Chapter 6 - Investment Decision

Chapter 6
Investment Decisions
Capital Budgeting Techniques
Payback Period
Question 1 - Study Material
Suppose a project costs ₹ 20,00,000 and yields annually a profit of ₹ 3,00,000 after depreciation @ 12.5%
(Straight Line Method) but before tax 50%.What would be the payback period?

Question 2 - Study Material

Consider the following cash flows from two projects.(In ₹)
No. of years Project A Project B
1 Nil 40,000
2 Nil 50,000
3 5,000 1,20,000
4 20,000 10,000
5 50,000 10,000
6 1,50,000 Nil
7 50,000 Nil
8 40,000 Nil
Total 3,15,000 2,30,000
Both projects cost ₹ 1,50,000 each. You are required to compute the payback period for both projects. Which
project will you prefer?

Payback Reciprocal
Question 3 - Study Material
Suppose a project requires an initial investment of ₹ 20,000 and it would give annual cash inflow of ₹ 4,000.
The useful life of the project is estimated to be 5 years. What will be the Payback Reciprocal?

Accounting or Average Rate of Return (ARR)

Question 4 - Study Material
Suppose a project requiring an investment of ₹ 10,00,000 yields profit after tax and depreciation as follows:
Years Profit after tax and depreciation (₹)
1 50,000
2 75,000
3 1,25,000
4 1,30,000
5 80,000
Total 4,60,000
Suppose further that at the end of 5 years, the plant and machinery of the project can be sold for ₹ 80,000.
Calculate Average Rate of Return?

Question 5 - Study Material

Times Ltd. is going to invest in a project a sum of ₹ 3,00,000 having a life span of 3 years. Salvage value of
machine is ₹ 90,000. The profit before depreciation for each year is ₹1,50,000. The Profit after Tax and value of
Investment in the Beginning and at the End of each year shall be as follows:
Year Profit before Depreciation Profit after Value of investment
depreciation depreciation Beginning End
1 1,50,000 70,000 80,000 3,00,000 2,30,000
2 1,50,000 70,000 80,000 2,30,000 1,60,000
3 1,50,000 70,000 80,000 1,60,000 90,000
Compute ARR.

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 Chapter 6 - Investment Decision

Net Present Value (NPV)

Question 6 - Study Material
Compute the net present value for a project with a net investment of ₹ 1,00,000 and the following cash flows if
the company’s cost of capital is 10%? Net cash flows for year one is ₹ 55,000; for year two is ₹ 80,000 and for
year three is ₹ 15,000. [PVIF @ 10% for three years are 0.909, 0.826 and 0.751].

Question 7 - Study Material

ABC Ltd. is a small company that is currently analyzing capital expenditure proposals for the purchase of
equipment; the company uses the net present value technique to evaluate projects. The capital budget is
limited to ₹ 5,00,000 which ABC Ltd. believes is the maximum capital it can raise. The initial investment and
projected net cash flows for each project are shown below. The cost of capital of ABC Ltd. is 12%.
You are required to compute the NPV of the different projects. (In ₹)

Particulars Project A Project B Project C Project D

Initial 2,00,000 1,90,000 2,50,000 2,10,000
Investment
Project Cash
Inflows
Year 1 50,000 40,000 75,000 75,000
Year 2 50,000 50,000 75,000 75,000
Year 3 50,000 70,000 60,000 60,000
Year 4 50,000 75,000 80,000 40,000
Year 5 50,000 75,000 1,00,000 20,000

Question 8 - Study Material

Cello Limited is considering buying a new machine which would have a useful economic life of 5 years, a cost
of ₹ 1,25,000 and a scrap value of ₹ 30,000, with 80 per cent of the cost being payable at the start of the
project and 20 per cent at the end of the first year. The machine would produce 50,000 units per annum of a
new project with an estimated selling price of ₹ 3 per unit. Direct costs would be ₹ 1.75 per unit and annual
fixed costs, including depreciation calculated on a straight-line basis, would be ₹ 40,000 per annum. In the first
year and the second year, special sales promotion expenditure, not included in the above costs, would be
incurred, amounting to ₹ 10,000 and ₹ 15,000 respectively. Evaluate the project using the NPV method of
investment appraisal, assuming the company’s cost of capital to be 10 percent.
A. When tax rate is 50%
B. When tax rate is not mentioned (ignoring tax).

Desirability / Profitability Index

Question 9 - Study Material
There are three projects involving discounted cash outflow of ₹ 5,50,000, ₹ 75,000 and ₹ 1,00,20,000
respectively. Suppose that the sum of discounted cash inflows for these projects are ₹ 6,50,000, ₹ 95,000 and
₹ 1,00,30,000 respectively. Calculate the desirability factors for the three projects.

Question 10 - Rtp Nov 2022

K. K. M. M Hospital is considering purchasing an MRI machine. Presently, the hospital is outsourcing the work
received relating to MRI machine and is earning commission of
₹ 6,60,000 per annum (net of tax). The following details are given regarding the machine:
(₹)
Cost of MRI machine 90,00,000
Operating cost per annum (excluding Depreciation) 14,00,000
Expected revenue per annum 45,00,000
Salvage value of the machine (after 5 years) 10,00,000
Expected life of the machine 5 years
Assuming tax rate @ 40%, whether it would be profitable for the hospital to purchase the machine?
Give your RECOMMENDATION under:
1. Net Present Value Method, and
2. Profitability Index Method.
PV factors at 10% are given below:

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Year 1 2 3 4 5
PV factor 0.909 0.826 0.751 0.683 0.620

Internal Rate Of Return

Question 11 - Study Material
Calculate the Internal Rate of Return of an Investment of ₹ 1,36,000 which yields the following cash inflows:
YEAR CASH INFLOWS(RS)
1 30000
2 40000
3 60000
4 30000
5 20000

Question 12 - Study Material

A company proposes to install machine involving a capital cost of ₹ 3,60,000.The life of the machine is 5 years
and its salvage value at the end of the life is nil. The machine will produce the net operating income after
depreciation of ₹ 68,000 per annum. The company’s tax rate is 45% The Net present value factor for 5 years
are as under:
Discounting Rate 14 15 16 17 18
Cumulative Factor 3.43 3.35 3.27 3.20 3.13
You are required to calculate the internal rate of return of the proposal.

Modified Internal Rate Of Return

Question 13 - Study Material
An investment of ₹ 1,36,000 yields the following cash inflows. Determine the MIRR if the Cost of Capital = 8%
Year 1 2 3 4 5
CFAT(RS) 30,000 40,000 60,000 30,000 20000

Discounted Payback Period

Question 14 - Study Material
Suppose a project costs ₹ 20,00,000 and yields annually a profit of ₹ 3,00,000 after depreciation @ 12.5%
(Straight Line Method) but before tax 50%.What would be the Discounted payback period? Using discounting
rate as 10%.

Question 15 - Study Material

Consider the following cash flows from two projects.(In ₹)
No. of years Project A Project B
1 Nil 40,000
2 Nil 50,000
3 5,000 1,20,000
4 20,000 10,000
5 50,000 10,000
6 1,50,000 Nil
7 50,000 Nil
8 40,000 Nil
Total 3,15,000 2,30,000
Both projects cost ₹ 1,50,000 each. You are required to compute the Discounted payback period for both
projects. Which project will you prefer? Using discounting rate as 10%.

Using More than One Technique of Capital Budgeting

Question 16 - Rtp
A Ltd is considering a new 5-year project. Its investment costs and annual profits are projected as follows:
Investment Profits
Year 0 1 2 3 4 5
Amount(₹) (2,50,000) 40,000 30,000 20,000 10,000 10,000

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 Chapter 6 - Investment Decision

Residual Value at the end of the project is expected to be ₹ 40,000 and Depreciation of the Original Investment
is on straight line basis. Using Average profits and Average Capital Employed, calculate ARR for the project and
also the payback period.

Question 17 - Study Material

The Alpha Co. Ltd, is considering the purchase of a new machine. Two alternative machines (A & B) have been
suggested, each costing ₹ 4,00,000. Earnings after taxation but before depreciation are expected to be as
follows:
YEAR CASH FLOWS
Machine A Machine B
1 40,000 1,20,000
2 1,20,000 1,60,000
3 1,60,000 2,00,000
4 2,40,000 1,20,000
5 1,60,000 80,000
Total 7,20,000 6,80,000
The company has a target rate return on capital @ 10 percent and on this basis, you are required: (a) Compare
profitability of the machines and state which alternative you consider financially preferable;
(b) Compute the payback period for each project; and (c) Compute annual rate of return for each project.
[Present value of machine B is higher than that of machine A; Payback period machine A – 3 years 4 months,
machine B 2 years 7.2 months; Annual return machine A – 16%, machine B – 14%]

NPV, IRR, Payback Period, ARR

Question 18 - Study Material
Hind lever Company is considering a new product line to supplement its range line. It is anticipated that the
new product line will involve cash investment of ₹ 7,00,000 at time 0 and ₹ 10,00,000 in year 1. After-tax cash
inflows of ₹ 2,50,000 are expected in year 2, ₹ 3,00,000 in year 3, ₹ 3,50,000 in year 4 and ₹ 4,00,000 each year
thereafter through year 10. Although the product line might be viable after year 10, the company prefers to be
conservation and end all calculation at that time.
(a) If the required rate of return is 15 percent, what is the net present value of the project? Is it acceptable?
(b) What would be the case if the required rate of return were 10 per cent?
(c) What is its internal rate of return?
(d) What is the project’s payback period?
(e) Discounted PBP at 10%.

Question 19 - Mtp Mar 2021

MT Limited is considering to purchase a new plant worth ₹. 1,60,00,000. The expected net cash flows after
taxes and before depreciation are as follows:
Year Net Cash Flows (₹.)
1 28,00,000
2 28,00,000
3 28,00,000
4 28,00,000
5 28,00,000
6 32,00,000
7 40,00,000
8 60,00,000
9 40,00,000
10 16,00,000
The rate of cost of capital is 10%.
You are required to calculate:
(i) Pay-back period
(ii)Net present value at 10% discount factor
(iii)Profitability index at 10% discount factor
(iv)Internal rate of return with the help of 10% and 15% discount factor
The following present value table is given for you:
Year Present value of ₹. 1 Present value of ₹. 1 at
at 10% discount rate 15% discount rate

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1 0.909 0.870
2 0.826 0.756
3 0.751 0.658
4 0.683 0.572
5 0.621 0.497
6 0.564 0.432
7 0.513 0.376
8 0.467 0.327
9 0.424 0.284
10 0.386 0.247

Question 20 - Study Material

Alpha company is considering the following investment projects:
PROJECTS CASH FLOWS
C0 C1 C2 C3
A -10,000 10,000
B -10,000 7500 7500
C -10,000 2000 4000 12000
D -10,000 10000 3000 3000
a) Rank the projects according to each of the following methods: (i) Payback, (ii) ARR, (iii) IRR and (iv) NPV,
assuming discount rates of 10 and 30 per cent.
b) Assuming the projects are independent, which one should be accepted? If the projects are mutually
exclusive, which project is the best?

NPV and PI with Differential Cash flows

Question 21 - Nov 09
New Thought Company is evaluating an Investment proposal of ₹ 3,06,000 with expected cash flows as –
YEAR 1 2 3 4
CFAT(Rs) 100000 130000 150000 100000
The Company’s Cost of Capital is 10%. Compute the NPV and PI for this project.

NPV and PI with Uniform Cash Flows

Question 22 - Rtp
Bhilwara Co.’s cost of capital is 10% and it is subject to 50% tax rate. The Company is considering buying a
new finishing machine. The machine will cost ₹ 2 Lakhs and will reduce materials waste by an estimated
amount of ₹ 50,000 a year. The machine will last for 10 years and will have a zero salvage value. Assume
straight line method of depreciation on assets.
1. Compute the Annual Cash Inflows, Present Value, Net Present Value, and profitability Index.
2. Should the company purchase the new finishing machine?

Payback, ARR, NPV, IRR and PI

Question 23 - May 08
C Ltd. is considering investing in a project. The expected original investment in the project will be ₹ 2,00,000,
the life of project will be 5 year with no salvage value. The expected net cash inflows after depreciation but
before tax during the life of the project will be as following:
YEAR 1 2 3 4 5
(Rs) 85000 100000 80000 80000 40000
The project will be depreciated at the rate of 20% on original cost. The company is subjected to 30% tax rate.
Required:
(i) Calculate payback period and average rate of return (ARR).
(ii) Calculate net present value and net present value index, if cost of capital is 10%.
(iii) Calculate internal rate of return. Note:

The P.V. factors are

YEAR P.V. at 10% P.V. at 37% P.V. at 38% P.V. at 40%
1 0.909 0.730 0.725 0.714
2 0.826 0.533 0.525 0.510

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3 0.751 0.389 0.381 0.364

4 0.683 0.284 0.276 0.260
5 0.621 0.207 0.200 0.186

Simple & Discounted Payback Period, NPV and PI

Question 24 - Nov 07, May 19
Consider the following mutually exclusive projects:
Cash Flows (₹)
Projects C0 C1 C2 C3 C4
A -10,000 6,000 2,000 2,000 12,000
B -10,000 2,500 2,500 5,000 7,500
C -3,500 1,500 2,500 500 5,000
D -3,000 0 0 3,000 6,000

Required:
(i) Calculate the payback period for each project.
(ii) If the standard payback period is 2 years, which project will you select? Will your answer differ, if standard
payback period is 3 years?
(iii)If the cost of capital is 10%, compute the discounted payback period for each project. Which projects will
you recommend, if standard discounted payback period is (i) 2 years; (ii) 3 years?
(iv) Compute NPV of each project. Which project will you recommend on the NPV criterion? The cost of capital
is 10%. What will be the appropriate choice criteria in this case? The PV factors at 10% are:
YEAR 1 2 3 4
PV factor at 10% (PV/F 0.10,t) 09091 08264 0.7513 0.6830

NPV and IRR

Question 25 - Study Material
A sole trader installs plant and machinery in rented premises for the production of luxury article, the demand
for which is expected to last only 5 years. The total capital put in by the sole trader is as under:
Plant and machinery ₹ 2,70,500
Working capital ₹ 40,000
₹ 3,10,500
The working capital will be fully realized at the end of 5th year. The scrap value of the plant expected to be
realized at the end of the 5th year is only ₹ 5,500. The trader’s earning are expected to be as under:
Year Cash profit (before depreciation & tax) (₹) Tax payable (₹)
1 90,000 20,000
2 1,30,000 30,000
3 1,70,000 40,000
4 1,16,000 26,000
5 19,500 5,000
Present value factors of various rates of interest are given below:
Years 11% 12% 13% 14% 15%
1 0.9009 0.8929 0.8850 0.8770 0.8696
2 0.8116 0.7972 0.7831 0.7695 0.7561
3 0.7312 0.7118 0.6931 0.6750 0.6675
4 0.6587 0.6355 0.6133 0.5921 0.5718
5 0.5935 0.5674 0.5428 0.5194 0.4972
You are required to compute the present value of cash flows discounted at the various rates of interests given
above and state the return from the project.

Question 26 - May 07
A company is considering the proposal of taking up a new project which requires an investment of ₹ 400 lakhs
on machinery and other assets. The project is expected to yield the following earnings (before depreciation
and taxes) over the next five years:
Year Earnings (₹ in lakhs)
1 160

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2 160
3 180
4 180
5 150
The cost of raising the additional capital is 12% and assets have to be depreciated at 20% on ‘Written Down
Value’ basis. The scrap value at the end of the five years’ period May be taken as zero. Income-tax applicable
to the company is 50%. You are required to calculate the net present value of the project and advise the
management to take appropriate decision. Also calculate the Internal Rate of Return of the Project.
Note: Present values of Re. 1 at different rates of interest are as follows:
Year 10% 12% 14% 16%
1 0.91 0.89 0.88 0.86
2 0.83 0.80 0.77 0.74
3 0.75 0.71 0.67 0.64
4 0.68 0.64 0.59 0.55
5 0.62 0.57 0.52 0.48

Computing Missing Figure with IRR, PI, NPV

Question 27 - Nov 98, May 15
Following are the data on a Capital project being evaluated by the management of X Ltd.
Particulars Project M
Annual cost saving ₹ 40,000
Useful life 4 years
I.R.R 15%
Profitability Index (P.I) 1.064
NPV ?
Cost of capital ?
Cost of project ?
Payback ?
Salvage value 0

Find the missing values considering the following table discount factor only:
Discount factor 15% 14% 13% 12%
1 year 0.869 0.877 0.885 0.893
2 year 0.756 0.769 0.783 0.797
3 year 0.658 0.675 0.693 0.712
4 year 0.572 0.592 0.613 0.636
2.855 2.913 2.974 3.038

Question 28 - Nov 09
A Doctor is planning to buy an X-Ray machine for his hospital. He has two options – he can either purchase it
by making a cash payment of ₹ 5 lakhs or ₹ 6,15,000 are to be paid in six equal annual instalments. Which
option do you suggest to the Doctor assuming the Rate of Return is 12%? Present Value of ₹ 1 at 12% rate of
discount for 6 year is 4.111.

Question 29 - Study Material

A large profit making company is considering the installation of a machine to process the waste produced by
one of its existing manufacturing process to be converted into a Marketable product. At present, the waste is
removed by a contractor for disposal on payment by the company of ₹ 150 lakh per annum for the next four
years. The contract can be terminated upon installation of the aforesaid machine on payment of a
compensation of ₹ 90 lakh before the processing operation starts. This compensation is not allowed as
deduction for tax purposes.
The machine required for carrying out the processing will cost ₹ 600 lakh to be financed by a loan repayable in
4 equal instalments commencing from end of the year- 1. The interest rate is 14% per annum. At the end of the
4th year, the machine can be sold for ₹ 60 lakh and the cost of dismantling and removal will be ₹ 45 lakh.
Sales and direct costs of the product emerging from waste processing for 4 years are estimated as under:
(₹ In lakh)
Year 1 2 3 4

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 Chapter 6 - Investment Decision

Sales 966 966 1,254 1,254

Material consumption 90 120 255 255
Wages 225 225 255 300
Other Expenses 120 135 162 210
Factory overheads 165 180 330 435
Depreciation (as per 150 114 84 63
income tax rules)
Initial stock of materials required before commencement of the processing operations is ₹ 60 lakh at the start
of year 1. The stock levels of materials to be maintained at the end of year 1, 2 and 3 will be ₹ 165 lakh and the
stocks at the end of year 4 will be nil. The storage of materials will utilise space which would otherwise have
been rented out for ₹ 30 lakh per annum. Labour costs include wages of 40 workers, whose transfer to this
process will reduce idle time payments of ₹ 45 lakh in the year- 1 and ₹ 30 lakh in the year- 2. Factory
overheads include apportionment of general factory overheads except to the extent of insurance charges of ₹
90 lakh per annum payable on this venture. The company’s tax rate is 30%.
Present value factors for four years are as under:
Year 1 2 3 4
PV factors @14% 0.877 0.769 0.674 0.592
ADVISE the management on the desirability of installing the machine for processing the waste. All calculations
should form part of the answer.

Replacement Decision based on NPV, Discounted Payback and PI

Question 30 - Study Material
Lockwood Limited wants to replace its old machine with a new automatic machine. Two models A and B are
available at the same cost of ₹ 5 lakhs each. Salvage value of the old machine is ₹ 1 lakh. The utilities of the
existing machine can be used if the company purchases A. Additional cost of utilities to be purchased in that
case are ₹ 1 lakh. If the company purchases B then all the existing utilities will have to be replaced with new
utilities costing ₹ 2 lakhs. The salvage value of the old utilities will be ₹ 0.20 lakhs. The earnings after taxation
are expected to be:
(Cash Inflows of)
Year A (₹) B(₹) P.V. Factor @15%
1 1,00,000 2,00,000 0.87
2 1,50,000 2,10,000 0.76
3 1,80,000 1,80,000 0.66
4 2,00,000 1,70,000 0.57
5 1,70,000 40,000 0.50
Salvage value at the 50,000 60,000
end of year 5
The targeted return on capital is 15%. You are required to (i) Compute, for the two machines separately, Net
present value, Discounted payback period and Desirability factor and (ii) Advice which of the machines is to be
selected?

Question 31 - Study Material

Ae Bee Cee Ltd. is planning to invest in machinery, for which it has to make a choice between the two identical
machines, in terms of Capacity, ‘X’ and ‘Y’. Despite being designed differently, both machines do the same job.
Further, details regarding both the machines are given below:
Particulars Machine ‘X’ Machine ‘Y’
Purchase Cost of the Machine (₹) 15,00,000 10,00,000
Life (years) 3 2
Running cost per year (₹) 4,00,000 6,00,000
The opportunity cost of capital is 9%. You are required to:
IDENTIFY the machine the company should buy? The present value (PV) factors at 9% are:
Year t1 t2 t3
PVIF0.09.t 0.917 0.842 0.772

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Decision of Acceptance – Rejection based on Payback, NPV and IRR

Question 32 - May 06
A company is considering a proposal of installing drying equipment. The equipment would involve a cash
outlay of ₹ 6,00,000 and net working capital of ₹ 80,000. The expected life of the project is 5 years without any
salvage value. Assume that the company is allowed to charge depreciation on straight-line basis for
income-tax purpose. The estimated before-tax cash inflows are given below:
Before-Tax Cash Inflows (₹ ‘000)
Year 1 2 3 4 5
240 275 210 180 160
The applicable Income-tax rate to the company is 35%. If the company’s opportunity cost of capital is 12%,
calculate the equipment’s discounted payback period, payback period, net present value and internal rate of
return.
The PV factors at 12%, 14% and 15% are:
Year 1 2 3 4 5
PV factor at 12% 0.8929 0.7972 0.7118 0.6355 0.5674
PV factor at 14% 0.8772 0.7695 0.6750 0.5921 0.5194
PV factor at 15% 0.8696 0.7561 0.6575 0.5718 0.4972

Decisions of Acceptance – Rejections based on NPV and PI

Question 33 - Nov 09, May 14
A Hospital is considering purchasing a Diagnostic Machine costing ₹ 80,000. The projected life of the machine
is 8 years, and it has an expected Salvage Value of ₹ 6,000 at the end of 8 years. The annual operating cost of
the machine is ₹ 7,500. It is expected to generate revenues of ₹ 40,000 per year for 8 years. Presently, the
Hospital is outsourcing the diagnostic work and is earning Commission Income of ₹ 12,000 per annum, net of
taxes. Required: Whether it would be profitable for the Hospital to purchase the machine? Give your
recommendation under Net Present Value and Profitability Index Methods. PV Factors at 10% are given below:
Year 1 2 3 4 5 6 7 8
PV Factor 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467
[Additional Cash Flow p.a. by Purchasing new Diagnostic Machine: ₹ 11,200; Net Present Value: (17,457);
Profitability Index: 0.78]

Question 34 - Nov 2022

A hospital is considering to purchase a diagnostic machine costing ₹ 80,000. The projected life of the machine
is 8 years and has an expected salvage value of ₹ 6,000 at the end of 8 years. The annual operating cost of the
machine is ₹ 7,500. It is expected to generate revenues of ₹ 40,000 per year for eight years. Presently, the
hospital is outsourcing the diagnostic work and is earning commission income of ₹ 12,000 per annum.
Consider tax rate of 30% and Discounting Rate as 10%. Advise:
Whether it would be profitable for the hospital to purchase the machine?
Give your recommendation as per Net Present Value method and Present Value Index method under below
mentioned two situations:
1. If Commission income of ₹ 12,000 p.a. is before taxes.
2. If Commission income of ₹ 12,000 p.a. is net of taxes.
t 1 2 3 4 5 6 7 8
PVIF (t, 10%) 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467

Mutually Exclusive Decisions – NPV and Simple Payback

Question 35 - Nov 09
PR Engineering Ltd. is considering the purchase of a new machine which will carry out some operations which
are at present performed by manual labour. The following related to the alternative models – ‘MX’ and ‘MY’ are
available:
Particulars Machine ‘MX’ Machine ‘MY’
Cost of Machine ₹ 8,00,000 ₹ 10,20,000
Expected Life 6 year 6 year
Scrap value ₹ 20,000 ₹ 30,000

Estimated Net Income before Depreciation and Tax are as under:

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Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Machine MX 2,50,000 2,30,000 1,80,000 2,00,000 1,80,000 1,60,000
Machine MY 2,70,000 3,60,000 3,80,000 2,80,000 2,60,000 1,85,000
Depreciation will be charged on Straight Line basis. Tax rate is 30%
You are required to:
1. Calculate the payback period of each proposal.
2. Calculate the Net Present Value of each proposal, if the PV Factor at 10% is 0.909, 0.826, 0.751, 0.683,
0.621 and 0.564.
3. Which proposal you would recommend and why?

Mutually Exclusive Projects/ Independent Project Evaluation using NPV & IRR
Question 36 - Rtp
The Director of Damon Electronics Co. has asked you analyse two proposed investment projects X and Y. Each
project has an initial investment of ₹ 10,000 at a cost of 12%. The Cash Flows are expected as under:
Year 1 2 3 4
Cash Flows of X ₹ 6,500 ₹ 3,000 ₹ 3,000 ₹ 1,000
Cash Flows of Y ₹ 3,500 ₹ 3,500 ₹ 3,500 ₹ 3,500
1. Calculate for each project – (a) Simple payback period, (b) NPV, and (c) IRR.
2. Which project(s) should be accepted if the projects were independent?
3. Which project should be accepted if they were mutually exclusive?

Question 37 - Rtp Nov 2023

PQR Limited is considering buying a new machine which would have a useful economic life of five years, at a
cost of ₹ 40,00,000 and a scrap value of ₹ 5,00,000, with 80 per cent of the cost being payable at the start of
the project and 20 per cent at the end of the first year. The machine would produce 80,000 units per annum of
a new product with an estimated selling price of ₹ 400 per unit. Direct costs would be ₹ 375 per unit and
annual fixed costs, including depreciation calculated on a straight- line basis, would be₹ 10,40,000 per annum.
In the first year and the second year, special sales promotion expenditure, not included in the above costs,
would be incurred, amounting to ₹ 1,25,000 and ₹ 1,75,000 respectively.
EVALUATE the project using the NPV method of investment appraisal, assuming the company’s cost of capital
to be 12 percent.

Mutually Exclusive Projects unequal life

Question 38 - May 10, May 13
The Management of P Limited is considering to select a machine out of the mutually exclusive machines. The
company’s Cost of Capital is 12% and Corporate Tax Rate for the Company is 30%. Details of the machines are
as follows
Particulars Machine – I Machine – II
Cost of Machine ₹ 10,00,000 ₹ 15,00,000
Expected life 5 years 6 years
Annual Income before Tax Depreciation ₹ 3,45,000 ₹ 4,55,000
Depreciation is to be charged on straight line basis. You are required to:
1. Calculate the Discounted Payback Period, Net Present Value and Internal Rate of Return for each machine.
2. Advise the Management of P Limited as to which Machine they should take up.

Question 39 - Nov11,Nov12 (SIMILAR)

A Ltd. is considering the purchase of a machine which will perform some operations which are at present
performed by workers. Machines X and Y are alternative models. The following details are available:
Particulars Machine X (₹) Machine Y (₹)
Cost of machine 1,50,000 2,40,000
Estimated life of machine 5 years 6 years
Estimated cost of maintenance p.a. 7,000 11,000
Estimated cost of indirect material p.c. 6,000 8,000
Estimated savings in scrap p.a. 10,000 15,000
Estimated cost of supervision p.a. 12,000 16,000
Estimated savings in wages p.a. 90,000 1,20,000
Depreciation will be charged on straight line basis. The tax rate is 30%. Evaluate the alternatives according to:

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(i) Average rate of return method, and

(ii) Present value index method assuming cost of capital being 10%.

NPV – IRR Conflict

Question 40 - May 03
The Cash flows of projects C and D are reproduced below:
Project C0 C1 C2 C3 NPV at 10% IRR
C -₹ 10,000 + 2,000 + 4,000 + 12,000 + ₹ 4,139 26.5%
D -₹ 10,000 + 10,000 + 3,000 + 3,000 + ₹ 3,823 37.6%

(i) Why there is a conflict of ranking?

(ii) Why should you recommend project C in spite of lower internal rate of return?
Discount Rate 1 2 3
10% 0.9090 0.8264 0.7513
14% 0.8772 0.7695 0.6750
15% 0.8696 0.7561 0.6575
30% 0.7692 0.5917 0.4552
40% 0.7143 0.5102 0.3644

Question 41 - May 08
A Firm can make investment in either of the following two projects. The firm anticipates its cost of capital to
be 10% and the net (after taxes). Cash flows of the five years are as follows: (in ₹ ‘000)
Year 0 1 2 3 4 5
Project A (500) 85 200 240 220 70
Project B (500) 480 100 70 30 20

The discount factors are as under:

Year 0 1 2 3 4 5
PVF (10%) 1 0.91 0.83 0.75 0.68 0.62
PVF (20%) 1 0.83 0.69 0.58 0.48 0.41
1. Calculate the NPV and IRR of each project.
2. State with reasons which project you would recommend.
3. Explain the inconsistency in ranking of two projects.

Service or replace parts

Question 42 - Study Material
Alley Pvt. Ltd. is planning to invest in a machinery that would cost ₹ 1,00,000 at the beginning of year 1. Net
cash inflows from operations have been estimated at ₹ 36,000 per annum for 3 years. The company has two
options for smooth functioning of the machinery- one is service, and another is replacement of parts. If the
company opts to service a part of the machinery at the end of year 1 at ₹ 20,000, in such a case, the scrap
value at the end of year 3 will be ₹ 25,000. However, if the company decides not to service the part, then it will
have to be replaced at the end of year 2 at ₹ 30,800. And in this case, the machinery will work for the 4th year
also and get operational cash inflow of ₹ 36,000 for the 4th year. It will have to be scrapped at the end of year 4
at ₹ 18,000.
Assuming cost of capital at 10% and ignoring taxes, DETERMINE the purchase of this machinery based on the
net present value of its cash flows?
If the supplier gives a discount of ₹ 10,000 for purchase, what would be your decision?
Note:
The PV factors at 10% are:
Year 0 1 2 3 4 5 6
PV Factor 1 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645

Question 43 - Rtp
Fair Ltd. is a manufacturer of high quality running shoes. Hari, President, is considering computerizing the
company’s ordering, inventory and billing procedures. He estimates that the annual savings from
computerization include a reduction, of 10 clerical employees with annual salaries of ₹ 15,000 each, ₹ 8,000
from, reduced production delays caused by raw materials inventory problems, ₹ 12,000 from lost sales due to

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inventory stock out and ₹ 3,000 associated with timely billing procedures. The purchase price of the system is
₹ 2,00,000 and installation costs are ₹ 50,000. These outlays will be capitalized (depreciated) on a straight-line
basis to a zero book salvage value, which is also its Market value at the end of 5 years. Operation of the new
system requires two computer specialists with annual salaries of ₹ 40,000 per person. Also annual
maintenance and operating (cash) expenses of ₹ 12,000 are estimated to be required. The company’s tax rate
is 40% and its required rate of return (cost of capital) for this project is 12%. You are required to:
(i) Find the project’s initial net cash outlay;
(ii) Find the project’s operating and terminal value cash flows over its 5-year life;
(iii) Evaluate the project using NPV method;
(iv) Evaluate the project using PI method;
(v) Calculate the project’s payback period;
(vi) Find the project’s cash flows and NPV *parts (i) through (iii)+ assuming that the system can be sold for ₹
25,000 at the end of five years even though the book salvage value will be zero; and
(vii) Find the project’s cash flows and NPV *parts (i) through (iii)+ assuming that the book salvage value for
depreciation purposes is ₹ 20,000 even though the machine is worthless in terms of its resale value.
Note: Present value of annuity of Re. 1 at 12% rate of discount for 5 years is 3.605.
Present value of Re. 1 at 12% rate of discount, received at the end of 5 years is 0.567.

Question 44 - Nov07
XYZ Ltd. is planning to introduce a new product with a project life of 8 years. The project is to be setup in
Special Economic Zone (SEZ), Qualifies for one time (at starting)tax free subsidy from the State Government
of ₹ 25,00,000 on Capital investment. Initial equipment cost will be ₹ 1.75 crores. Additional equipment cost
₹12,50,000 will be purchased at the end of the third year from the cash inflow of this year. At the end of 8
years, the original equipment will have no resale value, but additional equipment can be sold for ₹ 1,25,000. A
Working Capital of ₹20,00,000 will be needed and it will be released at the end of the eight year. The project will
be financed with sufficient amount of Equity Capital.
The sales volumes over eight years have been estimated as follows:
Year 1 2 3 4-5 6-8
Units 72,000 1,08,000 2,60,000 2,70,000 1,80,000
A sales price of ₹120 per unit is expected and variable expenses will amount to 60% of sales revenue. Fixed
Cash operating costs will amount ₹ 18,00,000 per year. The loss of any year will be set off from the profits of
subsequent two years. The company is subject to 30 percent tax rate and consider 12 percent to be an
appropriate after tax cost of capital for this project. The company follows straight line method of depreciation.
Required: Calculate the net present value of the project and advise the management to take appropriate
decision.
Note: The PV factors at 12% are:
Year 1 2 3 4 5 6 7 8
0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404

Question 45 - JAN 2021

ABC Ltd., a profit-making company, is engaged in the business of car manufacturing. In order to be
independent in terms of its electricity needs, the company's management has proposed to put up a Solar
Power Plant to generate the electricity. The details of the proposal are as follows:
Cost of the power plant ₹ 280 lakhs
Cost of land ₹ 30 lakhs
Subsidy of ₹ 25 lakhs from state government to be received at the end of first year of installation.
Sale of electricity to State Electricity Board will be at ₹ 2.25 per unit in year 1. This will increase by ₹ 0.25 per
unit every year till year 7. After that it will increase by ₹ 0.50 per unit every year.
(1)Maintenance cost will be ₹ 4 lakhs in year 1 and the same will increase by ₹ 2 lakhs every year.
(2)Estimated life is 10 years.
(3)Cost of capital 15%.
(4)Residual value of power plant is nil. However, land value will go up to ₹ 90 lakhs at the end of year 10.
(5)Depreciation will be 100% of the cost of the power plant in year 1 (entire ₹ 280 lakhs is to be depreciated in
year 1 without considering subsidy) and the same will be allowed for tax purposes.
(6)Gross electricity generated will be 25 lakhs units per annum. 4% of this electricity generated will be
committed free to the State Electricity Board as per the agreement.
(7)Tax rate is 50%.

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 Chapter 6 - Investment Decision

You are required to suggest the viability of the proposal by calculating the 'Net Present Value' while ignoring
the tax on capital profit. Assume that the tax savings, if any, are utilized in the year of their occurrence.
Present value (PV) factor @ 15% for the year 1 to year 10 are as given below and should be used for
calculating present value of various cash flows.
Year 1 2 3 4 5 6 7 8 9 10
PV Factor 0.870 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.284 0.247

100% Depreciation in year one

Question 46 - Study Material, Nov 91
Modern Enterprises Ltd. is considering the purchase of a new computer system for its Research and
Development Division, which would cost ₹ 35 lakhs. The operation and maintenance costs (excluding
depreciation) are expected to be ₹ 7 lakhs per annum. It is estimated that the useful life of the system would
be 6 years, at the end of which the disposal value is expected to be ₹ 1 lakh.
The tangible benefits expected from the system in the form of reduction in designing costs would be ₹ 12
lakhs per annum. Besides, the disposal of used drawing, office equipment and furniture, initially, is anticipated
to net ₹ 9 lakhs. Capital expenditure in research and development would attract 100% write-off for tax purpose.
The gains arising from disposal of used assets May be considered tax-free. The company’s effective tax rate is
50%.
The average cost of capital to the company is 12%. The present value factors at 12% discount rate are:
Year PVF
1 0.892
2 0.797
3 0.711
4 0.635
5 0.567
6 0.506
After appropriate analysis of cash flows, please advise the company of the financial viability of the proposal.

Asset Replacement
Question 47 - Rtp, Study Material
Beta Electronics is considering a proposal to replace one of its machines. The following information is
available to you.
The existing machine was bought 3 years ago for ₹ 10 Lakhs. It was depreciated at 25% p.a. on reducing
balance basis. It has remaining useful life of 5 years, but its annual maintenance cost is expected to increase
by ₹ 50,000 from the sixth year of its installation. Its present realisable value is ₹ 6 Lakhs. The company has
several machines, having 25% depreciation.
The new Machine costs ₹ 15 Lakhs and is subject to the same rate of depreciation. On sale after 5 years, it is
expected to net ₹ 9 Lakhs. With the new machine, the annual operating costs (excluding depreciation) are
expected to decrease by ₹ 1 Lakh. In addition, the new machine would increase productivity on account of
which Net Revenues would increase by ₹ 1.5 Lakhs annually.
The tax-rate application to the company is 35% and cost of Capital is 10%. Advise the company, on the basis of
NPV of the proposal, whether the proposal is financially viable. .

Question 48 - Rtp May2021

The General Manager of Merry Ltd. is considering the replacement of five -year-old equipment. The company
has to incur excessive maintenance cost of the equipment. The equipment has zero written down value. It can
be modernized at a cost of ₹ 1,40,000 enhancing its economic life to 5 years. The equipment could be sold for
₹ 30,000 after 5 years. The modernization would help in material handling and in reducing labour ,
maintenance & repairs costs.
The company has another alternative to buy a new machine at a cost of ₹ 3,50,000 with an economic life of 5
years and salvage value of ₹ 60,000. The new machine is expected to be more efficient in reducing costs of
material handling, labour , maintenance & repairs, etc.
The annual cost are as follows:
Existing Equipment Modernization (₹) New Machine (₹)
(₹)
Wages & Salaries 45,000 35,500 15,000
Supervision 20,000 10,000 7,000
Maintenance 25,000 5,000 2,500

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 Chapter 6 - Investment Decision

Power 30,000 20,000 15,000

1,20,000 70,500 39,500
Assuming tax rate of 50% and required rate of return of 10%, should the company modernize the equipment or
buy a new machine?
PV factor at 10% are as follows:
7B Year 1 2 3 4 5
PV factor 0.909 0.826 0.751 0.683 0.621

Concept of additional and allocated overheads

Question 49 -
ABC Ltd. manufactures toys and other gift items. The R & D Division has come up with a product that would
make a good promotional gift for office equipment dealers. As a result of efforts by the sales personnel, the
Firm has commitments for this product.
To produce the quantity demanded, the company will need to buy additional machinery and rent additional
space. It appears that about 25,000 square feet will be needed. 12,500 square feet of presently unused space,
but leased at the rate of ₹ 3 per square foot per year, is available. There is another 12,500 square feet available
at an annual rent of ₹ 4 per square foot.
The Machinery will be purchased for ₹ 9,00,000. It will require ₹ 30,000 for modifications, ₹ 60,000 for
installation and ₹ 90,000 for testing. The machinery will have a salvage value of about ₹ 1,80,000 at the end of
the third. No additional General Overheads Costs are expected to be incurred.
The estimated revenues and costs for this product for the three years have been developed as follows:(₹)
Particulars Year I Year II Year III
Sales 10,00,000 20,00,000 8,00,000
Less: Material and 4,00,000 7,50,000 3,50,000
Labour 40,000 75,000 35,000
Overheads allocated 50,000 50,000 50,000
Rent 3,00,000 3,00,000 3,00,000
Depreciation
Earnings Before 2,10,000 8,25,000 65,000
Taxes 1,05,000 4,12,500 32,500
Less: Taxes
Earnings After Taxes 1,05,000 4,12,500 32,500
If the Company sets a required rate of return of 20% after taxes, should this product be manufactured?

Question 50 - Nov 94
Swastik Ltd. manufactures of special purpose machine tools, have two divisions, which are periodically
assisted by visiting terms of consultants. The management is worried about the steady increase of expenses
in this regard over the years. An analysis of last year’s expenses reveals the following:
Particulars ₹
Consultant's Remuneration 2,50,000
Travel and Conveyance 1,50,000
Accommodation Expenses 6,00,000
Boarding charges 2,00,000
Special Allowances 50,000

12,50,000
The management estimates accommodation expenses to increase by ₹ 2,00,000 annually. As part of a cost
reduction drive, Swastik Ltd. is proposing to construct a consultancy centre to take care of the
accommodation requirements of the consultants. This centre will additionally save the company ₹ 50,000 in
boarding charges and ₹ 2,00,000 in the cost of Executive Training Programmes hither to conducted outside the
company’s premises, every year.
The following details are available regarding the construction and maintenance of the new centre:
a) Land: At a cost of ₹ 8,00,000 already owned by the company will be used.
b) Construction cost: ₹ 15,00,000 including special furnishings.
c) Cost of annual maintenance: ₹ 1,50,000.
d) Construction cost will be written off over 5 years being the useful life.

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Assuming that the write-off of construction cost as aforesaid will be accepted for tax purposes, that the rate
of tax will be 50% and that desired rate of return is 15%, you are required to analyse the feasibility of the
proposal and make recommendations. The relevant Present Value Factors are:
Year 1 2 3 4 5
PV Factor 0.87 0.76 0.66 0.57 0.50

Question 51 - May 2022

Alpha Limited is a manufacturer of computers. It wants to introduce artificial intelligence while making
computers. The estimated annual saving from introduction of the artificial intelligence (AI) is as follows:
● Reduction of five employees with annual salaries of ₹ 3,00,000 each
● Reduction of ₹ 3,00,000 in production delays caused by inventory problem
● Reduction in lost sales ₹ 2,50,000 and
● Gain due to timely billing ₹ 2,00,000
The purchase price of the system for installation of artificial intelligence is ₹ 20,00,000 and installation cost is
₹ 1,00,000. 80% of the purchase price will be paid in the year of purchase and remaining will be paid in next
year.
The estimated life of the system is 5 years and it will be depreciated on a straight -line basis.
However, the operation of the new system requires two computer specialists with annual salaries of ₹ 5,00,000
per person.
In addition to above, annual maintenance and operating cost for five years are as below:
Year 1 2 3 4 5
Maintenance & Operating Cost 2,00,000 1,80,000 1,60,000 1,40,000 1,20,000
Maintenance and operating cost are payable in advance.
The company's tax rate is 30% and its required rate of return is 15%.
Year 1 2 3 4 5
PVIF 0.10, t 0.909 0.826 0.751 0.683 0.621
PVIF 0.12, t 0.893 0.797 0.712 0.636 0.567
PVIF 0.15, t 0.870 0.756 0.658 0.572 0.497
Evaluate the project by using Net Present Value and Profitability Index.

NPV Based Evaluation – Replacement Decision

Question 52 - May 97, May 07
Excel Ltd. Manufacture a special chemical for sale at ₹ 30 per Kg. The variable cost of manufacture is ₹ 15 per
kg. Fixed cost excluding depreciation is ₹ 2,50,000. Excel Ltd. is currently operating at 50% capacity. It can
produce a maximum of 1,00,000 kgs. at full capacity.
The production manager suggests that if the existing machines are fully replaced, the company can achieve
maximum capacity in the next five years, gradually increasing the production by 10% per year.
The finance Manager estimates that for each 10% increase in capacity, the additional increase in fixed cost will
be ₹ 50,000. The existing machines with a current book value of ₹ 10,00,000 can be disposed of for ₹ 5,00,000.
The Vice President (finance) is willing to replace the existing machines provided the NPV on replacement is
about ₹ 4,53,000 at 15% cost of capital after tax.

(i) You are required to compute the total value of machines necessary for replacement.
For your exercise you May assume the following:
a) The company follows the block of assets concept and all the assets are in the same block. Depreciation
will be in straight line basis and the same basis is allowed for tax purposes.
b) There will be no salvage value for the machines newly purchased. The entire cost of the assets will be
depreciated over five years period.
c) Tax rate is at 40%
d) Cash inflows will arise at the end of the year.
e) Replacement outflow will be at beginning of the year (Year 0)
Year 0 1 2 3 4 5
Discount Factor at 15% 1 0.87 0.76 0.66 0.57 0.49

(ii) On the basis of data given above, the managing director feels that the replacement, if carried out, would at
yield post tax return of 15% in the three years provided the capacity build up is 60%, 80% and 100%
respectively. Do you agree?

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Repair – Replace – Conflict

Question 53 - May 98,May 05
S Engineering Company is considering to replace or repair a particular machine, which has just broken down.
Last year this machine costed₹ 20,000 to run and maintain. These costs have been increasing in real terms in
recent years with the age of the machine. A further useful life of 5 years is expected, if immediate repairs of ₹
19,000 are carried out. If the machine is not repaired it can be sold immediately to realise about ₹ 5,000
(Ignore loss/gain on such disposal).
Alternatively, the company can buy a new machine for ₹ 49,000 with an expected life of 10 years with no
salvage value after providing depreciation on straight line basis. In this case, running and maintenance costs
will reduce to ₹ 14,000 each year and are not expected to increase much in real terms of a few years at least. S
Engineering Company regards a normal return of 10% p.a. after tax as a minimum requirement on any new
investment. Considering capital budgeting techniques, which alternative will you choose? Take corporate tax
rate of 50% and assume that depreciation on straight line basis will be accepted for tax purposes also. Given
cumulative present value of Re. 1 p.a. at 10% for 5 years ₹ 3.791, 10 years ₹ 6.145.

Question 54 - Rtp May 2022

ABC & Co. is considering whether to replace an existing machine or to spend money on revamping it. ABC &
Co. currently pays no taxes. The replacement machine costs ₹ 18,00,000 now and requires maintenance of ₹
2,00,000 at the end of every year for eight years. At the end of eight years, it would have a salvage value of ₹
4,00,000 and would be sold. The existing machine requires increasing amounts of maintenance each year and
its salvage value fall each year as follows:
Year Maintenance (₹) Salvage (₹)
Present 0 8,00,000
1 2,00,000 5,00,000
2 4,00,000 3,00,000
3 6,00,000 2,00,000
4 8,00,000 0
The opportunity cost of capital for ABC & Co. is 15%.
REQUIRED:
When should the company replace the machine?
The following present value table is given for you:
Present value of ₹ 1 at
Year 15% discount rate
1 0.8696
2 0.7561
3 0.6575
4 0.5718
5 0.4972
6 0.4323
7 0.3759
8 0.3269

Mutually Exclusive Decision – Retain or Replace – Incremental NPV

Question 55 - July 2021
An existing company has a machine which has been in operation for two years , its estimated remaining useful
life is 4 years with no residual value in the end. Its current Market value is ₨ 3 lakhs. The management is
considering a proposal to purchase an improved model of a machine which gives increase output. The details
are as under :
Particulars Existing Machine New Machine

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 Chapter 6 - Investment Decision

Purchase price ₨ 6,00,000 ₨ 10,00,000

Estimated life 6 years 4 years
Residual value 0 0
Annual operating days 300 300
Operating hours per day 6 6
Selling price per unit ₨ 10 ₨ 10
Material cost per unit ₨2 ₨2
Output per hours in unit 20 40
Labour cost per hour ₨ 20 ₨ 30
Fixed overhead per annum excluding ₨ 1,00,000 ₨ 60,000
depreciation ₨ 1,00,000 ₨ 2,00,000
Working capital 30% 30%
Income tax rate
Assuming that the – cost capital is 10% and the company uses written down value of depreciation @ 20% and
it has several machines in 20% block.
Advise the management on the Replacement of Machine as per the NPV method.
The discounting factors table given below :
Discounting factors Year 1 Year 2 Year 3 Year 4
10% 0.909 0.826 0.751 0.683

Question 56 - Mtp April 2021

WX Ltd. is considering a proposal to replace an existing machine.
The details of existing machine and new machine are as under:
Particulars Existing Machine New Machine
Cost of Machine ₹ 3,75,000 ₹ 5,25,000
Estimated life (in years) 10 5
Present Book value ₹ 1,87,500 -
(i)Out of the Life of 10 years of present machine, five years have already lapsed. The management can
continue with this machine for the remaining lifetime.
(ii)The activity level of both the machines is same.
(iii)Residual value of new machine at the end of the life - ₹. 60,000.
(iv)There will be a saving of ₹. 2,40,000 in the variable cost each year by new machine.
(v)If the old machine is sold, then it will fetch ₹. 90,000.
(vi)WX Ltd. expects a minimum return of 11 % on the investment.
(vii)Corporate tax - 30%
(viii)No depreciation is to be charged in the year of sale.
(ix)Present value of ₹. 1 @ 11% is as under:
Year 1 2 3 4 5
P/V Factor 0.901 0.812 0.731 0.659 0.593
You are required to comment on the suitability of replacement of the old machine.

Only outflow & unequal life

Question 57 - May 00, Nov 06
Company X is forced to choose between two machines A and B. The two machines are designed differently,
but have identical capacity and do exactly the same job. Machine A costs ₹ 1,50,000 and will last for 3 years. It
costs ₹ 40,000 per year to run. Machine B is an ‘economy’ model costing only ₹ 1,00,000, but will last only for 2
years, and costs ₹ 60,000 per year to run. These are real cash flows. The costs are forecasted in rupees of
constant purchasing power. Ignore tax. Opportunity cost of capital is 10 percent. Which machine company X
should buy?

Question 58 - May 09
A Company is required to choose between two machines A and B. The two machines are designed differently,
but have identical capacity to do exactly the same job. Machine A costs ₹ 6,00,000 and will last for 3 years. It
costs ₹ 1,20,000 per year to run.
Machine B is an Economy Model costing ₹ 4,00,000 but will last only for two years, and cost ₹ 1,80,000 per
year to run. These are real cash flows. The costs are forecasted in rupees of constant purchasing power.
Opportunity Cost of Capital is 10%. Which Machine should the Company buy? Ignore tax. Given: PVIF0.10,1=
0.9091, PVIF0.10,2 = 0.8264, PVIF0.10,3= 0.7513.

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Question 59 - Nov 2022

A firm is in need of a small vehicle to make deliveries. It is in tending to choose between two options. One
option is to buy a new three wheeler that would cost ₹ 1,50,000 and will remain in service for 10 years.
The other alternative is to buy a second hand vehicle for ₹ 80,000 that could remain in service for 5 years.
Thereafter the firm, can buy another second hand vehicle for ₹ 60,000 that will last for another 5 years.
The scrap value of the discarded vehicle will be equal to it written down value (WDV). The firm pays 30% tax
and is allowed to claim depreciation on vehicles @ 25% on WDV basis.
The cost of capital of the firm is 12%.
You are required to advise the best option. Given:
t 1 2 3 4 5 6 7 8 9 10
PVIF (t,12%) 0.892 0.797 0.711 0.635 0.567 0.506 0.452 0.403 0.360 0.322

Replacing Part or Servicing

Question 60 - Nov 08
(a) A company wants to invest in machinery that would cost ₹ 50,000 at the beginning of year 1. It is estimated
that the net cash inflows from operations will be ₹ 18,000 per annum for 3 years, if the company opts to
service a part of the machine at the end of year 1 at ₹ 10,000. In such a case, the scrap value at the end of year
3 will be ₹ 12,500. However, if the company decides not to service the part, then it will have to be replaced at
the end of year 2 at ₹ 15,400. But in this case, the machine will work for the 4th year also and get operational
cash inflow of ₹ 18,000 for the 4th year. It will have to be scrapped at the end of year 4 at ₹ 9,000. Assuming
cost of capital at 10% and ignoring taxes, will you recommend the purchase of this machine based on the net
present value of its cash flows?

(b) If the supplier gives a discount of ₹ 5,000 for purchase, what would be your decision?
(The present value factors at the end of years 0,1,2,3,4,5 and 6 are respectively
1,0.9091,0.8264,0.7513,0.6830,0.6209 and 0.5644).

Question 61 - Mock April 2023

Rambow Ltd. is contemplating purchasing machinery that would cost ₹ 10,00,000 plus GST @ 18% at the
beginning of year 1. Cash inflows after tax from operations have been estimated at
₹ 2,56,000 per annum for 5 years. The company has two options for the smooth functioning of the machinery -
one is service, and another is replacement of parts. The company has the option to service a part of the
machinery at the end of each of the years 2 and 4 at ₹ 1,00,000 plus GST @ 18% for each year. In such a case,
the scrap value at the end of year 5 will be ₹ 76,000. However, if the company decides not to service the part,
then it will have to be replaced at the end of year 3 at ₹ 3,00,000 plus GST@ 18% and in this case, the
machinery will work for the 6th year also and get operational cash inflow of ₹ 1,86,000 for the 6th year. It will
have to be scrapped at the end of year 6 at ₹ 1,36,000.
Assume cost of capital at 12% and GST paid on all inputs including capital goods are eligible for input tax
credit in the same month as and when incurred.
(i) DECIDE whether the machinery should be purchased under option 1 or under option 2 or it
shouldn’t be purchased at all.
(ii) If the supplier gives a discount of ₹ 90,000 for purchase, WHAT would be your decision? Note: The PV
factors at 12% are:
Year 0 1 2 3 4 5 6
PV Factor 1 0.8928 0.7972 0.7118 0.6355 0.5674 0.5066

Labour Savings by Utilisation of Machine

Question 62 - Study Material
An investment in new machinery is being considered. The machine will cost ₹ 80,000 and will last for seven
years. It is expected to yield savings in raw material cost of ₹ 8,000 p.a. (due to lower wastage) and it is hoped
also to achieve labour savings of ₹ 14,000 p.a., however the arrangement have not yet been discussed with the
trade union. The company’s cost of capital is 12%.
What percentage change in the estimated labour savings will render the project not viable? Given that the
present value of an annuity for 7 years at 12% = ₹ 4.564.

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Waste processed and sold

Question 63 - Nov 2020
A chemical company is presently paying an outside firm ₹ 1 per gallon to dispose off the waste resulting from
its manufacturing operations. At normal operating capacity, the waste is about 50,000 gallons per year.
After spending ₹ 60,000 on research, the company discovered that the waste could be sold for ₹ 10 per gallon
if it was processed further. Additional processing would, however, require an investment of ₹ 6,00,000 in new
equipment, which would have an estimated life of 10 years with no salvage value. Depreciation would be
calculated by straight line method.
Except for the costs incurred in advertising ₹ 20,000 per year, no change in the present selling and
administrative expenses is expected, if the new product is sold. The details of additional processing costs are
as follows:
Variable : ₹ 5 per gallon of waste put into process.
Fixed : (Excluding Depreciation) ₹ 30,000 per year.
There will be no losses in processing, and it is assumed that the total waste processed in a given year will be
sold in the same year. Estimates indicate that 50,000 gallons of the product could be sold each year.
The management when confronted with the choice of disposing off the waste or processing it further and
selling it, seeks your advice. Which alternative would you recommend? Assume that the firm's cost of capital is
15% and it pays on an average 50% Tax on its income.
You should consider Present value of Annuity of ₹ 1 per year @ 15% p.a. for 10 years as 5.019.

New product introduced

Question 64 - Nov 18
PD Ltd. an existing company, is planning to introduce a new product with projected life of 8 years. Project cost
will be ₹ 2,40,00,000. At the end of 8 years no residual value will be realized. Working capital of ₹ 30,00,000 will
be needed. The 100% capacity of the project is 2,00,000 units p.a. but the Production and Sales Volume is
expected are as under :
Year Number of Units
1 60,000 units
2 80,000 units
3-5 1,40,000 units
6-8 1,20,000 units
Other Information:
(i) Selling price per unit ₹ 200
(ii) Variable cost is 40% of sales.
(iii) Fixed cost p.a. ₹ 30,00,000.
(iv) In addition to these advertisement expenditure will have to be incurred as under:
Year 1 2 3-5 6-8
Expenditure 50,00,000 25,00,000 10,00,000 5,00,000
(v) Income Tax is 25%.
(vi) Straight line method of depreciation is permissible for tax purpose.
(vii) Cost of capital is 10%.
(viii) Assume that loss cannot be carried forward.
Present Value Table
Year 1 2 3 4 5 6 7 8
PVF @ 10% 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467
Advise about the project acceptability.

Investment at Different Point of time – NPV Based Evaluation

Question 65 - May 02
X Ltd. an existing profit-making company, is planning to introduce a new product with a projected life of 8
years. Initial equipment cost will be ₹ 120 lakhs and additional equipment costing ₹ 10 lakhs will be needed at
the beginning of third year. At the end of the 8 years, the original equipment will have resale value equivalent to
the cost of removal, but the additional equivalent would be sold for ₹ 1 lakh. Working Capital of ₹ 15 lakhs will
be needed. The 100% capacity of the plant is of 4,00,000 units per annum, but the production and
sales-volume expected are as under:
Year Capacity in percentage
1 20

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2 30
3-5 75
6-8 50
A sale price of ₹ 100 per unit with a profit-volume ratio of 60% is likely to be obtained. Fixed Operating Cash
Cost are likely to be ₹ 16 lakhs per annum. In addition to this the advertisement expenditure will have to be
incurred as under
Year 1 2 3-5 6–8
Expenditure in ₹ 30 15 10 4
lakhs each year
The company is subject to 50% tax, straight-line method of depreciation, (permissible for tax purposes also)
and taking 12% as appropriate after tax cost of capital, should the project be accepted?

Question 66 - Study Material

XYZ Ltd. is planning to introduce a new product with a project life of 8 years. Initial equipment cost will be ₹
3.5 crores. Additional equipment costing ₹ 25,00,000 will be purchased at the end of the third year from the
cash inflow of this year. At the end of 8 years, the original equipment will have no resale value, but additional
equipment can be sold for ₹ 2,50,000. A working capital of ₹ 40,00,000 will be needed and it will be released at
the end of eighth year. The project will be financed with sufficient amount of equity capital.
The sales volumes over eight years have been estimated as follows:
Year 1 2 3 4-5 6-8
Units 72,000 1,08,000 2,60,000 2,70,000 1,80,000
A sales price of ₹ 240 per unit is expected and variable expenses will amount to 60% of sales revenue. Fixed
cash operating costs will amount ₹ 36,00,000 per year. The loss of any year will be set off from the profits of
subsequent two years. The company is subject to 30 per cent tax rate and considers 12 per cent to be an
appropriate after tax cost of capital for this project. The company follows straight line method of depreciation.
Required:
CALCULATE the net present value of the project and advise the management to take appropriate decision.
Note:
The PV factors at 12% are
Year 1 2 3 4 5 6 7 8
PV Factor 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404

Selection based on NPV

Question 67 - Study Material
Elite Cooker Company is evaluating three investment situations: (1) Produce a new line of aluminium skillets,
(2) expand its existing cooker line to include several new sizes, and (3) develop a new, higher-quality line of
cookers. If only the project in question is undertaken, the expected present value and the amounts of
investment required are:
Project Investment required (₹) Present value of Future Cash-Flows (₹)
1 2,00,000 2,90,000
2 1,15,000 1,85,000
3 2,70,000 4,00,000
If projects 1 and 2 are jointly undertaken, there will be no economies; the investment required and preset value
will simply be the sum of the parts. With projects 1 and 3, economies are possible in investment because one
of the machines acquired can be used in both production processes. The total investment required for projects
1 and 3 combined is ₹ 4,40,000.If projects 2 and 3 are undertaken, there are economies to be achieved in
Marketing and producing the products but not in investment. The expected present value of future cash flows
for projects 2 and 3 is ₹ 6,20,000. If all three projects are undertaken simultaneously, the economies noted will
still hold. However, a ₹ 1,25,000 extension on the plant will be necessary, as space is not available for all three
projects. Which project or projects should be chosen?

Choice of machine to be purchased

Question 68 - Mtp Mar 2021
GG Pathology Lab Ltd. is using 2D sonography machine which has reached the end of its useful life. The lab is
intending to upgrade along with the technology by investing in 3D sonography machine as per the choices
preferred by the patients. Following new 3D sonography machine of two different brands with same features is
available in the Market:

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Brand Cost of Life of Maintenance Cost (₹.) SLM

machine machine Depreciation rate
(₹.) (₹.) Year 1-5 Year 6-10 Year 11-15 (%)
X 15,00,000 15 50,000 70,000 98,000 6
Y 10,00,000 10 70,000 1,15,000 - 6
Residual Value of machines shall be dropped by 10% and 40% of Purchase price for Brand X and Y respectively
in the first year and thereafter shall be depreciated at the rate mentioned above on the original cost.
Alternatively, the machine of Brand Y can also be taken on rent to be returned back to the owner after use on
the following terms and conditions:
● Annual Rent shall be paid in the beginning of each year and for first year it shall be ₹. 2,24,000. Annual
Rent for the subsequent 4 years shall be ₹. 2,25,000.
● Annual Rent for the final 5 years shall be ₹. 2,70,000.
● The Rent/Agreement can be terminated by GG Labs by making a payment of ₹. 2,20,000 as penalty.
● This penalty would be reduced by ₹. 22,000 each year of the period of rental agreement.
You are required to:
(i)ADVISE which brand of 3D sonography machine should be acquired assuming that the use of machine
shall be continued for a period of 20 years.
(ii)STATE which of the option is most economical if machine is likely to be used for a period of 5 years?
The cost of capital of GG Labs is 12%.
The present value factor of ₹. 1 @ 12% for different years is given as under:
Year PVF Year PVF
1 0.893 9 0.361
2 0.797 10 0.322
3 0.712 11 0.287
4 0.636 12 0.257
5 0.567 13 0.229
6 0.507 14 0.205
7 0.452 15 0.183
8 0.404 16 0.163

Question 69 - Nov 2020

CK Ltd. is planning to buy a new machine. Details of which are as follows:
Cost of the Machine at the commencement ₹ 2,50,000
Economic Life of the Machine 8 year
Residual Value Nil
Annual Production Capacity of the Machine 1,00,000 units
Estimated Selling Price per unit ₹6
Estimated Variable Cost per unit ₹3
Estimated Annual Fixed Cost ₹ 1,00,000
(Excluding depreciation)
Advertisement Expenses in 1st year in addition of
annual fixed cost ₹ 20,000
Maintenance Expenses in 5th year in addition of
annual fixed cost ₹ 30,000
Cost of Capital 12%
Ignore Tax.
Analyse the above mentioned proposal using the Net Present Value Method and advice.
P.V. factor @ 12% are as under:
Year 1 2 3 4 5 6 7 8
PV Factor 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404

Capital Rationing
Question 70 - Nov 19
A company has ₹ 1,00,000 available for investment and has identified the following four investments in which
to invest.
Project Investment (₹) NPV (₹)
C 40,000 20,000

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 Chapter 6 - Investment Decision

D 1,00,000 35,000
E 50,000 24,000
F 60,000 18,000
You are required to optimize the returns from a package of projects within the capital spending limit if:
(i) The projects are independent of each other and are divisible.
(ii) The projects are not divisible

Question 71 - Nov 98
S. Ltd. has ₹ 10,00,000 allocated for capital budgeting purposes. The following proposals and associated
profitability indexes have been determined.
Project Amount (₹) Profitability Index (₹)
1 3,00,000 1.22
2 1,50,000 0.95
3 3,50,000 1.20
4 4,50,000 1.18
5 2,00,000 1.20
6 4,00,000 1.05
Which of the above investments should be undertaken? Assume that projects are indivisible and there is no
alternative use of the money allocated for capital budgeting.

Question 72 - Rtp
Venture Ltd. has ₹ 30 lakhs available for investment in capital projects. It has the option of making investment
in projects 1, 2, 3 and 4. Each project is entirely independent and has a useful life of 5 years. The expected
present values of cash flows from the projects are as follows:
Projects Initial outlay (₹) Present value of Cash Inflows (₹)
1 8,00,000 10,00,000
2 15,00,000 19,00,000
3 7,00,000 11,40,000
4 13,00,000 20,00,000
Which of the above investments should be undertaken? Assume that the cost of capital is 12% and risk free
interest rate is 10% per annum. Given compounded sum of Re. 1 at 10% in 5 years is ₹ 1.611 and discount
factor of Re. 1 at 12% rate for 5th year is 0.567.

Question 73 - Study Material

Shiva Limited is planning its capital investment programme for next year. It has five projects all of which give a
positive NPV at the company cut-off rate of 15 percent, the investment outflows and present values being as
follows:
Project Investment (₹ '000) NPV @ 15% (₹ '000)
A (50) 15.4
B (40) 18.7
C (25) 10.1
D (30) 11.2
E (35) 19.3

The company is limited to a capital spending of ₹ 1,20,000.You are required to optimize the returns from a
package of projects within the capital spending limit. The projects are independent of each other and are
divisible (i.e., part-project is possible).

Traditional approach
Question 74 - Mtp Nov 2021
Superb Ltd. constructs customized parts for satellites to be launched by USA and Canada. The parts are
constructed in eight locations (including the central headquarter) around the world. The Finance Director, Ms.
Kuthrapali, chooses to implement video conferencing to speed up the budget process and save travel costs.
She finds that, in earlier years, the company sent two officers from each location to the central headquarter to
discuss the budget twice a year. The average travel cost per person, including air fare, hotels and meals, is ₹
27,000 per trip. The cost of using video conferencing is ₹ 8,25,000 to set up a system at each location plus ₹
300 per hour average cost of telephone time to transmit signals. A total 48 hours of transmission time will be

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needed to complete the budget each year. The company depreciates this type of equipment over five years by
using straight line method. An alternative approach is to travel to local rented video conferencing facilities,
which can be rented for ₹ 1,500 per hour plus ₹ 400 per hour average cost for telephone charges. You are
Senior Officer of Finance Department. You have been asked by Ms. Kuthrapali to EVALUATE the proposal and
SUGGEST if it would be worthwhile for the company to implement video conferencing.

Question 75 - Rtp May 2022

ABC & Co. is considering whether to replace an existing machine or to spend money on revamping it. ABC &
Co. currently pays no taxes. The replacement machine costs
₹ 18,00,000 now and requires maintenance of ₹ 2,00,000 at the end of every year for eight years. At the end of
eight years, it would have a salvage value of ₹ 4,00,000 and would be sold. The existing machine requires
increasing amounts of maintenance each year and its salvage value fall each year as follows:
Year Maintenance (₹) Salvage (₹)
Present 0 8,00,000
1 2,00,000 5,00,000
2 4,00,000 3,00,000
3 6,00,000 2,00,000
4 8,00,000 0
The opportunity cost of capital for ABC & Co. is 15%. REQUIRED:
When should the company replace the machine? The following present value table is given for you:
Year Present value of ₹ 1 at 15% discount rate
1 0.8696
2 0.7561
3 0.6575
4 0.5718
5 0.4972
6 0.4323
7 0.3759
8 0.3269

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