The document provides cash flow information for 5 projects (Projects A, B, C, D and E) being considered by Alpha Limited for the years 2003 to 2006. It mentions that the company's cost of capital is 12% and all projects are divisible with no limitations on funds in subsequent years after 2003 which has a capital limitation of Rs. 110,000. The assistant is asked to calculate which project Alpha Limited should undertake based on the cash flow information and present value factors provided for 2003 to 2006.

1. Illustration 1 :
Zenith Industrial Ltd. are thinking of investing in a project
costing Rs. 20 lakhs. The life of the project is five years
and the estimated salvage value of the project is zero.
Straight line method of charging depreciation is followed.
The tax rate is 50%. The expected cash flows before tax
are as follows :
Year 1 2 3 4 5
Estimated Cash flow before
Depreciation and tax (Rs. lakhs) 4 6 8 8
10
You are required to determine the : (i) Payback Period for
the investment, (ii) Average Rate of Return on the
investment, (iii) Net Present Value at 10% Cost of
Sambattina Rambabu

2. Illustration 2 :
The relevant information for two alternative systems of internal transportation
are given below :
(Rs.)
Particulars System 1
System 2
Initial investment 60,00,000 40,00,000
Annual operating costs 10,00,000 900,000
Life 6 years 4 years
Salvage value at the end 20,00,000 15,00,000
Which system would you prefer if the cost of capital is 6%? Justify your
recommendation
with appropriate analysis.
[Present value of annuity at 6% for 6 years = 4.917 and for 4 years = 3.465.
Present value of
Rs. 1.00 at 6% at the end of 6the year 0.705 and that at the end of 4th year
0.792].
Sambattina Rambabu

3. Capital rationing
 Capital rationing is a situation where a
constraint or budget ceiling is placed on the
total size of capital expenditures during a
particular period. Often firms draw up their
capital budget under the assumption that the
availability of financial resources is limited.
 Under this situation, a decision maker is
compelled to reject some of the viable projects
having positive net present value because of
shortage of funds. It is known as a situation
involving capital rationingSambattina Rambabu

4. The total available budget for a company is Rs. 20 crores and
the total cost of the projects is Rs. 25 crores. The projets
listed below have been ranked in order of profitability. There
is possibility of submitting X project where cost is assumed to
be Rs. 13 crores and it has the Profitability Index of 140
Project Cost Profitability index
A 60000000 1.50
B 5 0000000 1.25
C 7 0000000 1.20
D 20000000 1.15
E 5 0000000 1.10
Which projects, including X, should be acquired by the
company?
Sambattina Rambabu

5. In a capital rationing situation (investment limit
Rs. 25 lakhs), suggest the most desirable
feasible combination on the basis of the
following data (indicate justification): Projects
B and C are mutually exclusive.
Projects Net cash flows NPV
A 1500000 600000
B 1000000 450000
C 750000 360000
D 600000 300000
Sambattina Rambabu

6. S. Ltd., has Rs. 10,00,000 allocated for capital
budgeting purpose. The following proposal and
associated profitability indexes have been determined.
Which of the above investment should be undertaken?
Assume that projects are indivisible and there is no
alternative use of the money allocated for capital
budgeting?
Projects Cost Profitability Index
1 3,00,000 1.22
2 1,50,000 0.95
3 3,50,000 1.2
4 4,50,000 1.18
5 2,00,000 1.2
6 64,00,000 1.05
Sambattina Rambabu

7. Alpha Limited is considering five capital projects
for the years 2003 and 2004. The company is
financed by equity entirely and its cost of
capital is 12%. The expected cash flows of the
projects are as belows:
Projects
Year end cashflows
2003 2004 2005 2006
A -70 35 35 20
B -40 -30 45 55
C -50 -60 70 80
D nil -90 55 65
E -60 -20 40 50
Sambattina Rambabu

8. All projects are divisible i.e., size of investment can
be reduced, if necessary in relation to availability
of funds. None of the projects can be delayed or
undertaken more than once. Calculate which
project Alpha Limited should undertake if the
capital available for investment is limited to Rs.
1,10,000 in 2003 and with no limitation in
subsequent years. For your analysis,
use the following present value factors :
Years 2003 2004 2005
2006
Factors 1.00 0.89 0.80 0.71
Sambattina Rambabu

9. Sambattina Rambabu

10. Terminal Value Method
Assumption :
(1) Each cash flow is reinvested in another project at
a predetermined rate of interest.
(2) Each cash inflow is reinvested elsewhere
immediately after the completion of the project.
Decision-making
If the P.V. of Sum Total of the Compound reinvested
cash flows is greater than the P.V. Of the outflows
of the project under consideration, the project will
be accepted otherwise not.
Sambattina Rambabu

11. Illustration :
 Original Investment Rs. 40,000
 Life of the project 4 years
 Cash Inflows Rs. 25,000 for 4 years
 Cost of Capital 10% p.a
Expected interest rates at which the cash inflows
will be reinvested :
Year-end 1 2 3 4
% 8 8 8 8
Sambattina Rambabu

12. Sambattina Rambabu

13. Sambattina Rambabu

14. RISK AND UNCERTAINLY IN CAPITAL
BUDGETING
Capital budgeting requires the projection of cash
inflow and outflow of the future. The future in
always uncertain, estimate of demand,
production, selling price, cost etc., cannot be
exact.
For example: The product at any time it become
obsolete therefore, the future in unexpected.
The following methods for considering the
accounting of risk in capital budgeting. Various
evaluation methods are used for risk and
uncertainty in capital budgeting are as follows:Sambattina Rambabu

15. (i) Risk-adjusted cut off rate (or method of
varying discount rate)
(ii) Certainly equivalent method.
(iii) Sensitivity technique.
(iv) Probability technique
(v) Standard deviation method.
(vi) Co-efficient of variation method.
(vii) Decision tree analysis.
Sambattina Rambabu

16. (i) Risk-adjusted cutoff rate
(or Method of varying)
This is one of the simplest method while
calculating the risk in capital budgeting increase
cut of rate or discount factor by certain
percentage an account of risk.
Sambattina Rambabu

17. Example 1
The Ramakrishna Ltd., in considering the purchase of a
new investment. Two alternative investments are available
(X and Y) each costing Rs. 150000. Cash inflows are
expected to be as follows:
Cash Inflows Year Investment X Investment Y
Rs. Rs.
1 60,000 65,000
2 45,000 55,000
3 35,000 40,000
4 30,000 40,000
The company has a target return on capital of 10%. Risk
premium rate are 2% and 8% respectively for investment X
and Y. Which investment should be preferred?
Sambattina Rambabu

18. Answer
Project X Project Y
Years
Discounting factor=
Cost of capital + Risk
premium
Rate(10%+2%=12%)
Cash
inflows
Present
Value
of CFAT
Discounting factor=
Cost of capital + Risk
premium
Rate(10%+8%=18%)
Cash
inflows
Present
Value
of CFAT
1 0.893 60000 0.847 85000
2 0.797 45000 0.718 55000
3 0.712 35000 0.609 40000
4 0.636 30000 0.516 40000
TOTAL PRESENT VALUE OF
CFAT TOTAL PRESENT VALUE OF CFAT
Sambattina Rambabu

19. (ii) Certainly equivalent
method
It is also another simplest method for calculating
risk in capital budgeting. It reduces expected
cash inflows by certain amounts. it can be
calculated by multiplying the expected cash
inflows by certainly equivalent co-efficient in
order to convert the uncertain cash inflow to
certain cash inflows.
Sambattina Rambabu

20. Exercise 14
There are two projects A and B. Each involves an
investment of Rs. 50,000. The expected cash
inflows and the certainly co-efficient are as under:
Risk-free cutoff rate is 10%. Suggest which of the
two projects. Should be preferred
Sambattina Rambabu

21. Step 1: calculate certainly cash inflows at
certainly co efficient factors.
Step 2: calculate present value of cash inflows at
discounting rate.
Step 3: Calculate NPV and take decision.
Sambattina Rambabu

22. Project A
Year
s
Cash
inflows(
1)
Certainly
Co
efficient(2)
Certainly
cash
inflows=3(1X2
)
(4)Presen
t value
factors
(5)PV
certainly
cash
inflows
1 35000 0.8 0.909
2 30000 0.7 0.826
3 20000 0.9 0.751
Sambattina Rambabu

23. Project B
Year
s
Cash
inflows(
1)
Certainly
Co
efficient(2)
Certainly
cash
inflows=3(1X2
)
(4)Presen
t value
factors
(5)PV
certainly
cash
inflows
1 25000 0.9 0.909
2 35000 0.8 0.826
3 20000 0.7 0.751
Sambattina Rambabu

24. (iii) Sensitivity technique
When cash inflows are sensitive under different
circumstances more than one forecast of the
future cash inflows may be made. These inflows
may be regarded on ‘Optimistic’, ‘most likely’ and
‘pessimistic’. Further cash inflows may be
discounted to find out the net present values
under these three different situations.
If the net present values under the three situations
differ widely it implies that there is a great risk in
the project and the investor’s is decision to accept
or reject a project will depend upon his risk
bearing activities. Sambattina Rambabu

25. Mr. Ritik is considering two mutually exclusive
project ‘X’ and ‘Y’. You are required to advise
him about the acceptability of the projects from
the following information
Sambattina Rambabu

26. Sambattina Rambabu

27. The net present values on calculated above
indicate that project Y is more risky as
compared to project X. But at the same time
during favourable condition, it is more
profitable also. The acceptability of the project
will depend upon Mr. Selva’s attitude towards
risk. If he could afford to take higher risk,
project Y may be more profitable.
Sambattina Rambabu

28. (iv) Probability technique
Probability technique refers to the each event of
future happenings are assigned with relative
frequency probability. Probability means the
likelihood of future event. The cash inflows of
the future years further discounted with the
probability. The higher present value may be
accepted.
Sambattina Rambabu

29. Example
Year
s
Project 1 Probability Project 2 Probabili
ty
0 10000 - 10000 -
1 10000 0.2 12000 0.2
2 18000 0.6 16000 0.6
3 8000 0.2 14000 0.2
Cost of capital is 15%
Sambattina Rambabu

30. (v) Standard deviation
method
Two Projects have the same cash outflow and
their net values are also the same, standard
durations of the expected cash inflows of the
two Projects may be calculated to measure the
comparative and risk of the Projects. The
project having a higher standard deviation in
said to be more risky as compared to the
other.
Sambattina Rambabu

31. From the following information, ascertain which
project should be selected on the basis of
standard deviation.
Year
s
Project 1 Probability Project 2 Probabili
ty
1 3200 0.2 3200 0.1
2 5500 0.3 5500 0.4
3 7400 0.3 7400 0.4
4 8900 0.2 8900 0.1
Sambattina Rambabu

32.  N= sum of all probabilities
Sambattina Rambabu

33. Inflow
s
(1)
Deviatio
n
(d) from
mean(2)
Square
deviation(3
)
Probability
(4)(f)
Weighted
deviation
(3*4)
Sambattina Rambabu

34. Inflow
s
(1)
Deviatio
n
(d) from
mean(2)
Square
deviation(3
)
Probability
(4)(f)
Weighted
deviation
(3*4)
Sambattina Rambabu

35. Mr. Kumar in considering an investment
proposal of Rs.40,000. The expected returns
during the life of the investment are as under:
Year I
Event Cash Inflow Probability
(i) 16,000 0.3
(ii) 24,000 0.5
(iii) 20,000 0.2
Sambattina Rambabu

36. Sambattina Rambabu

37. Sambattina Rambabu

38. Example 1
From the following information, calculate the
pay-back periods for the 3 projects. Which
requires Rs. 2,00,000 each? Suggest most
profitable project.
Year Project I Project II Project III
1 50,000 60,000 35,000
2 50,000 70,000 45,000
3 50,000 75,000 85,000
4 50,000 45,000 50,000
5 50,000 ------ 35,000
Sambattina Rambabu

39. Example 2
The machine cost Rs. 1,00,000 and has scrap
value of Rs. 10,000 after 5 years. The net
profits before depreciation and taxes for the
five years period are to be projected that Rs.
20,000, Rs. 24,000, Rs. 30,000, Rs. 26,000
and Rs. 22,000. Taxes are 50%. Calculate
pay-back period and accounting rate of return.
Sambattina Rambabu

40. Example 3
A company has to choose one of the following two
actually exclusive machine. Both the machines have
to be depreciated. Calculate NPV.
Cash inflows
Year Machine X Machine Y
0 –20,000 –20,000
1 5,500 6,200
2 6,200 8,800
3 7,800 4,300
4 4,500 3,700
5 3,000 2,000
Sambattina Rambabu

41. Example 4
A machine cost Rs. 1,25,000. The cost of capital is
15%. The net cash inflows are as under:
Year Rs.
1 25,000
2 35,000
3 50,000
4 40,000
5 25,000
Calculate internal rate of return and suggest
whether the project should be accepted of cost.
Sambattina Rambabu

42. Example 5
Which project will be selected under NPV and IRR?
A B
Cash outflow 2,00,000 3,00,000
Cash inflows at the end of
1 Year 60,000 40,000
2 Year 50,000 50,000
3 Year 50,000 60,000
4 Year 40,000 90,000
5 Year 30,000 1,00,000
Cost of capital is 10%.
Sambattina Rambabu

43. Example 6
SP Limited company is having two projects, requiring a
capital outflow of Rs. 3,00,000. The expected annual
income after depreciation but before tax is as follows:
Depreciation may be taken as 20% of original cost and
taxation at 50% of net income:
You are required to calculate:
(a) Pay-back period (b) Net present value
(c) According rate of return (d) Net present value
index.
(e) Internal rate of return.
Years 1 2 3 4 5
Rs 90000 80000 70000 60000 50000
Sambattina Rambabu

44. Example
From the following information, select which project
is better.
Cash Inflows (Year) I II
0 –20,000 –20,000
1 7,000 8,000
2 7,000 9,000
3 6,000 5,000
Risk less discount rate is 5%. Project I is less risks
as compared to project II. The management
consider risk premium rates at 5% and 10%
respectively appropriate for discounting the cash
inflows.
Sambattina Rambabu

45. There are two mutually exclusive projects I and II. Each
projects requires an investment of Rs. 60,000. The
following are the cash inflows and certainly co-efficient
are as follows.
Risk-free cutoff rate is 10%. Evaluate which project will
be considered
Sambattina Rambabu