Lecture 26 capital budgeting

Amity Business School
1
Financial Management

2
2. DECISION CRITERIA
TECHNIQUES OF EVALUATION
Traditional or Time-adjusted or
Non-discounting Discounted cash flows
1.Payback period
2. Accounting Rate of 1. Net present value (NPV)
Return (ARR) 2. Profitability Index (PI)
3. Internal Rate of Return (IRR)

Payback Period
• The payback period is the time duration required to
recover the initial cash outflows. This method is
based on cash flows and not on accounting data.
Initial cash outflow
• Payback period =
Annual cash inflow

If the cash inflows are not uniform then
Payback period = time period in which the
cumulative cash flows are equal to initial
inflows.
Payback period = time period in which the cumulative cash flows
are equal to initial inflows.
Cash Flow yet to be recovered
Completed Years +
Cash flow for the next year

Q.A company is considering a proposal to spend Rs.
1,00,000 on a new proposal. The cash inflows are
expected as follows, year I Rs. 20,000, year II Rs.
30,000, year III Rs. 30,000, year IV Rs. 40,000, year
V Rs. 40,000,
Calculate Payback period for the above proposal.

Year Cash
inflows
(Rs.)
Cumulative
Cash inflows
(Rs.)
I 20,000 20,000
II 30,000 50,000
III 30,000 80,000
IV 40,000 1,20,000
V 40,000 1,60,000
Cash Flow yet to be recovered
Completed Years +
Cash flow for the next year
20,000
= 3 +
40,000
=3.5 Years

ACCEP/REJECT RULE
If the calculated payback is less than any predicted value then an
investment proposal is acceptable, otherwise it will be
rejected. i.e.
• Accept the project if Payback Period ≤ Maximum
Acceptable Payback Period.
• Reject the project if Payback Period > Maximum
Acceptable Payback Period
RANKING MUTUALLY EXCLUSIVE PROJECT
So far as ranking is concerned, the lower the value of the
payback, the higher will be the ranking of any investment
proposal. i.e.
Shortest Payback Period should be selected

Evaluation of Payback Method:
• It is a simple method in concept and
understanding.
• Since its emphasis is on early recovery of
investment, it automatically takes care of risk.
• Projects with smaller payback period is considered
safer and secure as compared to the projects with
longer payback

Drawbacks
It takes in to account only early cash flows
which determine the payback and ignores
those which come later. This may often
leading to wrong conclusions.

Year Project X Project Y
0 - 50,000 - 50,000
1 15,000 10,000
2 20,000 15,000
3 30,000 20,000
4 20,000 30,000
5 0 40,000
6 0 30,000
Total Cash Inflow 85,000 1,45,000

Interpretation
• If we calculate the payback period for the
above projects it is 2.5 years for project X
whereas for project Y it is 3 years two months.
• However a comprehensive analysis of projects
would show the project Y is superior with
greater value of inflows.
• Secondly, payback method ignores time value
of money.

Example:
Year Project X Project Y
0 -60,000 -60,000
1 10,000 30,000
2 20,000 20,000
3 30,000 10,000
Year Cumulative
CFATs
Project X
Cumulative
CFATs
Project Y
1 10,000 30,000
2 30,000 50,000
3 60,000 60,000
Total
Cash
inflow
60,000 60,000

Payback period =
Cash Flow yet to
be recovered
Completed Years +
Cash flow for the next
year
= 3 years for Project X & Y

Interpretation:
• The payback period for both the project is 3
years.
• On the basis of time value of money the project
Y will be superior.
• Payback period is considered only a measure of
capital recovery and it is not a perfect of
measure for profitability.

•In spite of these limitations of the payback
method, it is still widely used in modern
project appraisal mainly because of its
simplicity.
•However, it used only for a preliminary
screening and not for final decision
making

Discounted Payback Period
To overcome the limitation of the payback
that it does not use time value of money,
we may use the discounted cash flows in
order to calculate the payback period.
Obviously the discounted payback will be
longer than the simple payback period.

Example
• A company is
considering a project
with initial outflow of
Rs. 1,00,000. The Cash
inflows from the
project are expected
to be as follows. Find
out the payback
period by the
traditional method as
well as by discounted
method @ 10%
discount.
Year Cash Flows
(Rs. )
1 20,000
2 30,000
3 30,000
4 40,000
5 30,000
6 20,000

Year Cash
Flows
Disc
ount
@10
Cumulativ
e Cash
flows
Discounted
Cash flows
@ 10%
Discounte
d
Cumulativ
e Cash
flows
1 20,000 .909 20,000 18,182 18,182
2 30,000 .826 50,000 24,793 42,975
3 30,000 .751 80,000 22,539 65,514
4 40,000 .683 1,20,000 27,321 92,835
5 30,000 .621 1,50,000 18,628 1,11,463
6 20,000 .564 1,70,000 11,289 1,22,752

Solution
The Traditional Payback
period =
Annual cash inflows
1,00,000-80,000
=
1,20,000-80,000
= 3.5 Years
The discounted Payback
period =
Annual discounted cash
inflows
1,00,000-92,385
=
1,11,463–92,385
= 4.38 Years

Q1. Zap ltd has no funds constraints in considering the following projects
Project A B C D E
Pay back period 3.5yrs 3 yrs 2.5yrs 2 yrs 1 yrs
Management acceptable maximum Pay back period is 2.5 yrs
Suggest which project should be undertaken.
Case1. if all the projects are independent
Case2. If all the projects are mutually exclusive projects
Case3. if project B, C, D and E are independent and A is complimentary to E
Case4. if project D and E are mutually exclusive project and project B is complimentary
to project E

Q2.Gopal Industries Ltd is considering the purchase of a new machine which
would carry out some operations at present being performed by hands.
The two alternative models under consideration are “X” and “Y”.
The following information is available in respect of the two models:
X Y
Cost of Machine 10,00,000 15,00,000
Estimated Life (Years) 10 15
Estimated Savings in
Scrap (p.a.)
60,000 80,000
Additional Cost of
Supervision(p.a.)
65,000 85,000
Additional Cost of
Maintenance(p.a.)
35,000 50,000
Cost of Indirect Material
(p.a.)
30,000 40,000
Estimated savings in
wages:
(i) Wages per worker p.a. 3,000 3,000
(ii) No. of Workers not
required
200 250
Using the method of Pay-back Period, suggest
as to which model should be bought. Tax
@50%

Q3. Sun National is considering the purchase of a new machine, which will replace
Some manual operations. There are two alternatives X and Y. From the following
Information prepare a profitability statement and work out the payback period for each.
Model X Model Y
Cost of machine Rs. 1,50,000 Rs. 2,50,000
Estimated life 5 yrs 5 yrs
Cost of indirect materials Rs.6000 Rs.8000
Estimated savings in scrap Rs.10,000 Rs.15,000
Additional Cost of maintenance Rs.19,000 Rs.27,000
Estimated Savings in direct wages:
Employees not required 15 20
Wages per employee p.a. Rs.6000 Rs.6000
Tax rates is 50 per cent
Suggest which machine is preferred.
Q4 A project costs Rs.2,50,000 & yield an annual profits of Rs. 40,000 after depreciation
Of Rs.30,000 p.a. but before taxes @ 50%. Calculate payback period.

Accounting Rate of Return
Accounting Rate of Return means the
average annual yield on the project.
It is calculated by dividing the annual
average profits after taxes by the average
investment

Average PAT
ARR =
Average Investment

Annual Average profit After Tax is calculated as follows:
Total Expected Earning after Depreciation and taxes
Total Period of the Project=
Average Investment can be calculated as follow:
Average investment = Opening investment* + closing investment*/ 2
(for each period) (* including working capital)
(1)
(2)
Average Investment = Average investment1 + Average Investment 2 +……
average investment n
n
(for each year)
Average Investment =1/2 (original investment – scrap value) + working capital + scrap

Q5. Zoom Ltd provides you with the following information
Purchase price of machine Rs. 80,000
Installation charges Rs 20000
Estimated salvage value Rs 40,000
Useful Life is 4 yrs
Working capital required Rs10000
Annual Earnings before Depreciations and Taxes Rs.65000
Tax Rate 30%
Calculate the accounting rate of Return if the method of depreciation is
i. Straight line method
ii. Written down value method.( Depreciation is 20%)

Scientific Methods
•Net Present Value (NPV)
•Internal Rate of Return (IRR)
•Benefit- Cost (B-C) Ratio or
Profitability Index (PI)

Net Present Value (NPV)
• It is net present value of all the cash flows that occur during
the entire life span of a project
• The outflows will have negative values while the inflows will
have positive values.
• Obviously, if the present value of inflows is greater than
outflows, we get a positive NPV and if the present value of
outflows is greater than inflows, we get a negative NPV.

• The positive NPV means a net gain in value maximization and,
therefore, any project which gives a positive NPV is an
acceptable project and if it gives a negative NPV, then the
project should not be accepted.

NPV can be expressed as follows;
n
NPV = Σ Ct − C0
t=1 (1+k)t
Where
Ct= Net Cash Inflows in different Years (t)
k =The rate of interest or cost of capital at which
funds are to be discounted
C0 = Initial Investment, The initial amount spent on a project

Acceptance Criterion
NPV > 0, Accept
NPV < 0, Reject
NPV = 0 , Indifferent to accepting or rejecting the
project.

Example:
A firm is considering an
investment proposal worth
Rs.80,000. The CFATs (cash
flows after tax) are expected to
be as given.
The rate of discount is 10%.
Find out whether the project is
worthwhile or not.
Year CFATs
(Rs.)
1 15,000
2 22,000
3 27,000
4 29,000
5 21,000

Solution:
n Ct
NPV = Σ − C0
t = 1 (1+k) t
= 15,000/ (1.1) + 22,000/ (1.1)² + 27,000/ (1.1)³ +
29,000 / (1.1)4
+ 21,000/ (1.1)5
− 80,000
= 13,636.36 + 18,181.82 + 20,285.50 + 19807.39 +
13039.43 − 80,000
= 84,950.50 − 80,000 = Rs. 4,950.50

Interpretation:
In this project the PV of inflows is Rs. 84,950.50 while the PV of
outflows is Rs. 80,000. Hence the NPV is Rs. 4,950.50 which
makes the project an acceptable project because NPV is
positive.

Properties of NPV
The NPV method is a very scientific and appropriate technique
of capital budgeting and is therefore, widely used for investment
decision making.
The following properties can be identified.
• It is based on cash flows over the entire life of project.
• It considers time value of money.

• It is an absolute value.
• It possesses the property of additions, i.e. the total NPV of two
projects is the summation of their individual NPVs.
• NPV for different rates of interest can be found separately, and
• It allows different rates of interest for different time period in the
life of a project.

Limitations of NPV:
• It gives the absolute value and therefore, comparison between two
different projects is not easy, especially when they are of different
sizes.
• Many a times, it is not possible to know in advance the rate of
interest at which discounting is to be done. Similarly a given NPV
may not be appropriate if the rate of interest has changed.
• It may lead to wrong decision making especially when limited
funds are available and we have to choose between different
options.

Profitability Index (PI) OR
Benefit- Cost (B-C) Ratio
• NPV is an absolute value and therefore it is not appropriate for
comparing the relative profitability between different projects.
• In order to overcome this limitation of NPV, we make one
modification in it to make it a relative measurement. This is called
Profitability Index (P.I.) or Benefit Cost Ratio (B-C Ratio).

Profitability
Index
Present value cash inflows
Present value of cash outflows
=

Acceptance and Ranking Rule: -
• If the P.I. is greater than 1, then the project is to be accepted
and if it is less than 1 then it is to be rejected.
• However, if we have, several projects then the project with a
higher P.I. or B.C. ratio should have a higher ranking.

NPV & PI
• The NPV and PI are both based on a given rate of discount
and, therefore, the NPV and PI values change as soon as
the rate of discount is changing.
• Hence, any project which is acceptable at, say, 10% rate of
discount may not be the same at, say, 12% rate.
• Therefore, there is need to find out a technique which is
autonomous in itself and not dependent upon any
externally determined rate of interest.

Q. From the following information calculate the NPV of the two projects and suggest
Which of the two project should be accepted assuming discount rate of 10%.
project X Project Y
Initial investment Rs. 80,000 Rs.70,000
Estimated life 5 yrs 5 yrs
Scrap value Rs.10000 Rs.12000
Cash flows are as follows;
year1 year2 year3 year4 year5
Project X 25000 22000 18000 15000 12000
Project Y 28,000 26,000 25000 20000 15000

Q. No project will be accepted unless the yield is 10%. Cash inflows as well as the
Cash outflow of a project is given as follows;
Year outflow inflow
0 1,50,000 -
1 1,20,000 90,000
2 75,000
3 70,000
4 60,000
5 50,000
Salvage value at the end of the 5th
year is Rs 40,000. Calculate the NPV.

Q. From the following information analyse the two machines and suggest which
Machine should be purchase on the basis of NPV.
Machine X Machine Y
Purchase price Rs.500000 Rs.800000
Life of the machine 5 yrs 8 yrs
Salvage value nil nil
Method of depreciation straight line straight line
Tax rate 30% 30%
Annual sales Rs.10,00000 Rs.10,00000
Variable cost 40% of sales 30% of sales
Fixed cost other than depreciation Rs.100000 Rs.200000
Annuity factor for 5yrs and 8 yrs @ 10% 3.791 5.335

Internal Rate of Return (IRR)
• IRR is that rate of discount at which NPV is
zero.
It can be expressed as follows.
n Ct
0 = Σ
t=0 (1+k) t

Contd.
• The relationship
between discount
rate and NPV for
the previous
illustration of NPV
is calculated as
follows.
Rate of
Interest (%)
NPV (Rs.)
9 7,320.67
10 4,950.50
11 2,677.54
12 496.06
13 −1600.02
14 − 3611.29

Contd.
• This table shows that as the discount rate increase the
NPV goes on diminishing. It can therefore be
understood that a project which is acceptable at a
given rate of discount, say 11% may not be accepted
at 13% or 14%.
• It is therefore essential to know, the cut-off rate
where positive NPV converts into a negative NPV.
This cut off rate is the Internal Rate of Return (IRR)
where NPV is zero.

It can be expressed as follows
The Internal Rate of Return IRR can be calculated by use of
log or by a scientific calculator or by computer instantly.
However, the following method can be used for the purpose.
x
IRR = r +
x − y
Where r = the closest rate at which NPV is positive
x = value of positive NPV at that level
y = value of negative NPV at next higher rate

• For example, in the above illustration, the
value of r = 12%, the value of x = 496.06 and
the value of y = − 1600.02. Hence the IRR is
496.06
= 12 +
2096.08
= 12 + .2367 = 12.2367%

Acceptance and Ranking Rule for IRR
• The IRR should be greater than the given discount
rate (cost of capital) to make a project acceptable.
• If IRR is less than the cost of capital then, the
proposal can not be accepted as it will lead to a
negative NPV.
• Since, IRR is a rate of return, the project with a
higher IRR should be ranked higher than the other
project which has a lower IRR.

Properties of IRR
• It considers cash flows of projects in their entirety.
• It takes into account time value of money.
• It is useful in ranking of projects because it is a rate and not
any absolute value.
• It is independent of any externally determined rate
(discount rate or cost of capital), and hence ranking of
projects will not change with variation in cost of capital.
• It is particularly useful as it helps a businessman and also a
financer in assessing the margin of safety in a project.
• It is more appealing to the businessmen who are used to
thinking in terms of cost and return.

NPV Vs IRR
• Both NPV and IRR are considered scientific techniques of
a project’s financial appraisal and both are commonly
used.
• The NPV is an absolute value of a gain or loss, while IRR
is a rate of return from a given investment and, therefore,
more appropriate for comparison between different project
proposals as well as between a given IRR and different
costs of capital.
• In this respect IRR seems to be having an advantage. This,
however, may not always be so.

Q1.Initial investment Rs. 60,000. Life of the Asset 4 yrs
Estimated annual cash flows are as follows;
1st
year Rs. 15000
2nd
year Rs.20,000
3rd
year Rs.30,000
4th
year Rs.20,000
Calculate IRR
Q2. Q.A company proposes to install a machine involving a capital expenditure of Rs.
360000.
The Life of the machine is 5 yrs and its salvage value is nil at the end of the year.
The machine will produce the net income after depreciation is Rs.68000.P.a
The company pay taxes @ 45%. You are required to calculate the internal rate of return
of the Proposal.

Lecture 26 capital budgeting

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