Production & Operation Management

1. CHAPTER 6: Capital Budgeting
Responses to Questions:
1. Operations management involves decisions to invest in plant and
machinery – new plants at new locations and replacement of the old.
These are decisions regarding allocation of available funds i.e. Capital
budgeting.
2. Since ‘sunk cost’ is, by definition, an entity that does not affect present
decisions being made for the future, it does not affect the capital
budgeting process.
3. Depreciation is a notional allocation of capital cost used in tax calculations
and in profit after tax calculations. Therefore while calculating operational
cash flows of a project, depreciation may be used as follows:
Operational cash flow = Profit after tax + Interest on long-term borrowings
(1-tax rate) + Depreciation + Other non-cash charges
(Note: ‘Other non-cash charges’ include amortization of patent cost and
write-off of preliminary expenses)
Operational cash flows are vital figures in the Capital budgeting decisions.
4. These have been mentioned in the chapter.
5. An explicit measure/criterion like NPV would only be relevant. IRR will not
be relevant, as it is only a ‘rate’.
6. IRR is the rate of return on unrecovered balance. This is one
interpretation. Another interpretation is that IRR represents the compound
rate of return or yield earned on initial investment for the life of the project.
The second interpretation of IRR is based on the assumption that the
intermediate inflows can be re-invested at IRR. However, it may not be
possible for a firm to re-invest intermediate funds at IRR. The first
interpretation is more realistic.
7. One incorporates risk into the discount rate, whereas the other reduces
the NPV by using a coefficient. The second method is more flexible; if in
the 10th
year the income is going to be more certain than the income in the
5th
year, the risk equivalence coefficient in the 10th
year will be higher than
that for the 5th
year. The first method classifies projects into different risk
categories, unlike the second method.
Their similarity is that both are only approximations of the risk complexion
of any project and are one-dimensional.

2. 2
8. a) The investment is paid back after 4 years (years have been rounded
off). Payback period = 4 years.
b) NPV = - 10000 + 3000 + 3000 + 3000 + 3000 + 3000
(1+0.1) (1+0.1)2
(1+0.1)3
(1+0.1)4
(1+0.1)5
= -10,000 + 2727 + 2479 + 2254 + 2049 + 1863
= Rs. 1,372
c) To calculate IRR, we equate investment and discounted cash flows for
the five years (life as given):
10000 = 3000 + 3000 + 3000 + 3000 + 3000
(1+ i) (1+i)2
(1+i)3
(1+i)4
(1+i)5
The value of ‘i’ i.e. IRR is 15.2 per cent approximately.
9. (a) Project X: NPV = -700 + 450 + 450
(1+0.1) (1+0.1)2
= -700 + 409 + 372
= 81.
Project Y: NPV = -7,000 + 4,100 + 4,100
(1+0.1) (1+0.1)2
= -7,000 + 3,272 + 3388
= 115.
(b) Project X: IRR = 18.4 % & Project Y: IRR = 11.6 % (approximately).
(c) Under ‘no capital rationing’, select Y between the two mutually
exclusive projects as Y’s NPV is higher than that of Project X.
(d) The selection between the two will, in addition to NPV, depend upon
the budget constraint.
If budget < 7,000 : select X
If budget ≥ 7,000 : select Y
10. We shall compare the NPVs and choose one of the two projects.
Project A : NPV = -100,000 + 30000 + 35000 + 40000 + 45000
(1+0.1) (1+0.1)2
(1+0.1)3
(1+0.1)4
= -100,000 + 27273 + 28926 + 30052 + 30736
= 16,987

3. 3
Project B: = -100,000 + 15000 + 17500 + 20000 + 22500 + 25000
(1.1) (1.1)2
(1.1)3
(1.1)4
(1.1)5
27.500 + 30000 + 32500
(1.1)6
(1.1)7
(1.1)8
= -1,00,000 + 13636 + 14463 + 15026 + 15368 + 15523 +
15523 + 15395 + 15161
= 20,095
Since project B has a larger NPV, we choose project B.
11. With 12 total periods, there are 12 different series of outflows
corresponding to different periods of replacement. Each series can be
considered as a project and these 12 projects could be compared for
their NPV.
However each project has a different life. Therefore, in order to bring in
uniformity, we need to convert the NPVs into uniform annual cash flows
(uniform annual series or UAS as it is known in the literature).
UAS = NPV
PVFA
(where PVFA is Present Value Factor for Annuity. PVFAs are given for
different discount rates and different lives in readily available tables.)
Let us show, as an example, the comparison of two replacement periods
viz. 5 years and 8 years.
NPV5 = -1600 - 50__ - 70___ - 90___ - 120___ - 150
(1.1) (1.1) 2
(1.1) 3
(1.1) 4
(1.1) 5
= -1600 – 45.55 – 57.85 – 67.62 – 81.96 – 93.14
= -1946.02
NPV8
=
-1600 - 50__ - 70___ - 90___ - 120___ - 150 - 190 - 230 - 270_
(1.1) (1.1) 2
(1.1) 3
(1.1) 4
(1.1) 5
(1.1) 6
(1.1) 7
(1.1) 8
= -2297.26
PVFA for 5 years = 3.7908 for i = 10 %.
PVFA for 8 years = 5.3349 for i = 10 %.
UAS5 = -1946.02 = - 513.35
3.7908
UAS8 = -2297.26 = - 430.61
5.3349

4. 4
Between these two replacement periods, the period of 8 years is chosen
as it has less negative UAS.
Such comparisons should be made between the 12 different possibilities
of replacement periods. The least negative UAS replacement period
should be the optimal replacement cycle.
Note that the revenues have not been mentioned in this problem. So
essentially we had to compare all negative flows (outflows).
12. We have the following relationship in which ‘i’ (IRR) is to be calculated:
25000 = 20000 + 10000 – 10000 + 15000 + 10000
(1+i) (1+i)2
(1+i)3
(1+i)4
(1+i)5
Let us try i = 0.30. It gives:
25000 = 15384 + 5917 – 4552 + 5252 + 2693
= 246494
This is very close. The IRR could be a little lower; perhaps, we could try
i= 0.29. You may try and verify.
Although there are two changes in sign, there is only one IRR (Reader
may verify). ‘n’ changes in sign is only a necessary, not sufficient,
condition for ‘n’ positive roots (IRRs) to the polynomial.
13. Projects in the social sector may be selected even if they have low
IRR. One is not looking for financial performance in this sector; instead
one is looking for a good ‘economic’ performance, i.e. the social cost
benefit analysis should indicate a clear benefit to the society.
Moreover, many social sector projects have a very long gestation
period. For instance, the work done in the primary and secondary
schooling may show results after nearly a generation.
14. ‘Risk’ in the context of social sector amounts to the long term costs to
the society. Not all cost components can be quantified. Many are in the
qualitative realm. Social sector projects are not entirely amenable to a
mathematical analysis.

5. 5
CHAPTER 6: Capital Budgeting
Objective Questions:
1. Merit of the ‘Pay-back Period’ criterion to appraise projects is:
a. it does not discount the cost and income flows.
b. it assumes the same value of money over the different periods.
√c. it implicitly covers risk.
d. none of the above.
2. The project appraisal method that does not depend on the method of
depreciation used for tax purposes is:
a. NPV
b. IRR
c. PI
√d. none of the above
3. Mutually exclusive projects are best selected based upon:
√a. NPV
b. IRR
c. Capital rationing
d. none of the above
4. An investment that pays a fixed number of Rupees per year for a limited
number of years is called:
a. a good investment
b. an NPV
c. a perpetuity
√ d. an annuity
5. A project involved an initial investment of Rs. 5 crore. If the NPV of the
project is Rs. 10 crore, the Profitability Index is:
√ a. 3.0
b. 2.0
c. 1.0
d. 0.5
6. Different discount rates can be used for different years under:
√ a. NPV
b. IRR
c. Payback period
d. all of the above

6. 6
7. Linear programming is used in project appraisal in cases where:
a. risk is being considered.
b. projects are mutually exclusive
√c. capital is rationed
d. none of the above
8. A bio-tech plant has an initial investment of Rs. 200 crore. The benefits,
before depreciation and taxes, are estimated at Rs. 70 crore per year for
the next 10 years which is the life of the plant. If the depreciation is on a
straight line basis for the life of the plant and if there is no salvage value
for the plant, what is the NPV at a 15 per cent required rate of return?
Assume the taxes to be nil.
a. Rs. 551 crore
√b. Rs. 51 crore
c. Rs. 5.1 crore
d. Rs.140 crore
9. For the above problem, the Payback period is :
a. 2 years
b. 3 years
√ c. 4 years
d. 5 years
10 For the above problem, the Profitability Index is (roughly):
a. 2.5
b. 1.25
c. 0.50
√ d. 0.25
11. Sainath & Co. is considering investment in a new machine costing Rs.
1,00,000, replacing the existing old machine. The old machine was bought
5 years ago for Rs. 40,000 and has a present salvage value of Rs. 20,000.
If Sainath decides to replace the old machine by the new, then at the
required rate of return of 10 per cent the net investment now would be:
a. Rs 32,211
b. Rs 67, 789
c. Rs 75,164
√d. Rs 80,000

7. 7
12. A machine in a factory costs Rs 2 million and lasts for 10 years. What
should be the minimal cost saving per year in order to make the purchase
of the machine worthwhile if the cost of capital is 15 per cent and the tax
rate is 50 per cent?
a. Rs. 0.2 million approximately
b. Rs. 0.4 million approximately
√ c. Rs. 0.8 million approximately
d. Rs. 0.1 million approximately
13. Service sector projects may be appraised by using:
a. NPV criterion
b. IRR criterion
c. PI criterion
√d. all of the above