INDIAN ACADEMY SCHOOL OF MANAGEMENT
STUDIES
HENNUR CROSS, KALYAN NAGAR POST, BANAGLORE
1. ABC Limited is evaluating two proposals A1 and A2, both having
cash flows of Rs. 30,000 each. However, these alternatives may
result in different cash inflows depending upon different
economic conditions, i.e., Good, Average and Bad. The
following information is available.
Particulars
Alternati
ve 1
10 years
Alternati
ve 2
15 years
Economic Life
Cash inflows :
(Annual)
Good Economic
8,000
6,000
condition
Average Economic
6,000
5,500
condition
Poor Economic
4,500
4,500
condition
Evaluate the proposals and advise the firm given that the minimum
required rate of return of the firm is 10%.
2 The following forecasts are made about a proposal which is being
evaluated by a firm.
Initial cash outlay = Rs. 12,000
Life = 4 years
Cash inflows = Rs. 4,500 (annual)
Cost of capital = 14%
Present Value Annuity Factor for 4 years at 14% = 2.9137
Present Value Annuity Factor for 3 years at 14% = 2.3216
Analyse the sensitivity of different variables with respect to NPV.
3.X Limited has to decide between rental of two types of machine
manufacturing the same product. Machine A, an expensive economy
model, rents for Rs. 1000 per month, but the variable production cost
is Rs. 0.25 per unit. Machine B rents for Rs. 3,000 per month, but the
variable production cost is only Rs 0.10 per unit. Monthly demand
varies between 10,000 and 19,000 units to the following
probabilities.
Demand
Probabili
(Units)
ties
10,000
0.12
12,000
0.17
15,000
0.41
17,000
0.24
19,000
0.06
Make a comparison of the two machines. Which machine has to be
rented ? If the demand is definitely known to be 10,000 units, would
the decision reverse ?
4.A company considering the purchase of a new machine for Rs.
3,50,000. It feels quite confident that it can sell the goods produced
by the machine so as to yield an annual cash surplus of Rs. 1,00,000.
There is however, some uncertainty as to the machine’s life. A
recently published Trade Association Survey shows that members of
the Association have between then owned 250 of these machines and
have found the lives of the machines vary as under :
Number of years of
Number of machines having
machine life
given life
3
20
4
50
5
100
6
70
7
10
Assuming a discount rate of 10%, the Net Present Value for each
different machine life is as follows:
Machine life
Net Present
(Years)
Value (Rs)
3
-1,01,000
4
-33,000
5
29,000
6
86,000
7
1,37,000
You are required to advise whether the Company should purchase a
new machine or not.
5. A company is considering two mutually exclusive projects X and Y.
Project X costs Rs. 30,000 and Project Y costs Rs. 36,000. You have
been given below the Net Present Value probability distribution for
each project.
Project X
Project Y
NPV (Rs)
Probability
NPV (Rs)
Probability
3000
0.1
3000
0.2
6000
0.4
6000
0.3
12,000
0.4
12,000
0.3
15,000
0.1
15,000
0.2
a.Compute the Expected Net Present Value of Projects X and Y.
b.Compute the risk attached to each project, i.e., standard deviation
of each probability distribution
c.Which project do you consider more risky, and why ?
6.Pioneer Projects Limited is considering accepting one of the two
mutually exclusive Projects X and Y. The cash flows and probabilities
are estimated as follows:
Project X
Project Y
Probability
Cash flows (Rs) Probability
Cash flows (Rs.)
0.10
12,000
0.10
8,000
0.20
14,000
0.25
12,000
0.40
16,000
0.30
16,000
0.20
18,000
0.25
20,000
0.10
20,000
0.10
24,000
Advise the Pioneer Projects Limited.
7.A company is considering investing in a new product with an
expected life of three years. It is estimated that if the demand for
the product is favourable in the first year, then, it is certain to be
favourable in the subsequent years. And, if it is low in the first year,
it would remain low in the years 2 and 3. The company feels that
cash flows over time are perfectly correlated. The cost of the project
is Rs. 50,000 and the possible cash flows for three years are as
follows:
Year 1
Year 2
Year 3
Cash flow Probabilit Cash Flow Probabilit Cash Flow Probabilit
(Rs)
y
(Rs.)
y
(Rs.)
y
NIL
0.10
5,000
0.15
NIL
0.15
10,000
0.20
20,000
0.20
7500
0.20
20,000
0.40
35,000
0.30
15,000
0.30
30,000
0.20
50,000
0.20
22,500
0.20
40,000
0.10
65,000
0.15
30,000
0.15
Assume a risk free discount rate of 5%. Calculate the Expected
Value and Standard Deviation of the Probability distribution of
possible Net Present Values. Assuming a normal distribution, what is
the probability of the Project providing a Net Present Value of (i) zero
or less (ii) of Rs. 15,000 or more ?
8. A project under evaluation is thought to involve a medium degree
of risk. The risk free discount rate is 4% and the appropriate risk
premium is believed to be 6%. The Project costing Rs. 1000 has the
following estimated NPV and the probabilities of different economic
conditions:
Market
NPV at 4%
NPV at 10%
Probability
Conditions
Good
1775
1487
Average
1220
989
Medium
665
492
Poor
110
-5
Bad
-445
-503
Analyse the expected NPV and its variability.
0.10
0.20
0.40
0.20
0.10
9.X Limited is considering a Project with the following cash flows :
(Rs.)
Year
Purchase of
Running Cost
Savings (Rs)
Plant
(Rs)
0
-7000
1
2,000
6,000
2
2,500
7,000
The cost of capital is 8%. Measure the sensitivity of the Project to
changes in the plant value, running costs and savings (considering
one factor at a time) such that NPV becomes zero. Which factor is
most sensitive to affect the acceptability of the project.
10. The Management of ABC Company is considering the question of
marketing a new product. The fixed cost required in the project is Rs.
4,000. Three factors are uncertain, viz., the selling price, variable
cost and the annual sales volume. The product has a life of only one
year. The Management has the data on these three factors as under :
Selling
Probabilit Variable
Probabilit Sales
Probabilit
Price (Rs) y
cost (Rs)
y
volume
y
(Rs)
3
0.20
1
0.30
2000
0.30
4
0.50
2
0.60
3000
0.30
5
0.30
3
0.10
5000
0.40
Consider the following sequence of thirty random numbers:
81, 32, 60, 04, 46, 31, 67, 25, 24, 10, 40, 02, 39, 68, 08, 59, 66, 90,
12, 64, 79, 31, 86, 68, 82, 89, 25, 11, 98, 16.
Using the sequence (First 3 random numbers for the first trial etc.,),
simulate the average profit for the above project on the basis of 10
trials.
11.X Limited is considering the purchase of a new plant requiring a
cash outlay of Rs. 20,000. The plant is expected to have a useful life
of 2 years without any salvage value. The cash flows and their
associated probabilities for the two years are as follows :
I year
II year
Year
Cash flow
Probability
Cash Flow
Probability
(Rs)
(Rs)
1
8000
0.3
4000
0.2
10,000
0.6
15,000
0.2
11,000
0.4
13,000
0.3
15,000
0.4
16,000
0.3
15,000
0.3
16,000
0.1
20,000
0.8
24,000
0.1
Presuming that 10% is the cost of capital, calculate the NPV of the
Project under different conditions of cash flows and suggest whether
the Project should be taken up or not.
12. D Limited has to choose one between two machines – Machine A
has low fixed costs and high unit variable costs, whereas Machine B
has high fixed cost and low unit variable costs. Consequently,
Machine A is suited to low level demand while Machine B is suited to
high level demand. It is assumed that there are only two possible
demand levels – low and high – and the estimated probability of each
of these events is 0.5. The estimated profits for each demand level
are as follows:
Low Demand
High Demand
Machine A
1,00,000
1,60,000
Machine B
10,000
2,00,000
There is a probability of employing a firm of marketing consultants
who would be able to provide a perfect prediction of the actual
demand. What is the maximum amount the company should be
prepared to pay the consultants for the additional information ?
13. The initial outlay for a capital investment project consists of Rs.
100 lakhs for Plant and Machinery and Rs. 40 lakhs for Working
Capital. Other details are summarized below:
Sales
1 Lakh units of output per year
for years 1 to 5
Selling price
Rs. 120 per unit of output
Variable cost
Rs. 60 per unit of output
Fixed overheads (excluding
Rs. 15 lakhs per year for years 1
depreciation)
to 15
Rate of depreciation on Plant and 25% on Written Down Value
Machinery
Method
Salvage value of Plant and
Equal to the Written Down Value
Machinery
method value at the end of 5th
year
Tax rate
40%
Time Horizon
5 years
Post tax cut-off rate
12%
Required :
I. Indicate the financial viability of the Project by calculating the
Net Present Value.
II. Determine the Sensitivity of the Project’s NPV under each of the
following conditions :
a. Decrease in Selling Price by 5%
b. Increase in Selling Price by 10%
c. Increase in cost of Plant and Machinery by 10%
14. MN Integrated Limited is considering a proposal for which the
following relevant information is provided.
Cost of the Project : Rs. 30,000
Life of the Project : 5 years
Annual sales at Rs. 30 each : 1400 units
Variable cost per unit : Rs. 20
Fixed cost : Rs. 3000
Depreciation : Rs. 2000
It is estimated that the following variables may take the values given
here under for different economic situations :
Particulars
Pessimistic
Optimistic
Number of units sold
800
1800
Selling price
Rs. 20
Rs. 20
Variable cost per unit Rs. 15
Rs. 4
Given the tax rate 50% and cost of capital 10%, analyse the
sensitivity of the NPV of the proposal with respect to (i) Number of
units sold; (ii) Selling price, and (iii) Variable cost per unit
15. Santaram Limited is considering to diversity into a new line of
business by acquiring a running firm by paying Rs. 20,00,000 in cash.
The Finance Department of the firm has prepared the following
report in support of the proposal.
Annual Projection
Sales
18,00,000
Less : Variable cost
12,00,000
Contribution
6,00,000
Less : Fixed Cost
1,00,000
Less : Depreciation
2,00,000
Profit Before tax
3,00,000
Less : Tax
1,00,000
Profit after tax
2,00,000
Cash flow (Profit after tax +
4,00,000
Depreciation)
Present Value Annuity Factor for
5.650
10 years at 12%
Present Value of Annual Cash
22,60,000
inflows (4,00,000 * 5.650)
Less : Cash outflow (Initial cost)
20,00,000
Net Present Value
2,60,000
However, as a Managing Director, you feel that the profit of the
project may vary widely as the variables contributing to NPV are
sensitive. For this purpose, the Sales, Variable Cost, Fixed Cost and
Initial Investment have been pointed out as sensitive. Under the
Optimistic, Pessimistic and Expected Situations, these variable may
take the following values.
Particulars
Optimistic
Expected
Pessimistic
Investment
18,00,000
20,00,000
24,00,000
Sales
21,00,000
18,00,000
15,00,000
Fixed Cost
80,000
1,00,000
1,30,000
Variable Cost
65%
66.67%
70%
(percentage)
Analyse the Sensitivity of these variables (one variable at a time) vis
a vis the NPV of the proposal.
16. A company is considering two mutually exclusinve projects,
Project X and Project Y. Project X costs Rs. 30,000 Project Y Rs.
36,000. You have been given below the NPV probability distribution
for each project.
Project X
Project Y
NPV
Probabil NPV
Probabil
estimate
ity
estimate
ity
3000
0.1
3000
0.2
6000
0.4
6000
0.3
12,000
0.4
12,000
0.3
15,000
0.1
15,000
0.2
I. Compute the Expected NPV of Projects X and Y.
II. Compute the risk attached to each project, i.e., Standard
Deviation of each probability distribution.
III.Which project do you consider more risky and why ?
IV.Compute the profitability index of each project.
17.Galpub and company proposes to install a central air conditioning
system on 1st January 2011 in their office which has been taken on
lease. The lease period is going to end after 3 years when the lessor
has agreed to pay Rs. 10,000 for the air conditioning system. Three
options of air conditioning are available, i.e., Gas, Oil and solid Fuel.
The cost of installation and running expenses of all these three
options under different weather conditions are as follows:
Particulars
Cost
Operating
expenses
Severe weather Mild
Other costs
weather
Gas
1,70,000
40,000
24,000
2,500 per
annum
Oil
1,50,000 53,000
37,000
2,500 per
annum
Solid Fuel
1,40,000 45,000
36,000
10,000 (year
2012)
The actual operating expenses will depend upon the weather
conditions and the rate of fuel prices. The fuel prices for the years
2012 and 2013 are expected to increase wither @15% per annum
(probability of 0.4) or @ 25% per annum (probability of 0.6). The
price increase of 2012 will be repeated in the year 2012 also. It is
estimated that chances of severe and mild weather are 70% and 30%
respectively in any year.
18. Shrimps Production Limited is to select a machine out of two
proposals P1 and P2. The former is a semi automatic model requiring
a fixed rental of Rs. 3000 per annum and variable cost of production
of Rs. 0.10 per unit. The later is an economy model requiring a field
rental of Rs. 1000 per annum and variable cost of production is Re.
0.25 per unit. The market demand has been showing fluctuations and
the probabilities of different demand levels have been put as follows:
Demand
Probability
10,000 units
0.12
12,000 units
0.17
15,000 units
0.41
17,000 units
0.24
19,000 units
0.06
Which model should be acquired ? What will be the decision, if the
demand level is known with certainty at 10,000 units ?
19. A firm has an investment proposal, requiring an outlay of Rs.
40,000. The investment proposal is expected to have 2 years
economic life with no salvage value. In year I, there is a 0.4
probability that cash inflow after tax will be Rs. 25,000 and 0.6
probability that cash inflow after tax will be Rs. 30,000. The
probabilities assigned to cash inflows after tax for the year II are as
follows :
Cash inflow
Rs. 25,000
for the year
I
Cash inflow
Probability
Probability
for the year
II
Rs. 12,000
0.2
Rs. 20,000
0.4
Rs. 16,000
0.3
Rs. 25,000
0.5
Rs. 22,000
0.5
Rs. 30,000
0.1
The firm uses 10% discount rate for the type of investment.
20.ABC Limited is evaluating two proposals A1 and A2, both having
cash flows of Rs. 30,000 each. However, these alternatives may
result in different cash inflows depending upon different economic
conditions, i.e., Good, Average and Bad. The following information is
available.
Particulars
Alternative 1
Alternative 2
Economic Life
10 years
15 years
Cash inflows :
(Annual)
Good Economic
8,000
6,000
condition
Average Economic
6,000
5,500
condition
Poor Economic
4,500
4,500
condition
Evaluate the proposals and advise the firm given that the minimum
required rate of return of the firm is 10%.
21. The following forecasts are made about a proposal which is being
evaluated by a firm.
Initial cash outlay = Rs. 12,000
Life = 4 years
Cash inflows = Rs. 4,500 (annual)
Cost of capital = 14%
Present Value Annuity Factor for 4 years at 14% = 2.9137
Present Value Annuity Factor for 3 years at 14% = 2.3216
Analyse the sensitivity of different variables with respect to NPV.
22.ABC Company is evaluating a proposal having initial outlay of Rs.
1,40,000 and economic life of 2 years. The cash inflows and the
respective probabilities have been found to be as follows :
Year 1
Year 2
Cash inflows
Probability
Cash inflows
Probability
(Rs.)
(Rs)
1,00,000
0.3
1,40,000
0.5
80,000
0.5
70,000
0.3
10,000
0.2
60,000
0.2
Evaluate the proposals given that the firm has minimum
required rate of return of 10%.
23.The following data in respect of proposal having an outlay of Rs.
6,000 has been submitted before PSR company.
Year
Cash
Probabilit Year
Cash
Probabilit
inflows
y
inflows
y
1
1000
0.1
3
1500
0.1
1500
0.2
2200
0.1
2000
0.4
2800
0.7
2500
0.2
3500
0.1
3000
0.1
2
2000
0.2
2500
0.3
2700
0.2
2800
0.3
Evaluate the proposal given that the discount rate is 15%.
24.XYZ is evaluating two equal size mutually exclusive proposals A
and B for which the respective cash flows together with associated
probabilities are as follows:
Cash inflows
Probabilities
Cash inflows
Probabilities
(Rs.)
(Rs)
2000
0.3
1000
0.1
4000
0.4
3000
0.1
6000
0.3
5000
0.4
7000
0.3
9000
0.1
Find out the risks of the proposals in terms of the standard deviation.
25. RST company is engaged in evaluating the following two mutually
exclusive proposals, P1 and P2, for which the relevant information is
as follows :
Proposal 1
Proposal 2
Cash inflows
Probability
Cash inflows
Probability
(Rs)
(Rs.)
1,50,000
0.3
-4,00,000
0.2
2,00,000
0.3
3,00,000
0.6
2,50,000
0.4
4,00,000
0.1
8,00,000
0.1
Evaluate the proposals in terms of the standard deviation and coefficient of variation.
26. ABC company is evaluating a project which requires an outlay of
Rs.20,000 and is expected to produce cash inflow for 3 years as
follows:
Year 1
Year 2
Year 3
Cash
Probabilit Cash
Probabilit Cash
Probabilit
inflow
y
inflow
y
(Rs)
(Rs)
6000
0.3
4000
0.2
10,000
0.4
8000
0.6
14,000
0.3
12,000
0.2
Evaluate the proposal given data, the risk free
inflow
y
(Rs)
6,000
0.3
10,000
0.4
14,000
0.3
rate of return 6%.
27.ABC company is considering a proposal having an initial outlay of
Rs. 1,50,000 and a life of 2 years. The firm’s required rate of return
is 10%. It is expected that the cash flow for the year 2 is affected by
the cash flow of the year 1. Other details of the cash inflows are as
follows:
Year 1
Year 2
Cash inflows
Probability
Cash inflows
Probability
(Rs)
(Rs)
1,00,000
0.4
1,40,000
0.5
60,000
0.3
70,000
0.2
60,000
0.6
2,00,000
0.6
1,20,000
0.3
80,000
0.1
Evaluate the proposal.
28. Simulation Model :
PQR company is evaluating the installation of a new automatic
machine in order to reduce the labour costs. The new machine can
also meet the demand for greater capacity needed to meet increase
in demand for the product and hence resulting in increase in profits
for atleast 3 years. However, due to uncertainty in the expected
demand for the product, the cash flows can not be accurately
estimated. The following probabilities have been assigned in this
reference.
Year 1
Year 2
Year 3
Cash
Probabilit Cash
Probabilit Cash
Probabiliti
inflows
ies
inflows
ies
inflows
es
(Rs.)
(Rs.)
(Rs)
10,000
0.3
10,000
0.1
10,000
0.3
15,000
0.4
20,000
0.2
20,000
0.5
20,000
0.3
30,000
0.4
30,000
0.2
40,000
0.3
The new machine is having a cost of Rs. 70,000 and the scrap value of
the old machine is estimated to be Rs. 28,000. Evaluate the proposal
given that the discount factor is 15%. Also analyse the risk inherent
in this situation by simulating the NPV values. Random numbers for
5 sets of cash flows are given here under. On the basis of simulation
exercise, also find out the expected NPV of proposal will be less than
0.
Year
Set 1
Set 2
Set 3
Set 4
Set 5
1
4
7
6
5
0
2
2
4
8
0
1
3
7
9
4
0
3
29. ABC Company has the funds of Rs.2,00,000 which expectedly are
not required for next few years and hence can be deposited in a bank
@ 15% interest payable annually. Alternatively, the funds can be
used to install a new machine for the production of a new item. For
this, the company has two options before it. Machine 1 costing Rs.
1,80,000 which is expected to give annual cash inflows of Rs.
1,00,000, Rs. 1,20,000 and Rs. 40,000 respectively for next three
years. Machine 2 costing Rs. 1,90,000 which is expected to give
annual cash inflows of Rs. 1,00,000, Rs. 1,00,000 and Rs. 50,000
respectively for the next 3 years. Present the decision situation in a
decision tree and evaluate the options.
30. Decision Trees :
A firm of investment consultants has been asked by one of its clients
with respect to investmet of a sum of Rs. 1,00,000 for a period of 2
years. After a thorough analysis of different opportunities, option A
and B have been short listed.
Option A will lead to a return of 8%, 10% or 12% in the first year, but
due to the nature of the option, there is a correlation between the
returns of the year 1 and year 2. The returns of the year 1 and the
probabilities of the different returns in year 2 are as follows:
Year 1
Year 2
Return
8%
10%
12%
8%
0.6
0.3
0.1
10%
0.2
0.5
0.3
12%
0.1
0.2
0.7
At this stage, the three different returns in year 1 are considered to
be equally likely. Option B has a certain return of 9.5% per annum.
Evaluate the options and draw a decision tree to represent the
alternative courses of action and outcome. On the basis of the
expected value of returns which option is preferable ?
31. PQR Company whose major product is X, is facing problems as the
product X, is facing problems as the product X deteriorates rapidly, it
can be produced on a monthly basis only and cannot be stored from 1
month to the next. At the start of each month, a production figure
for the month is decided and necessary raw materials are procured.
Unfortunately, the demand for the product X varies randomly and if
the demand is more than the monthly budgeted production, then the
sales are lost. If on the other hand, production is more than the
actual sales, then the sales are lost. If on the other hand, production
is more than the actual sale, then the goods unsold have no value.
The selling price per unit is Rs. 2,400 and the variable cost is Rs.
1,500 per unit.
On the basis of sales experienced, it is found that the monthly
demand for the product X is between 10 and 20 units. It may be
assumed that the demand of 10 units is considered as low demand,
demand of 15 units s medium demand and demand of 20 units as
high demand. These demand levels have the probabilities of 0.3, 0.6
and 0.1 respectively. Present the above information in the form of
decision tree and also evaluate the production level given that the
demand pattern does not change.
32. An investor has two alternative proposals for evaluation on the
basis of the following formation:
Project A
Project B
Cash inflows
Probability
Cash inflows
Probability
(Rs.)
(Rs)
75,000
0.6
52,500
1
25,000
0.4
His utility function states that he will get utilities of 6, 4 and 1 from
the first Rs. 25,000, second Rs. 25,000, third Rs. 25,000 and the
fourth Rs. 25,000 respectively. Evaluate the proposals with and
without utility function.
33. ABC Company is evaluating a proposal costing Rs. 3,00,000 and
an economic life of 2 years over which the expected cash flows
together with the probabilities have been estimated as follows:
Year 1
Year 2
Cash inflows
Probabilities
Cash inflows
Probabilities
(Rs. ‘000)
(Rs. ‘000)
200
0.3
100
0.3
200
0.5
300
0.2
300
0.4
200
0.3
300
0.5
400
0.2
400
0.3
300
0.3
400
0.4
500
0.3
Evaluate the project given that the abandonment value of the
proposal at the end of each year 1 is Rs. 2,50,000 and the rate of
discount is 12%.
34. ABC Company is considering two mutually exclusive machines X
and Y. The company uses a Certainty Equivalent approach to
evaluate the proposals. The estimated cash flow and certainty
equivalents are both machines are as follows :
Machine
Machine Y
X
Year
Cash
Certainty
Cash flow
Certainty
flows
equivalent
Equivalent
0
-30,000
100
-40,000
1.00
1
15,000
0.95
25,000
0.90
2
15,000
0.85
20,000
0.80
3
10,000
0.70
15,000
0.70
4
10,000
0.65
10,000
0.60
Which machine should be accepted, if the risk free rate of discount is
5%.
35. Determine the Risk Adjusted Net Present Value of the following
projects :
Particulars
A
B
C
Net cash
Rs. 1,00,000
Rs. 1,20,00
Rs.2,10,000
outlays
Project life
5 years
5 years
5 years
Annual cash
Rs. 30,000
Rs. 42,000
Rs. 70,000
inflow
Co-efficient of
0.4
0.8
1.2
variation
The company selects the risk adjusted rate of discount on the basis of
co-efficient of variation.
Co-efficient
Risk Adjusted
Present value factor 1 to 5 years
of variation
Rate of discount
at Risk Adjusted Rate of Discount
0.0
10%
3.791
0.4
12%
3.605
0.8
14%
3.433
1.2
16%
3.274
1.6
18%
3.127
2.0
22%
2.864
More than 2.0
25%
2.689
INDIAN ACADEMY SCHOOL OF MANAGEMENT
STUDIES
HENNUR CROSS, KALYAN NAGAR POST, BANAGLORE
IMPORTANT SUMS ON PROJECT ANALYSIS AND
IMPLEMENTATION – SELF STUDY SUMS
PROBABILITY ANALYSIS :
1.PQR Limited is considering the introduction of a new product. The
anticipated demand, probabilities of demand and profits for each products are
given below. Choice is to be made between Product X and Product Y.
Product X
Product Y
Product
Probability
Profit
Product
Probability
Profit
Demand
of demand
(Rs. in
Demand
of Demand
(Rs in
(units)
(%)
crores)
(units)
(%)
crores)
50,000
20
-8000
30,000
15
-12,000
60,000
10
-5000
40,000
15
-10,000
70,000
30
11,000
50,000
40
14,000
80,000
20
14,000
60,000
20
16,000
90,000
20
17,000
70,000
10
18,000
100
100
2.X Limited has to decide between rental of two types of machines
manufacturing the same product. Machine A, an inexpensive economy model,
rents for R. 1000 per month, but the variable production cost is Re.0.25 per
unit. Machine B rents for Rs. 3,000 per month, but the variable production
cost is only Re. 0.25 per unit. Machine B rents for Rs. 3,000 per month, but
the variable production cost is only Re.0.10 per unit. Monthly demand varies
between 10,000 and 19, 000 to the following probabilities:
Demand
10,0 12,0 15,0 17,0 19,0
(units)
00
00
00
00
00
Probability
0.12 0.17 0.41 0.24 0.06
Make a comparison of the two machines. Which machine X Limited should
rent ? If the demand is definitely known to be 10,000 units, would the decision
reverse ?
3.A firm wants to avoid risk and choose between either of two alternative
products. Both the products have the same contributory margin of Rs. 4 per
unit, the same increment in annual fixed costs (Rs.4 lakhs) and require similar
amounts of processing facilities. Both the product will have the same break
even volume of one lakh units and for any levels of sales will yield the same
profit contributions. Given the probability distribution of sales for Products 1
and 2, as under, which product the firm will prefer ?
Units
Product Product
sold
1
50,000
0.1
75,000
0.2
1,00,00
0.3
0
1,25,00
0.3
0
1,50,00
0.1
0
2,25,00
0
0
2
0.2
0.3
0.2
0.1
0.1
0.1
4.The following table presents the proposed cash flows for the projects M and
N with their associated probabilities. Which project has a higher preference
for acceptance ?
Possibilit
Project M
Project N
ies
Cash flow (Rs. in
Probabilit Cash Flow (Rs. in
Probabilit
lakhs)
ies
lakhs)
ies
1
7,000
0.10
12,000
0.10
2
8,000
0.20
8,000
0.10
3
9000
0.30
6,000
0.10
4
10,000
0.20
4,000
0.20
5
11,000
0.20
2,000
0.50
5.A Company has estimated the following demand level of the products :
Sales volume
10,0 12,0 14,0 16,0 18,0
(units)
00
00
00
00
00
Probability
0.10 0.15 0.25 0.30 0.20
It has assumed that the sales price of Rs. 6 per unit, marginal cost Rs. 3.50 per
unit, and fixed cost Rs. 34,000. What is the probability that : (a) the company
will break even in the period ? (b) the company will make a profit of atleast
Rs. 10,000 ?
6.A company has estimated the unit variable cost a product to be Rs. 10 and
the selling price is Rs. 15 per unit. Budgeted sales for the year are 20,000
units. Estimated fixed costs are as follows :
Fixed costs
50,0 60,0 70,0 80,0 90,0
(Rs)
00
00
00
00
00
Probability
0.10
0.3
0.3
0.2
0.1
What is the probability that the company will equal or exceed its target profit
of Rs. 25,000 for the year.
7.X Limited produces a range of products with an average contribution / sale
ratio of 30% on current prices. Currently, fixed costs are Rs. 1,50,000 per
annum and estimates are being prepared for the next budget period for which
the forecasts have been selected :
Sales at current 4,00,0 7,00,0 9,00,0
price
00
00
00
Probability
0.2
0.7
0.1
For the next budget period :
Inflation
12 6
2
rate
% % %
Probabilit 0.3 0. 0.
y
5
2
The inflation rate is expected to affect all the variable costs and 60% of the
fixed costs. The company anticipates being able to raise selling price in line
with inflation without losing sales. The probabilities shown are independent.
You are required to prepare a table of all positive results and calculate the
probability of atleast breaking even; Also calculate the probability of making at
least Rs. 70,000 profit.
8.Unique Products Limited is considering a proposal of whether to invest in a
project which would need an immediate expenditure on capital equipment of
Rs. 40,000. The Projected sales from the project has been estimated as
follows :
Sales volume
2,0 6,0 8,0 10,0 14,0
(units)
00
00
00
00
00
Probability
0.1 0.3 0.3 0.20 0.10
0
0
0
Once the sales are established at a certain volume in the first year, they will
continue at that same volume in subsequent years. The unit selling prices will
be Rs. 12, the unit variable cost will be Rs. 8. There will be additional fixed
cost of Rs. 20,000 (all cash items). The project will have a life of 6 years after
which equipment could be sold for scrap at a price of Rs. 3,000. You are
required to find out (a) the expected value of NPV of the project and (b) the
minimum volume of sales per annum required to justify the project. The cost
of capital of the company is 10%. Discount factor of Re.1 per annum for 6
years at 10% is 4.355 and the discount factor of Re.1 at the end of six years at
10% is 0.5645. Ignore taxation.
BEST AND WORST POSSIBLE ESTIMATES :
9. Forward Looking Limited is preparing their budget for 2009. In the
preparation of the budget, they would like to take no chances, but would like
to envisage all sorts of possibilities and incorporate them in the budget. Their
estimates are as under :
(a) If the worst possible happens, sales will be 8,000 units at a price of Rs. 19
per unit. The material cost will be Rs. 9 per unit, the Direct Labour will be Rs. 2
per unit and the variable overheads will be Rs. 1.50 per unit. The fixed cost
will be Rs. 60,000 per annum.
(b) If the best possible happens, sales will be 15,000 units at price of Rs. 20
per unit. The material cost will be Rs. 7 per unit, direct labour Rs. 3 per unit
and the variable overheads will be Re.1 per unit. The fixed cost will be Rs.
48,000 per annum.
(c) It is most likely however that the sales will be 2,000 units above the worst
possible level at a price of Rs. 20 per unit. The material cost Rs. 8, Direct
Labour Rs. 3, Variable overheads Re. 1 per unit. The fixed cost will be Rs.
50,000 per annum.
(d) There is a 20% probability that the worst will happen, a 10% probability
that the best will happen and a 70% possibility that the most likely outcome
will occur. What will be the expected value of profit as per the budget 2009?
10.Venkatesh Limited is always discarding old lines and introducing new lines
of products and is considering at present three alternative promotional plans
for ushering in new products. Various combination of prices, development
expenditure and promotional outlays are involved in these plans. High,
medium and low forecast of revenues under each plan have been formulated
and their respective probabilities of occurrence have been estimated. Their
budgeted revenues and probabilities along with other relevant data are
summarized below :
Particulars
Plan I Plan
Plan
II
III
Budgeted revenue with
probability :
High
30
24
50
(0.3)
(0.2)
(0.2)
Medium
20
20
25
(0.3)
(0.7)
(0.5)
Low
5
15
0
(0.4)
(0.1)
(0.3)
Variable cost as percentage
60%
75%
70%
of revenue
Initial Investment
25
20
24
Life in years
8
8
8
The company’s cost of capital is 12% and the income tax rate is 40%.
Investments in promotional programs will be amortised by the Straight Line
Method. The company will have net taxable income each year, regardless of
the success or failure of the new products.
(a)Substantiating with figures, make a detailed analysis and find out which of
the promotional plans is expected to be the most profitable ?
(b) In the worst event, which of the plans would result in maximizing the
profits.
11. Y Limited is reviewing the price that it charges for a major product line.
Over the past three years, the product has sales averaging 48,000 units per
annum at a standard selling price of Rs. 5.25. Costs have been raising steadily
over the past year and the company is considering raising this price to Rs.
5.75 or Rs. 6.25. The sales manager has produced the following schedule to
assist with the decision.
Price
Rs.
Rs.
5.75
6.25
Estimates of Demand :
Pessimistic Demand
35,00 10,00
(Probability 0.25)
0
0
Most likely Demand
40,00 20,00
(Probability 0.60)
0
0
Optimistic Demand
50,00 40,00
(Probability 0.15)
0
0
Currently the unit cost is estimated at Rs. 5 as follows:
Variable costs Rs.
:
Direct
2.5
Materials
0
Direct Labour 1.0
0
Direct
1.0
Overheads
0
4.5
0
Fixed
0.5
Overheads
0
Total
5.0
0
The company considers that the most likely value per unit variable cost over
the next year is Rs. 4.90 (probability 0.75), but it could be as high as Rs. 5.20
(probability 0.15) and it might even be as low as 4.75 (probability 0.10). Total
fixed costs currently are Rs. 24,000 per annum, but it is estimated that the
corresponding total for the coming year will be d: Rs. 25,000 with a probability
of 0.2; Rs. 27,000 with a probability of 0.6; Rs. 30,000 with a probability of 0.2.
(Demand quantities, unit costs and fixed costs can be assumed to be
statistically independent. Analyse the foregoing information in a way which
you consider will assist management with the problem, give your views on the
situation and advise on the new selling price. Calculate the expected level of
profit that would follow from the selling price that you recommend.
VALUE OF PERFECT INFORMATION :
12. A Limited has a choice between three projects X, Y and Z. The following
information has been estimated:
Projects
Market Demand Profit
(Rs. ‘000)
D1
D2
D3
190
50
15
110
200
160
150
140
110
0.6
0.2
0.2
X
Y
Z
Probabilit
ies
Which projects should be undertaken if the decision is made by Expected
Value Approach ? Calculate the Expected Value of Perfect Information.
13. Toys for Tiny Tots Limited manufactures high quality toys for children,
which are sold by mail order and through departmental stores. Kiddy Products
is prepared to sell the design and manufacturing rights for three products.
However, it will only sell the rights to one product, not to two or three. The
costs of the rights are : Pussy cat – Rs. 62,500; Teddy Bear – Rs. 75,000; Jack
in Box – Rs. 52,500. Toys for tiny tots Limited feel that any of these products
would make an attractive addition to its range through the products would
have sales life of only one year and wish to select the best of the three
products. The following information has been made available :
Particulars
Pussy
Teddy
Jack in
Cat
Bear
Box
Selling price per
199
140
115
unit
Variable cost per
98
75
65
unit
Fixed production 70,000
95,000
60,000
cost
Advertisement
55,000
40,000
20,000
These figures have been worked out with great care and circumspection. But,
when it comes to sales volumes, the Sales Manager could provide only the
following analysis of possibilities.
Pussy Cat
Teddy Bear
Jack in Box
Volume in
Probabil Volume in
Probabil Volume in
Probabili
units
ity
units
ity
units
ty
2000
0.7
Nil
0.1
2500
0.1
3000
0.2
3000
0.4
3000
0.3
4000
0.1
6000
0.5
4000
0.4
5000
0.2
You are required to advice the company of the best course of action based on
the above information . In the case of Teddy bear, it is felt that the company
should launch a market research study costing Rs. 20,000 which would be able
to determine precisely whether the sales would be NIL, 3000 or 600 units. Is it
worthwhile to undertake the study ? Assume all the costs are avoidable.
STANDARD DEVIATION :
14.Pioneer Projects Limited is considering accepting one of the two mutually
exclusive projects X and Y. The cash flow and probabilities are estimated as
follows :
Project X
Project Y
Probabil Cash flow
Probabil Cash Flow
ity
(Rs)
ity
(Rs.)
0.10
12,000
0.10
8,000
0.20
14,000
0.25
12,000
0.40
16,000
0.30
16,000
0.20
18,000
0.25
20,000
0.10
20,000
0.10
24,000
Advice the Pioneer Projects Limited.
15. Based on the data given below, ascertain which of the following two
projects would be more risky based on the criteria of co-efficient of variation ?
Project A
Project B
Cash flow
Probabil Cash flow
Probabili
(Rs)
ity
(Rs.)
ty
3000
0.10
2000
0.10
3500
0.20
3000
0.25
4000
0.40
4000
0.30
4500
0.20
5000
0.25
5000
0.10
6000
0.10
16. A company is trying to choose between two investment proposals A and B.
Project A has a standard deviation of Rs. 6500 while project B has a standard
deviation of Rs. 7,200. The Finance Manager wishes to know which
investment to choose, given each of the following combinations of the
expected values :
(a) Project A and Project B both have expected net present value of Rs. 15,000
(b) Project A has Expected NPV of Rs. 18,000 while Project B has Rs. 22,000.
17. Given the following information, find out which project is more risky,
either A or B.
State of the
Probability of
Actual cash flow
Market
occurrence
(Rs)
Project Project
A
B
High
0.2
1000
1200
Normal
0.6
800
800
Low
0.2
600
400
SENSITIVITY ANALYSIS
18. From the following project details, calculate the sensitivity of the (a)
Project Cost, (b) Annual Cash Flow and (c) Cost of Capital. Which variable is
the most sensitive ?
Project Cost Rs. 12,000; Annual Cash flow Rs. 4,500; Life of the Project 4
years; Cost of capital 14%. The annuity factor at 14% for 4 years is 2.9137
and at 18% for 4 years is 2.6667.
19. X Limited is considering a project with the following cash flows:
Yea Purchase of the
Running cost Savings
r
Plant
(Rs)
(Rs)
0
70,000
Nil
Nil
1
Nil
20,000
60,000
2
Nil
25,000
70,000
The cost of capital is 8%. Measure the sensitivity of the project to changes in
the level of running cost, savings and plant cost. Which factor is the most
sensitive ? The present values of Re.1 at 8% for the year 1 = 0.9259 and for
the year 2 = 0.8573.
20. VERY VERY IMPORTANT SUM ON SENSITIVITY ANALYSIS
:
The initial investment outlay for a capital investment project consists of Rs.
100 lakhs for plant and machinery and Rs. 40 lakhs for working capital. Other
details are summarized as follows:
Sales
:
1 lakh units of output per year for years 1
to 5.
Selling price
:
Rs. 120 per unit of output
Variable cost
:
Rs. 60 per unit of output
Fixed overheads (excluding depreciation) :
Rs. 15 lakhs per year for
years 1 to 5
Rate of depreciation on plant and machinery
:
25% on WDV method
Salvage value of plant and machinery
:
Equal to WDV method
Applicable tax rate
;
40%
Time Horizon
:
5 years
Post tax cut off rate
:
12%
Required ;
(a)Indicate the financial viability of the project by calculating the NPV.
(b) Determine the sensitivity of the project’s NPV under each of the following
conditions :
(i) Decrease in selling price by 5%; (ii) Increase ion variable cost by 10%; (iii)
increase in cost of plant and machinery by 10%.
SIMULATION MODELLING :
21. The Everalert Limited which has a satisfactory preventive maintenance
system in its plant, has installed a new Hot Air Generator based on electricity,
instead of fuel oil for drying its finished products. The Hot Air generator
requires periodicity shutdown maintenance. If the shutdown is scheduled
annually, the cost of maintenance will be as under :
Maintenance cost 15,0 20,0 25,0
(Rs.)
00
00
00
Probability
0.3
0.4
0.3
The costs are expected to be almost linear, i.e., if the shutdown is scheduled
twice a year the maintenance cost will be double. There is no previous
experience regarding the time taken between breakdowns. Costs associated
with break down will vary depending upon the periodicity of maintenance. The
probability distribution of break down cost is estimated as under :
Break down costs ( Rs per Shutdown once a Shutdown twice a
annum)
year
year
75,000
0.2
0.5
80,000
0.5
0.3
1,00,000
0.3
0.2
Simulate the total costs (maintenance costs and break down costs) and
recommend whether shutdown overhauling should be restored to once a year
or twice a year.
Random numbers for Alternative I : For Maintenance cost : 27, 44, 22, 32, 97
For Breakdown cost : 03, 50, 73, 87, 59
Random numbers for Alternative II : For Maintenance cost : 42, 04, 82, 38, 91
For Breakdown cost : 54, 65, 49, 03, 56
22. For a Washing Powder manufacturing company, frequency of contribution
(i.e., sale price – variable cost) per unit, annual demand and requirement of
investment were found as follows:
Contribution per unit 3 5 7 9 1
(Rs.)
0
Relative frequency
0. 0. 0. 0. 0.
1 2 4 2 1
Annual Demand (‘000
units)
Relative frequency
20
25
30
35
40
45
50
0.0 0.1 0.2 0.3 0.2 0.1 0.0
5
0
0
0
0
0
5
Required investment (Rs
in ‘000)
Relative frequency
1.7 2.0 2.5
50
00
00
0.2 0.5 0.2
5
0
5
Consider the random numbers 93, 03, 51, 59, 77, 61, 71, 623, 99, 15 for using
Monte Carlo simulation for 10 runs, to estimate the percentage of return on
investment (ROI) defined as :
ROI (%) = (Cash inflow / investment) * 100 for each run,
Recommend an optimum investment strategy based on model value dof ROI.
23. An investment company wants to study the investment projects based on
market demand, profit and the investment required, which are independent of
each other. Following probability distributions are estimated for each of these
three factors:
Annual Demand (‘000
25 30 35 40 45
50
55
units)
Probability
0.0 0.1 0.2 0.3 0.2 0.1 0.0
5
0
0
0
0
0
5
Profit per unit
3
5
7
9
10
Probability
0.1 0.2 0.4 0.2 0.1
0
0
0
0
0
Investment required (Rs.
275 300 350
in ‘000)
0
0
0
Probability
0.2 0.5 0.2
5
0
5
Using Simulation process, repeat the trial 10 times, compute the investment
on each trial taking these factors into trial. What is the most likely return ?
Use the following random numbers (30, 12, 16) (59, 09, 69), (63, 94, 26) (27,
08, 74), (64, 60, 61), (28, 28, 72), (31, 23, 57), (54, 85, 20), (64, 68, 18), (32,
31, 87). In the bracket above, the first random number is for annual demand,
the second one is for profit and the last one is for the investment required.
CERTAINTY EQUIVALENT AND RISK ADJUSTED DISCOUNT
RATE :
24. Delta Corporation is considering an investment in one of the two mutually
exclusive proposals.
Project A : It involves initial outlay of Rs. 1,70,000
Project B : It involves initial outlay of Rs. 1,50,000.
The Certainty Equivalent approach is employed in evaluating risky
investments. The current yield on treasury bills is 5% and the company uses
this as riskless rate. Expected values of net cash inflow which their respective
certainty equivalents are as follows :
Yea Project A
Project B
r
Cash inflow
Certainty
Cash inflow
Certainty
(Rs.)
Equivalent
(Rs.)
Equivalent
1
90,000
0.8
90,000
0.9
2
1,00,000
0.7
90,000
0.8
3
1,10,000
0.5
1,00,000
0.6
Answer the following with reasons :
(a)Which of the Project should be acceptable to the company ?
(b) Which Project is riskier and why ? Explain.
(c) If the company wants to use the risk adjusted discount rate method, which
project would be analysed with higher rate ?
25. Fast run Automobiles Spares Limited is considering the investment in one
of the three mutually exclusive projects Zeta 10, Meta 10, and Neta 10. The
company’s cost of capital is 15% and the risk free rate of return is 10%. The
income tax rate for the company is 40%. FASL has gathered the following
basic cash flow and risk index data for each project.
Projects
Zeta
Meta
Neta
10
10
10
Initial investment
15,00, 11,00, 19,00,0
000
000
00
Cash inflows after tax for
the year :
1
6,00,0 6,00,0 4,00,00
00
00
0
2
6,00,0 4,00,0 6,00,00
00
00
0
3
6,00,0 5,00,0 8,00,00
00
00
0
4
6,00,0 2,00,0 12,00,0
00
00
00
Risk index
1,80
1.00
0.60
Using the Risk Adjusted Discount Rate, Determine the Risk Adjusted NPV for
each of the project. Which project should be accepted by the company ? Give
reasons.
26. The projected cash flows and the Expected net abandonment values for a
project are given below:
Yea Cash
Abandonment
r
inflows
Values
0
(1,00,000
NIL
)
1
35,000
65,000
2
30,000
45,000
3
25,000
20,000
4
20,000
NIL
Should the project be abandoned and if so, when ? (Cost of capital may be
taken as 10%).