jis
Right. Sales of Jis Right shoes are estimated at 11,000 pair a year at an average price of
Rs 42 per pair. Sales of existing shoe lines are expected to decline by Rs 1,81,000 a yearif Jis Right shoes are added to the selection. The incremental increase in sales is Rs
1,70,000.
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(a) True
(b) False
7. The payments on loans and the payment of dividends are called operational cash
flows and are included in the incremental cash flows of a project.
(a) True
(b) False
8. Project shutdown costs include the after-tax proceeds from the sale of project assets
and the recovery of the investment in net working capital.
(a) True
(b) False
9. Eddie has an old truck that he uses for hauling trash from his shop to the garbagedump. The transmission just went out and so Eddie had to install a new one at a cost of
Rs650. On top of that, the engine is now starting to run rough and Eddie is afraid it mayneed a serious overhaul. In frustration, Eddie decides to trade the truck on a newer model
priced at Rs 4,500. The dealer will give Eddie Rs500 as a trade-in value for the old truck.
Eddie is trying to evaluate the purchase of the newer truck. In his analysis, Eddie shouldignore the Rs650 he paid to replace the transmission.
(a) True(b) False
10. A project that contains a real option has less value than a project that does not
contain such an option.
(a) True
(b) False
11. When analyzing real options a probability of occurrence is assigned to each
possible course of action.
(a) True
(b) False
12. Martha Rae is considering selling a piece of equipment that her firm owns. There
is 15% probability the equipment will sell for Rs 45, 000, a 40% probability it will sellfor Rs 33,000 and a 45% probability that she can sell it for Rs 25,000. Martha should use
a selling price of Rs 25, 000 in her analysis as she tries to decide whether or not to place
an ad to sell this equipment.
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(a) True(b) False
13. Installation and delivery costs for new equipment should be included in the initial
investment cash flow amount.
(a) True
(b) False
14. The Precision Company is analyzing the installation of new computer software to
manage their daily workflow. The cost of the software, including staff training, is Rs49,000. The software is expected to have no effect on sales but should reduce labor costs
by Rs 20, 000 a year for the next several years. Software is charged as an expense when
purchased. The marginal tax rate is 32%. The net incremental operating cash flow in Year2 of the project is an increase of Rs13, 600.
(a) True
(b) False
Answers to multiple choices;
1(c), 2(a), 3(c), 4(b), 5(b), 6(b), 7(d), 8(b), 9(b), 10(d).
Answers to True/False
1(F), 2(T), 3(F), 4(T), 5(T), 6(F), 7(F), 8(T), 9(T), 10(F), 11(T), 12(F), 13(T), 14(T)
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