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BEE Paper-1 — Chapter 7: Financial Management

151 questions — 78 objective (1 mark), 55 short (5 marks), 18 long (10 marks). Every answer is checked against the 2014 BEE guidebook and carries its book section reference plus an explanation.
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Objective questions (1 mark) — 78

📖 §7.3 Financial Analysis Techniques — Time Value of Money

1. What is the future value of a cash flow at the end of the 6th year, if the Present Value is Rs. 2 Lakhs and the interest rate is 9%?

  1. 3,28,540
  2. 3,35,420
  3. 2,84,980
  4. none of the above
Answer: B) 3,35,420
Confirmed vs Book-1 §7.3 — FV = PV(1+i)^n = 2,00,000 x (1.09)^6. (1.09)^6 = 1.6771, so FV = 2,00,000 x 1.6771 = Rs.3,35,420. The book's compounding relation is FV = NPV(1+i)^n; options (a) and (c) do not satisfy it at 9% for 6 years.
Source: Sep 2021
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

2. Return on investment (ROI) is ____.

  1. initial investment/annual return
  2. annual cost/capital cost
  3. annual net cash flow/capital cost
  4. none of the above
Answer: C) annual net cash flow/capital cost
Confirmed vs Book-1 §7.3 — Book: ROI = (Annual net cash flow / Capital cost) x 100; as a plain fraction it is annual net cash flow / capital cost. ROI is the inverse of the simple payback period (Example 7.3: 25,000/1,00,000 = 25%, payback = 4 yr).
Source: Sep 2021
📖 §7.5 Sensitivity and Risk Analysis

3. A sensitivity analysis is carried out for an energy saving project to make an assessment of

  1. cash flows
  2. risks due to assumptions
  3. capital investment
  4. best financing source
Answer: B) risks due to assumptions
Confirmed vs Book-1 §7.5 — Book, Section 7.5: 'Sensitivity analysis is an assessment of risk.' Cash flows rest on assumptions (capital cost, savings, escalation, project life) that carry uncertainty. It answers 'what if one or more factors are not as favourable as predicted', i.e. it quantifies the risk in the assumptions.
Source: Sep 2021
📖 §7.3 Financial Analysis Techniques — Simple Payback Period

4. A waste heat recovery system costs Rs. 54 lakh and Rs. 2 lakh per year to operate and maintain. If the annual savings is Rs. 20 lakhs, the payback period will be

  1. 8 years
  2. 2.7 years
  3. 3 years
  4. 10 years
Answer: C) 3 years
Confirmed vs Book-1 §7.3 — Simple payback = Capital cost / ANNUAL NET savings, and net savings = yearly benefit - yearly O&M cost. Net savings = 20 - 2 = Rs.18 lakh/yr; Payback = 54 / 18 = 3 years. (Dividing by the gross 20 lakh gives the trap answer 2.7 yr.)
Source: Apr 2010
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

5. The ratio of annual net cash flow to capital cost is ____

  1. net present value
  2. internal rate of return
  3. return on investment
  4. discount factor
Answer: C) return on investment
Confirmed vs Book-1 §7.3 — Book: 'ROI expresses the annual return expected from a project as a percentage of capital cost.' ROI = annual net cash flow / capital cost. NPV and IRR are discounted measures and the discount factor is 1/(1+k)^n, so only ROI matches the stated ratio.
Source: Apr 2010
📖 §7.3 Financial Analysis Techniques — Time Value of Money

6. Which of the following equation is used to calculate the future value of the cash flow?

  1. NPV (1 – i)n
  2. NPV / (1 – i)n
  3. NPV (1 + i)n
  4. NPV/ (1 + i)n
Answer: C) NPV (1 + i)n
Confirmed vs Book-1 §7.3 — Book relation: FV = NPV (1 + i)^n, and inversely NPV = FV / (1 + i)^n. Future value therefore requires COMPOUNDING at (1 + i)^n, e.g. Rs.100 at 10% becomes Rs.110 after one year.
Source: 2018
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

7. For a project to be viable, the ROI must always be ___ the interest rate.

  1. lower than
  2. higher than
  3. equal to
  4. no relation to
Answer: B) higher than
Confirmed vs Book-1 §7.3 — Book: 'ROI must always be higher than cost of money (interest rate) so as to make the project attractive; the greater the return on investment the better.' If ROI were below the borrowing rate the project would destroy value.
Source: Apr 2010
📖 §7.3 Financial Analysis Techniques — Internal Rate of Return Method

8. Which of the following is not true of IRR?

  1. it takes into account time value of money
  2. it considers the cash flow streams in its entirety
  3. does not distinguish between lending and borrowing
  4. none of the above
Answer: D) none of the above
Confirmed vs Book-1 §7.3 — Book lists as IRR advantages: it takes account of the time value of money and considers the cash-flow stream in its entirety - so (a) and (b) are true. Its stated limitation is that 'the internal rate of return figure cannot distinguish between lending and borrowing' - so (c) is also true of IRR. All three statements are true, hence 'none of the above' is the statement that is NOT true.
Source: Apr 2010
📖 §7.3 Financial Analysis Techniques — Internal Rate of Return Method

9. The internal rate of return is the discount rate for which the NPV is ____.

  1. Always positive
  2. Always negative
  3. negative or positive
  4. None of the above
Answer: D) None of the above
Confirmed vs Book-1 §7.3 — Book: 'The internal rate of return (IRR) of a project is the discount rate which makes its net present value (NPV) equal to zero.' NPV at the IRR is ZERO - not always positive, always negative, or either - so 'none of the above' is correct.
Source: Jul 2022
📖 §7.3 Financial Analysis Techniques — Time Value of Money

10. The present value of equipment is Rs. 10,000 and discount rate is 10%. The future value of the cash flow at the end of 2 years is:

  1. Rs. 10000
  2. Rs. 12,100
  3. Rs. 8100
  4. Rs. 8264
Answer: B) Rs. 12,100
Confirmed vs Book-1 §7.3 — FV = PV(1+i)^n = 10,000 x (1.10)^2 = 10,000 x 1.21 = Rs.12,100. Rs.8,264 and Rs.8,100 are discounted (present-value) figures, which is the reverse operation.
Source: Nov 2009
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

11. The cost of replacement of an inefficient chiller with an energy efficient chiller was Rs. 10 lakh. The net annual cash flow is Rs. 2.50 lakh. The return on investment is:

  1. 18%
  2. 20%
  3. 15%
  4. none of the above
Answer: D) none of the above
Confirmed vs Book-1 §7.3 — ROI = (Annual net cash flow / Capital cost) x 100 = (2.50 / 10.00) x 100 = 25%. 25% is not offered in (a), (b) or (c), so the answer is 'none of the above'.
Source: Nov 2009
📖 §7.7 Energy Performance Contracting and Role of ESCOs

12. The contractor provides the financing and is paid an agreed fraction of actual savings achieved, used to pay down the debt costs of equipment/services. This is known as

  1. traditional contract
  2. extended technical guarantee/service
  3. performance Contract
  4. shared savings performance contract
Answer: D) shared savings performance contract
Confirmed vs Book-1 §7.7 — Book, Types of Performance Contracting: 'In shared savings, ESCO designs, FINANCES and implements the project, verifies energy savings and shares an agreed percentage of the actual energy savings over a fixed period with the customer.' ESCO financing + payment out of an agreed fraction of actual savings = shared savings performance contract.
Source: Nov 2009
📖 §7.5 Sensitivity and Risk Analysis

13. In project financing, sensitivity analysis is applied because

  1. almost all the cash flows involve uncertainly
  2. it evaluates how sensitive the project is to change in the input parameters
  3. it assesses the impact of ‘what if one or more factors are different from what is predicted’
  4. it is applicable to all the above situations
Answer: D) it is applicable to all the above situations
Confirmed vs Book-1 §7.5 — Book, Section 7.5: cash flows contain uncertainty; sensitivity analysis asks 'How sensitive is the project's feasibility to changes in the input parameters?' and 'What if one or more of the factors is not as favourable as predicted?' All three statements are drawn from the same passage, so 'all of the above'.
Source: 2019
📖 §7.3 Financial Analysis Techniques — Internal Rate of Return Method

14. To calculate internal rate of return, the net present value is set to

  1. 1
  2. 0
  3. 10
  4. 100
Answer: B) 0
Confirmed vs Book-1 §7.3 — Book: 'By setting the net present value of an investment to zero ... the discount rate can be computed.' IRR is therefore the discount rate at which NPV = 0.
Source: Nov 2009
📖 §7.3 Comparison between Net Present Value and Internal Rate of Return

15. The discount rate is used as an input in determining _________.

  1. NPV
  2. IRR
  3. payback period
  4. all of the above
Answer: A) NPV
Confirmed vs Book-1 §7.3 — Book: 'In the net present value calculation, NPV of the project is determined by ASSUMING that the discount rate (cost of capital) is KNOWN. In the internal rate of return calculation, we set the net present value equal to zero and DETERMINE the discount rate.' So the discount rate is an INPUT to NPV, while for IRR it is the OUTPUT; simple payback ignores discounting altogether.
Source: 2019
📖 §7.3 Financial Analysis Techniques — Simple Payback Period

16. The cost of an economizer is Rs. 2 lakhs. The simple payback period (SPP) in years considering annual savings of Rs 1,10,000 and annual maintenance cost of Rs 10,000 is ___________.

  1. 1.8
  2. 2.5
  3. 2
  4. 0.5
Answer: C) 2
Confirmed vs Book-1 §7.3 — Annual net savings = 1,10,000 - 10,000 = Rs.1,00,000/yr (O&M must be subtracted first). SPP = 2,00,000 / 1,00,000 = 2 years. (Using the gross Rs.1.10 lakh gives the distractor 1.8 yr.)
Source: 2019
📖 §7.3 Financial Analysis Techniques — Internal Rate of Return Method

17. Which of the following is true?

  1. The internal rate of return is the discount rate for which the NPV is Zero
  2. NPV is the internal rate of return for which the discount rate is Zero
  3. The discount rate is the internal rate of return for which NPV is positive
  4. NPV is the discount rate for which internal rate of return is positive
Answer: A) The internal rate of return is the discount rate for which the NPV is Zero
Confirmed vs Book-1 §7.3 — Book: IRR is the discount rate that makes NPV equal to zero - statement (a) exactly. The other three statements invert the roles of NPV and the discount rate and are meaningless.
Source: 2019
📖 §7.3 Financial Analysis Techniques — Simple Payback Period

18. Which of the following statements are true regarding simple payback period?

  1. considers impact of cash flow even after payback period
  2. takes into account the time value of money
  3. considers cash flow throughout the project life cycle
  4. determines how quickly invested money is recovered
Answer: D) determines how quickly invested money is recovered
Confirmed vs Book-1 §7.3 — Book: payback 'is a measure of how long it will be before the investment recovers itself', i.e. how quickly the invested money comes back. Its stated limitations are that it ignores the time value of money and ignores all savings after the payback period - so (a), (b) and (c) are false.
Source: 2019
📖 §7.3 Financial Analysis Techniques — Simple Payback Period

19. A waste heat recovery system requires Rs. 50 lakhs investment and Rs. 2 lakhs per year to operate and maintain. If the annual savings is Rs. 22 lakhs, the payback period will be

  1. 2.28 years
  2. 2.5 years
  3. 3 years
  4. 10 years
Answer: B) 2.5 years
Confirmed vs Book-1 §7.3 — Annual net savings = 22 - 2 = Rs.20 lakh/yr. Simple payback = 50 / 20 = 2.5 years. (50/22 = 2.28 yr is the trap that forgets O&M.)
Source: 2018
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

20. For investment decision, ROI must always be _____ prevailing interest rate.

  1. Lower than
  2. Higher than
  3. Equal to
  4. No relation
Answer: B) Higher than
Confirmed vs Book-1 §7.3 — Book: 'ROI must always be higher than cost of money (interest rate) so as to make the project attractive.' Only then does the project earn more than the funds cost.
Source: 2018
📖 §7.4 Cash Flow — Capital Investment Considerations

21. If asset depreciation is considered, then net operating cash inflow would be

  1. lower
  2. higher
  3. no effect
  4. none of the above
Answer: B) higher
Corrected (was a) — Book-1 §7.4: Book, Section 7.4: net operating cash inflows are the annual benefits 'after adjusting for applicable taxes and effects of depreciation'; and the depreciation box states that tax law permits depreciation allowances as 'reasonable deductions from TAXABLE INCOME'. Depreciation is a NON-CASH charge, so it does not reduce cash; it only lowers taxable income and hence tax paid. The tax saved (depreciation x tax rate) is retained, so the net operating cash inflow becomes HIGHER. The book confirms depreciation is a benefit: a true lease gives 'no depreciation TAX BENEFITS', and with an ESCO 'the tax benefits of depreciation ... must be negotiated'.
Source: 2018
📖 §7.3 Comparison between Net Present Value and Internal Rate of Return

22. Which technique takes care of time value of money in evaluation?

  1. payback period
  2. IRR
  3. NPV
  4. Both (b) & (c)
Answer: D) Both (b) & (c)
Confirmed vs Book-1 §7.3 — Book: both NPV and IRR are discounted cash-flow methods whose stated advantage is 'It takes into account the time value of money.' The word 'simple' in simple payback denotes that time value of money is NOT considered, so the answer is both (b) and (c).
Source: 2018
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

23. The retrofitting of a variable speed drive in a plant costs Rs 2 lakh. The annual savings is Rs 0.5 lakh. The maintenance cost is Rs. 5,000/year. The return on investment is

  1. 25%
  2. 22.5%
  3. 24%
  4. 27.5%
Answer: B) 22.5%
Confirmed vs Book-1 §7.3 — Annual NET cash flow = 0.50 - 0.05 = Rs.0.45 lakh/yr (maintenance Rs.5,000 = Rs.0.05 lakh must be deducted). ROI = (0.45 / 2.00) x 100 = 22.5%. (Ignoring maintenance gives the distractor 25%.)
Source: 2017
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

24. The cost of replacement of inefficient chiller with an energy efficient chiller in a plant was Rs. 10 lakh .The net annual cash flow is Rs 2.50 lakh .The return on investment is:

  1. 18%
  2. 20%
  3. 15 %
  4. none of the above
Answer: D) none of the above
Confirmed vs Book-1 §7.3 — ROI = (2.50 / 10.00) x 100 = 25%, which is not listed in (a), (b) or (c). Hence 'none of the above'. (Equivalently payback = 4 years and ROI = 1/4 = 25%.)
Source: 2017
📖 §7.7 Energy Performance Contracting and Role of ESCOs

25. The contractor provides the financing and is paid an agreed fraction of actual savings achieved. This payment is used to pay down the debt costs of equipment and/or services. This is known as

  1. traditional contract
  2. extended technical guarantee/service
  3. performance Contract
  4. shared savings performance contract
Answer: D) shared savings performance contract
Confirmed vs Book-1 §7.7 — Book: in SHARED SAVINGS the ESCO 'designs, finances and implements the project, verifies energy savings and shares an agreed percentage of the actual energy savings over a fixed period with the customer.' ESCO-provided finance repaid out of an agreed fraction of measured savings = shared savings performance contract.
Source: 2017
📖 §7.3 / ECBC cross-reference (life-cycle cost objective)

26. Which of the following statements regarding ECBC are correct? i) ECBC defines the norms of energy requirements per cubic metre of area ii) ECBC does not encourage retrofit of Energy conservation measures iii) ECBC prescribes energy efficiency standards for design and construction of commercial and industrial buildings iv) One of the key objectives of ECBC is to minimize life cycle costs (construction and operating energy costs)

  1. i
  2. ii
  3. iii
  4. iv
Answer: D) iv
Confirmed vs Book-1 §7.3 — (i) is wrong - ECBC norms are per SQUARE metre, not cubic metre; (ii) is wrong - ECBC does encourage retrofit of energy conservation measures; (iii) is wrong as worded - ECBC prescribes standards for COMMERCIAL buildings, not industrial buildings. (iv) is correct: a key ECBC objective is to minimise LIFE CYCLE COST (construction plus operating energy cost) - the same life-cycle logic used in Chapter 7 investment appraisal.
Source: 2016
📖 §7.3 Financial Analysis Techniques — Time Value of Money

27. What is the future value of Rs.1000/- after 3 years, if the interest rate is 10%

  1. Rs. 1331
  2. Rs.1610
  3. Rs.3221
  4. none of the above
Answer: A) Rs. 1331
Confirmed vs Book-1 §7.3 — FV = PV(1+i)^n = 1,000 x (1.10)^3 = 1,000 x 1.331 = Rs.1,331. Rs.1,610 would be 1,000 x 1.10 x ... (simple mis-compounding) and Rs.3,221 is unrelated.
Source: 2016
📖 §7.2 Investment — Need, Appraisal and Criteria

28. Any management would like to invest in projects with

  1. Low IRR
  2. Low ROI
  3. Low NPV of future returns
  4. none of the above
Answer: D) none of the above
Confirmed vs Book-1 §7.2 — Book: management invests capital 'where it is going to obtain the greatest return'; a higher IRR, higher ROI and higher NPV are all preferred (the book: 'the higher the net present value, the more attractive is the proposed project'). All three options describe LOW values, which no management would prefer - hence 'none of the above'.
Source: 2016
📖 §7.3 Financial Analysis Techniques — Simple Payback Period

29. Which of these is not true of payback period

  1. Simple to calculate
  2. Considers cash flow beyond the payback period
  3. Shorter the period the better
  4. Does not take into account, time value of money
Answer: B) Considers cash flow beyond the payback period
Confirmed vs Book-1 §7.3 — Book limitation: 'The payback period does not consider savings that are accrued AFTER the payback period has finished.' The other three statements are true of payback (simple to calculate, shorter is better, ignores time value of money), so (b) is the false one.
Source: 2016
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

30. The return on investment (ROI), is expressed as

  1. annual cost / capital cost
  2. (first cost / first year benefits) x 100
  3. NPV / IRR
  4. (annual net cash flow x 100) / capital cost
Answer: D) (annual net cash flow x 100) / capital cost
Confirmed vs Book-1 §7.3 — Book formula: ROI = (Annual net cash flow / Capital cost) x 100. Example 7.3: (25,000 / 1,00,000) x 100 = 25%.
Source: 2012
📖 §7.3 Financial Analysis Techniques — Net Present Value Method

31. _________ considers impact of cash flow even after payback period

  1. net present value
  2. return on investment
  3. sensitivity analysis
  4. simple payback period
Answer: A) net present value
Confirmed vs Book-1 §7.3 — Book: NPV 'considers the cash flow stream in entire project life', i.e. it values every cash flow including those arising after the simple payback point. ROI and simple payback ignore post-payback cash flows and the time value of money; sensitivity analysis is a risk test, not a cash-flow criterion.
Source: 2013
📖 §7.5 Sensitivity and Risk Analysis

32. __________ determines the project viability in response to changes in input parameters.

  1. Life cycle analysis
  2. Financial analysis
  3. Sensitivity analysis
  4. Payback analysis
Answer: C) Sensitivity analysis
Confirmed vs Book-1 §7.5 — Book, Section 7.5: sensitivity analysis asks 'How sensitive is the project's feasibility to changes in the input parameters?' and identifies the switching values at which the decision flips from accept to reject. So it is sensitivity analysis that tests viability against changes in the inputs.
Source: 2013
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

33. For a project to be financially attractive, ROI must always be ___ than interest rate.

  1. lower
  2. higher
  3. equal
  4. no relation
Answer: B) higher
Confirmed vs Book-1 §7.3 — Book: 'ROI must always be higher than cost of money (interest rate) so as to make the project attractive.' A project returning less than the interest rate cannot service the cost of the funds.
Source: 2013
📖 §7.5 Sensitivity and Risk Analysis

34. Which of the following macro factors is used in the sensitivity analysis of project finance?

  1. Change in tax rates
  2. Changes in maintenance cost
  3. Changes in debt: equity ratio
  4. Change in forms of financing
Answer: A) Change in tax rates
Confirmed vs Book-1 §7.5 — Book lists MACRO factors as those the firm's management cannot change: changes in interest rates, CHANGES IN TAX RATES, accounting standards/depreciation methods and rates, subsidies, employment trends, regulations, energy price and technology changes. Maintenance cost, debt:equity (capital structure) and form of finance are listed as MICRO factors.
Source: 2013
📖 §7.3 / ECBC cross-reference (life-cycle cost objective)

35. Which of the following statements regarding ECBC are correct? ECBC defines the norms of energy requirements per sq. metre of area taking into account climatic region where building is located ii) ECBC does not encourage retrofit of Energy conservation measures iii) ECBC prescribes energy efficiency standards for design and construction of commercial and industrial buildings iv) One of the key objectives of ECBC is to minimize life cycle costs (construction and operating energy costs)

  1. i & ii
  2. i & iii
  3. ii & iii
  4. i & iv
Answer: D) i & iv
Confirmed vs Book-1 §7.3 — (i) is correct - ECBC fixes energy norms per SQ. METRE taking the climatic zone into account; (iv) is correct - a key objective is minimising life cycle cost (construction + operating energy cost). (ii) is wrong (ECBC does encourage retrofit) and (iii) is wrong as worded (commercial buildings, not industrial). Hence i & iv.
Source: 2012
📖 §7.3 Financial Analysis Techniques — Internal Rate of Return Method

36. Which of the following statements regarding Internal Rate of Return (IRR) is correct?

  1. IRR distinguishes between lending and borrowing
  2. Internal rate of return is the discount rate at which net present value is equal to zero
  3. if the IRR is higher than current interest rate, the investment is not attractive
  4. between two alternative projects, the project with lower internal rate of return would be considered more attractive
Answer: B) Internal rate of return is the discount rate at which net present value is equal to zero
Confirmed vs Book-1 §7.3 — Book: IRR is the discount rate at which NPV = 0; 'if this discount rate is greater than current interest rate, the investment is sound'; and among alternatives one chooses 'the investment with the highest rate of return'. So (a), (c) and (d) are contradicted by the book and only (b) is correct.
Source: 2012
📖 §7.3 Financial Analysis Techniques — Simple Payback Period

37. The cost of a new heat exchanger is Rs. 1.0 lakh. The simple payback period in years considering annual savings of Rs 60,000 and annual operating cost of Rs. 10,000 is

  1. 0.50
  2. 1.66
  3. 2.00
  4. 6.00
Answer: C) 2.00
Confirmed vs Book-1 §7.3 — Annual net savings = 60,000 - 10,000 = Rs.50,000/yr. SPP = 1,00,000 / 50,000 = 2.00 years. (1,00,000/60,000 = 1.66 yr is the trap that ignores operating cost.)
Source: 2012
📖 §7.3 Financial Analysis Techniques — Time Value of Money

38. What does the concept of time value of money imply

  1. present value of money
  2. future value of money
  3. discounting of cash flows
  4. all of the above
Answer: D) all of the above
Confirmed vs Book-1 §7.3 — Book: the value of money changes with time; discounting gives the PRESENT value of a future cash flow and compounding gives the FUTURE value of a present cash flow (FV = NPV(1+i)^n, NPV = FV/(1+i)^n). Time value of money therefore embraces present value, future value and discounting of cash flows - all of the above.
Source: Guidebook
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

39. Return on Investment (ROI) as a fraction means

  1. initial investment / annual return
  2. annual cost / cost of capital
  3. annual net cash flow / capital cost
  4. none of the above
Answer: C) annual net cash flow / capital cost
Confirmed vs Book-1 §7.3 — Book: ROI = (Annual net cash flow / Capital cost) x 100; as a fraction, annual net cash flow / capital cost. It is the inverse of the simple payback period.
Source: Guidebook
📖 §7.3 Financial Analysis Techniques — Net Present Value Method

40. The net present value (NPV) is

  1. equal to the sum of the present values of all cash flows
  2. equal to the sum of returns
  3. equal to the sum of all cash flows
  4. none of the above
Answer: A) equal to the sum of the present values of all cash flows
Confirmed vs Book-1 §7.3 — Book: 'The net present value (NPV) of a project is equal to the sum of the present values of all the cash flows associated with it', costs negative and savings positive. Adding undiscounted cash flows (option c) is exactly what NPV avoids.
Source: Guidebook
📖 §7.3 Financial Analysis Techniques — Internal Rate of Return Method

41. The Internal Rate of Return (IRR) of an investment is calculated by

  1. selecting a discount rate so that NPV = 0
  2. equating total discounted costs with total discounted benefits
  3. making sure the benefit / cost ratio equals unity
  4. all of the above
Answer: D) all of the above
Confirmed vs Book-1 §7.3 — Setting NPV = 0 and solving for the discount rate (a) is the definition; NPV = 0 also means discounted benefits equal discounted costs (b), which is the same as a benefit/cost ratio of unity (c). All three are equivalent statements of the IRR condition, so 'all of the above'.
Source: Guidebook
📖 §7.3 Comparison between Net Present Value and Internal Rate of Return

42. Project A has an IRR of 85% and NPV of Rs 15,000; project B has an IRR of 25% and NPV of Rs 200,000. Which project would you implement first if financing is available and project technical life is the same?

  1. B
  2. A
  3. cannot be decided
  4. question does not make sense
Answer: A) B
Confirmed vs Book-1 §7.3 — Book: 'The higher the net present value, the more attractive is the proposed project', and NPV 'is essentially a comparison tool which enables number of different projects to be compared'. With finance available and equal technical life, choose the larger absolute wealth gain: B (NPV Rs.2,00,000) over A (NPV Rs.15,000), despite A's higher IRR - the book notes a high IRR need not be desirable.
Source: Guidebook
📖 §7.3 Financial Analysis Techniques — Time Value of Money

43. Which of the following equation can be used to calculate the future value from the present value of cash?

  1. NPV = FV x (1 + i)^n
  2. FV = NPV x (1 - i)^n
  3. NPV = FV / (1 + i)^n
  4. none of the above
Answer: C) NPV = FV / (1 + i)^n
Confirmed vs Book-1 §7.3 — Book relation: FV = NPV (1 + i)^n, or equivalently NPV = FV / (1 + i)^n - the two are the same equation rearranged, so (c) is the only equation printed in the book that links present and future value. Options (a) and (b) are mathematically false forms (wrong side / (1 - i)^n), so (c) is the correct choice.
Source: Guidebook
📖 §7.3 Financial Analysis Techniques — Net Present Value Method

44. The Net Present Value of a project at a discount rate of 16% with an investment of Rs 50,000 at the beginning of the first year, and savings of Rs 23,000 and Rs 36,000 at the end of the first and second year respectively is

  1. 6,581
  2. -246
  3. 862
  4. -3,419
Answer: D) -3,419
Corrected (was a) — Book-1 §7.3: Investment is at the BEGINNING of year 1 (t = 0), so it is not discounted. PV factors at 16%: 0.862 (yr 1) and 0.743 (yr 2). NPV = -50,000 + 23,000(0.862) + 36,000(0.743) = -50,000 + 19,826 + 26,748 = -Rs.3,419 (exact factors give -3,418.5). The NPV is NEGATIVE Rs.3,419, so option (d) is correct (the guidebook prints the figure without its minus sign) and the project would be rejected at 16%.
Source: Guidebook
📖 §7.3 Financial Analysis Techniques — Time Value of Money

45. A sum of Rs 10,000 is deposited in a bank at the beginning of a year. The bank pays 6% interest annually. How much money is in the bank account at the end of the fifth year, if no money is withdrawn?

  1. 13,382
  2. 12,625
  3. 13,000
  4. 10,937
Answer: A) 13,382
Confirmed vs Book-1 §7.3 — FV = PV(1+i)^n = 10,000 x (1.06)^5 = 10,000 x 1.33823 = Rs.13,382. Rs.13,000 is simple (non-compounded) interest, so compounding gives (a).
Source: Guidebook
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

46. The broad indicator of the annual return expected from initial capital investment is

  1. NPV
  2. IRR
  3. ROI
  4. Discount factor
Answer: C) ROI
Confirmed vs Book-1 §7.3 — Book: 'ROI expresses the annual return expected from a project as a percentage of capital cost or initial investment.' NPV and IRR are discounted-cash-flow measures and the discount factor is only a multiplier, so ROI is the broad annual-return indicator.
Source: Guidebook
📖 §7.7 Energy Performance Contracting and Role of ESCOs

47. Which among the following is not a typical performance contract

  1. Shared savings
  2. Guaranteed savings
  3. Fixed fee
  4. Hire purchase
Answer: D) Hire purchase
Confirmed vs Book-1 §7.7 — Book: 'The ESCO will usually offer the following options: Fixed fee, Shared savings, Guaranteed savings.' Hire purchase is an equipment-purchase/credit arrangement, not a performance contract - payment is not linked to measured energy savings.
Source: Guidebook
📖 §7.3 Financial Analysis Techniques — Time Value of Money

48. If the NPV of an investment is Rs.10000 when calculated at a discount rate of 10%. What is the future value of the investment for a period of 2 years.

  1. 12100
  2. 12000
  3. 12110
  4. 12101
Answer: A) 12100
Confirmed vs Book-1 §7.3 — FV = NPV(1+i)^n = 10,000 x (1.10)^2 = 10,000 x 1.21 = Rs.12,100. The other options are not consistent with two years of compounding at 10%.
Source: Mar 2023
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

49. ROI should be always ____ than borrowing interest rate for economic feasibility of any project.

  1. Lower
  2. Equal
  3. No relation
  4. Higher
Answer: D) Higher
Confirmed vs Book-1 §7.3 — Book: 'ROI must always be higher than cost of money (interest rate) so as to make the project attractive.' Only a return above the borrowing rate leaves a surplus after servicing the loan.
Source: Mar 2023
📖 §7.3 Financial Analysis Techniques — Internal Rate of Return Method

50. Which of the following is true with respect to IRR?

  1. If IRR is high than the current interest rate, the investment is not attractive
  2. If between two projects the project with low IRR would be more attractive
  3. IRR is the discount rate at which the NPV is zero
  4. All of the above
Answer: C) IRR is the discount rate at which the NPV is zero
Confirmed vs Book-1 §7.3 — Book: IRR is the discount rate at which NPV = 0 - statement (c). The book also says a project is sound when IRR EXCEEDS the current interest rate and that one selects the HIGHEST rate of return, so (a) and (b) are wrong and 'all of the above' fails.
Source: Mar 2023
📖 §7.3 Financial Analysis Techniques — basic criteria

51. Select the wrong statement for financial analysis ____.

  1. Simple Payback is a measure of how long it will be before the investment makes money
  2. Return on Investment (ROI) and Internal Rate of Return (IRR) enable comparison with other investment options
  3. Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time
  4. Depreciation and payback are two deciding factors about the time value of money.
Answer: D) Depreciation and payback are two deciding factors about the time value of money.
Confirmed vs Book-1 §7.3 — Statements (a), (b) and (c) restate the book: payback measures how long before the investment recovers itself; ROI and IRR allow comparison with other investment options; NPV nets discounted inflows against discounted outflows. Statement (d) is wrong - the time value of money is handled by DISCOUNTING (NPV/IRR); depreciation is a tax allowance and simple payback expressly ignores time value.
Source: Mar 2023
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

52. The retrofitting of a variable speed drive in a plant costs Rs 2 lakh. The annual savings is Rs 0.4 lakh. The maintenance cost is Rs. 0.05 lakh/year. The return on investment is ____.

  1. 25%
  2. 22.5%
  3. 24%
  4. 17.5%
Answer: D) 17.5%
Confirmed vs Book-1 §7.3 — Annual NET cash flow = 0.40 - 0.05 = Rs.0.35 lakh/yr. ROI = (0.35 / 2.00) x 100 = 17.5%. (Forgetting the Rs.0.05 lakh maintenance gives the distractor 20-25% band.)
Source: Jul 2022
📖 §7.3 Financial Analysis Techniques — Time Value of Money

53. Find the future value of Rs. 1,000 at an interest rate of 10% in 10 years' time.

  1. Rs. 2,594
  2. Rs. 386
  3. Rs. 349
  4. Rs. 10,000
Answer: A) Rs. 2,594
Confirmed vs Book-1 §7.3 — FV = PV(1+i)^n = 1,000 x (1.10)^10 = 1,000 x 2.5937 = Rs.2,594. Rs.386 is the reverse operation (present value of Rs.1,000 due in 10 years).
Source: Jul 2022
📖 §7.3 / general energy-accounting term

54. "Toe" stands for ____.

  1. Total oil equivalent
  2. Tons of effluent
  3. Tons of energy equivalent
  4. Tons of oil equivalent
Answer: D) Tons of oil equivalent
Confirmed vs Book-1 §7.3 — 'toe' = tonne (ton) of oil equivalent, the common energy unit used to aggregate different fuels in energy and financial accounting (1 toe = 10^7 kcal). The other expansions are not standard energy units.
Source: Jul 2022
📖 §7.5 Sensitivity and Risk Analysis

55. Sensitivity analysis is an assessment of ____.

  1. Profits
  2. Losses
  3. Risks
  4. All of the above
Answer: C) Risks
Confirmed vs Book-1 §7.5 — Book, Section 7.5, opening line: 'Sensitivity analysis is an assessment of risk.' It tests how far an uncertain input can move before the project becomes unviable (e.g. feasible at 10% energy-cost escalation but break-even at 9% implies high risk).
Source: Jul 2022
📖 §7.6 Financing Options

56. Which of the following is NOT a conventional financing option?

  1. Debt financing
  2. Performance contracting
  3. Retained earnings
  4. Stock buyback
Answer: D) Stock buyback
Confirmed vs Book-1 §7.6 — Book, Section 7.6, lists the conventional financing options: debt financing, equity financing, retained earnings, capital lease, true lease and performance contracting. Stock buyback is a distribution of surplus to shareholders, not a source of funds for capital investment.
Source: Sep 2025
📖 §7.3 Comparison between Net Present Value and Internal Rate of Return

57. Two projects: X (IRR=40%, NPV= Rs 50,000/-) and Y (IRR=30%, NPV= Rs 1,20,000/-) having same life, no finance limit. Choose the best project.

  1. X
  2. Y
  3. Cannot decide
  4. Question invalid
Answer: B) Y
Confirmed vs Book-1 §7.3 — Book: 'The higher the net present value, the more attractive is the proposed project'; NPV measures absolute wealth added and is the comparison tool between projects. With equal life and no financing constraint, choose Y (NPV Rs.1,20,000) over X (NPV Rs.50,000) even though X has the higher IRR - the book warns a high IRR alone is not a desirable feature.
Source: Sep 2025
📖 §7.7 What is Depreciation? (box)

58. Term for asset value decrease over time:

  1. Discounting
  2. Inflation
  3. Depreciation
  4. Compounding
Answer: C) Depreciation
Confirmed vs Book-1 §7.7 — Book: 'Most assets used in the course of a business decrease in value over time. Tax law permits reasonable deductions from taxable income to allow for this. These deductions are called depreciation allowances.' Discounting/compounding relate present and future values, and inflation is a general price effect - only depreciation is the loss of asset value with time.
Source: Sep 2025
📖 §7.4 Cash Flow — Capital Investment Considerations

59. Life-cycle costing is better than simple purchase cost because it:

  1. Includes operation, maintenance and energy costs over life
  2. Ignores maintenance costs
  3. Forces single-supplier bidding
  4. Cuts down procurement cycle time
Answer: A) Includes operation, maintenance and energy costs over life
Confirmed vs Book-1 §7.4 — Book, Section 7.4, requires all four elements to be considered - initial capital cost, net operating cash inflows, economic life and salvage value - not the purchase price alone. Life-cycle costing therefore adds operating, maintenance and energy costs over the whole economic life to the first cost, which is why it is the sounder basis for a decision.
Source: Sep 2025
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

60. ROI for an investment of Rs 1,00,000 with an annual return of Rs 20,000 per year is_______

  1. 1%
  2. 10%
  3. 20%
  4. 200%
Answer: C) 20%
Confirmed vs Book-1 §7.3 — ROI = (Annual net cash flow / Capital cost) x 100 = (20,000 / 1,00,000) x 100 = 20%. Cross-check with the inverse relation: payback = 1,00,000/20,000 = 5 years, and 1/5 = 20%.
Source: Sep 2025
📖 §7.3 Financial Analysis Techniques — Simple Payback Period

61. What is the payback period in energy management?

  1. Time taken to identify savings
  2. Time taken to report savings
  3. Time taken to recover the investment through savings
  4. All of the above
Answer: C) Time taken to recover the investment through savings
Confirmed vs Book-1 §7.3 — Book: the payback period is 'the time (number of years) required to recover the initial investment (capital cost), considering only the Annual Net Savings'. It measures recovery of the investment out of savings, not the time to identify or report them.
Source: Sep 2024
📖 §7.6 Financing Options

62. Which of the following is a method for financing energy efficiency projects?

  1. Loans
  2. Leasing
  3. Performance contracting
  4. All of the above
Answer: D) All of the above
Confirmed vs Book-1 §7.6 — Book, Section 7.6: financing options include debt financing (loans and bonds), leases (capital lease and true lease) and performance contracting through ESCOs, besides equity and retained earnings. All three listed routes are used to finance energy efficiency projects.
Source: Sep 2024
📖 §7.3 Financial Analysis Techniques — Net Present Value Method

63. What is the primary financial metric used to evaluate energy projects?

  1. Gross margin
  2. Net present value (NPV)
  3. Revenue
  4. Operating income
Answer: B) Net present value (NPV)
Confirmed vs Book-1 §7.3 — Book: NPV 'takes into account the time value of money and it considers the cash flow stream in entire project life', and is the criterion used to accept (NPV > 0) or to rank competing energy projects. Gross margin, revenue and operating income are accounting results, not project-appraisal criteria.
Source: Sep 2024
📖 §7.3 Financial Analysis Techniques — Internal Rate of Return Method

64. The internal rate of return is discount rate for which NPV is

  1. Positive
  2. Zero
  3. Negative
  4. All of the above
Answer: B) Zero
Confirmed vs Book-1 §7.3 — Book: 'The internal rate of return (IRR) of a project is the discount rate, which makes its net present value (NPV) equal to zero.' In Example 7.5 the NPV falls from +2,791 at 8% to -1,508 at 16% and passes through zero at IRR = 12.88%.
Source: Sep 2024
📖 §7.3 Comparison between Net Present Value and Internal Rate of Return

65. Which techniques takes care of time value of money in evaluation?

  1. Payback Period
  2. IRR
  3. NPV
  4. Both B and C
Answer: D) Both B and C
Confirmed vs Book-1 §7.3 — Both NPV and IRR are discounted cash-flow methods; the book lists 'It takes into account the time value of money' as an advantage of each. Simple payback expressly excludes it - that is what the prefix 'simple' denotes - so the answer is both (b) and (c).
Source: Sep 2024
📖 §7.4 Cash Flow — Capital Investment Considerations

66. If asset depreciation is considered, then the net operating cash inflow will be

  1. Lower
  2. Higher
  3. No effect
  4. None of the above
Answer: B) Higher
Confirmed vs Book-1 §7.4 — Book, Section 7.4: net operating cash inflows are the annual benefits 'after adjusting for applicable taxes and effects of depreciation'; the depreciation box notes these allowances are deductions from TAXABLE INCOME. Depreciation is a non-cash charge, so it reduces tax payable without reducing cash; the tax saved is retained and the net operating cash inflow is HIGHER. The book treats depreciation as a benefit - a true lease offers 'no depreciation tax benefits' and with an ESCO 'the tax benefits of depreciation ... must be negotiated'.
Source: Sep 2024
📖 Book-1 §7.3 Financial Analysis Techniques — NPV & IRR "Advantages"

67. Which two appraisal techniques account for the time value of money?

  1. Simple payback and ROI
  2. NPV and IRR
  3. ROI and NPV
  4. Simple payback and IRR
Answer: B) NPV and IRR
Confirmed vs Book-1 §7.3 — the guidebook lists "It takes into account the time value of money" as the first advantage of BOTH the NPV method and the IRR method. Payback is explicitly excluded: "The word 'simple' is used as a prefix ... to denote that time value of money is not considered", and under ROI limitations: "It does not take into account the time value of money." Hence only NPV and IRR are discounted-cash-flow techniques → option (b).
Source: AI practice
📖 Book-1 §7.3 Simple Payback Period — Example 7.1

68. A cogeneration project costs Rs.90 lakh, saves Rs.23 lakh/yr in energy, and has an annual O&M cost of Rs.5 lakh. Its simple payback period is:

  1. 3.9 years
  2. 5 years
  3. 4 years
  4. 18 years
Answer: B) 5 years
Confirmed vs Book-1 §7.3 (Example 7.1) — Simple Payback = Capital cost / Annual NET savings, where "Annual Net savings is the cost savings achieved after all the operational costs have been met". Working: net savings = 23 − 5 = Rs.18 lakh/yr; payback = 90 / 18 = 5 years. The book prints this exact sum as 90/(23−5) = 5 years. Trap: dividing by the gross Rs.23 lakh gives 3.9 years — O&M must be netted off first.
Source: AI practice
📖 Book-1 §7.3 Return on Investment (ROI) — Example 7.3

69. An investment of Rs.1,00,000 yields an annual after-tax cash flow of Rs.25,000. The Return on Investment (ROI) is:

  1. 4%
  2. 25%
  3. 40%
  4. 2.5%
Answer: B) 25%
Confirmed vs Book-1 §7.3 (Example 7.3, identical figures) — ROI = (Annual net cash flow / Capital cost) × 100 = (25,000 / 1,00,000) × 100 = 25%. The book states "ROI is an inverse of payback period": payback here = 1,00,000/25,000 = 4 years and 1/4 = 25%. Ch-7 Objective Q2 of the guidebook confirms ROI = annual net cash flow / capital cost.
Source: AI practice
📖 Book-1 §7.3 Time Value of Money (compounding); Ch-7 Objective Q8

70. Rs.10,000 is invested at 6% compound interest for 5 years. The future value is approximately:

  1. Rs.13,000
  2. Rs.13,382
  3. Rs.12,625
  4. Rs.16,000
Answer: B) Rs.13,382
Confirmed vs Book-1 §7.3 — the compounding relation is FV = PV(1+i)ⁿ (the book writes it as FV = NPV(1+i)ⁿ). Working: FV = 10,000 × (1.06)⁵ = 10,000 × 1.33823 = Rs.13,382. This is Ch-7 Objective Q8 of the guidebook, whose printed answer is 13,382. Distractors: Rs.13,000 is the simple-interest result (10,000 + 5×600) and Rs.12,625 is (1.06)⁴, i.e. one year short.
Source: AI practice
📖 Book-1 §7.3 Time Value of Money / NPV Method — discounting

71. The present value of Rs.1,00,000 to be received in 3 years, at a discount rate of 10% (PV factor = 0.751), is:

  1. Rs.75,100
  2. Rs.1,33,100
  3. Rs.90,900
  4. Rs.70,000
Answer: A) Rs.75,100
Confirmed vs Book-1 §7.3 — "discounting determines the present value of future cash flows": PV = FV/(1+i)ⁿ = FV × PV factor. Working: PV = 1,00,000 × 0.751 = Rs.75,100. (0.751 = 1/1.10³, the same style of factor the book tabulates in Examples 7.4 and 7.5.) Rs.1,33,100 is the compounding (future-value) answer, i.e. the wrong direction.
Source: AI practice
📖 Book-1 §7.3 Internal Rate of Return Method; Ch-7 Objective Q4

72. The Internal Rate of Return (IRR) of a project is defined as the discount rate at which:

  1. NPV is maximum
  2. NPV equals zero
  3. Payback equals 1 year
  4. ROI equals 100%
Answer: B) NPV equals zero
Confirmed vs Book-1 §7.3 — "The internal rate of return (IRR) of a project is the discount rate, which makes its net present value (NPV) equal to zero." Guidebook Objective Q4 gives the same idea three ways (NPV = 0, discounted costs = discounted benefits, benefit/cost ratio = 1). "If this discount rate is greater than current interest rate, the investment is sound."
Source: AI practice
📖 Book-1 §7.3 NPV Method; Ch-7 Objective Q7 (16% factors 0.862 / 0.743 as used in Example 7.5)

73. A project needs Rs.50,000 now and returns Rs.23,000 in year 1 and Rs.36,000 in year 2. At a 16% discount rate (factors 0.862 and 0.743), the NPV is approximately:

  1. +Rs.9,000
  2. −Rs.3,426
  3. +Rs.3,426
  4. −Rs.9,000
Answer: B) −Rs.3,426
Confirmed vs Book-1 §7.3 — NPV = Σ(cash flow × PV factor) − capital cost, using the book’s own 16% factors 0.862 (yr 1) and 0.743 (yr 2) from Example 7.5. Working: 23,000×0.862 = 19,826; 36,000×0.743 = 26,748; total PV = 46,574; NPV = 46,574 − 50,000 = −Rs.3,426. Decision rule: "reject the project if the net present value is negative" — so this project is rejected at 16%. (The guidebook’s own Objective Q7 prints the magnitude 3,419, the same figure using unrounded factors.)
Source: AI practice
📖 Book-1 §7.3 IRR — interpolation method (Example 7.5)

74. Trial NPVs of a project are +Rs.495 at 12% and −Rs.65 at 13%. Using linear interpolation, the IRR is approximately:

  1. 12.5%
  2. 12.88%
  3. 13.12%
  4. 12.13%
Answer: B) 12.88%
Confirmed vs Book-1 §7.3 (Example 7.5, identical numbers) — IRR = Lower rate + [NPV at lower rate × (Higher − Lower)] / (NPV at lower − NPV at higher). Working: 12 + [495 × (13 − 12)] / [495 − (−65)] = 12 + 495/560 = 12 + 0.884 = 12.88%. The book quotes exactly 12.88%, and confirms it graphically in Figure 7.1 (NPV versus discount rate).
Source: AI practice
📖 Book-1 §7.7 Types of Performance Contracting; Ch-7 Objective Q10

75. Which of the following is NOT a type of energy performance contract?

  1. Fixed fee
  2. Shared savings
  3. Guaranteed savings
  4. Hire purchase
Answer: D) Hire purchase
Confirmed vs Book-1 §7.7 — "There are a few common types of contracts. The ESCO will usually offer the following options: Fixed fee, Shared savings, Guaranteed savings." Fixed fee = lump sum, ESCO bears least risk; shared savings = ESCO finances and shares a % of actual savings; guaranteed savings = ESCO does not finance but guarantees savings cover debt service. Hire purchase is an instalment-purchase financing arrangement, not a payment-on-performance contract — the answer to guidebook Objective Q10.
Source: AI practice
📖 Book-1 §7.7 What is Depreciation? (with §7.4 salvage value / economic life)

76. Straight-line depreciation of an asset is calculated as:

  1. (Cost − Salvage value) / Useful life
  2. Cost / Salvage value
  3. Cost × Useful life
  4. (Cost + Salvage value) / Useful life
Answer: A) (Cost − Salvage value) / Useful life
Confirmed vs Book-1 §7.7 / §7.4 — depreciation allowances are deductions from taxable income for assets that (i) produce income, (ii) wear out, and (iii) last more than a year. The straight-line method writes off the depreciable amount evenly: Annual depreciation = (Cost − Salvage value) / Useful life, using the book’s own terms salvage (terminal) value and economic life from §7.4. Being a non-cash deduction it lowers tax payable and so raises the after-tax net operating cash inflow — the "tax shield". Under a true lease (§7.6) no depreciation benefit exists because ownership never passes.
Source: AI practice
📖 Book-1 §7.3 Comparison between NPV and IRR; Ch-7 Objective Q5 (identical figures)

77. Project A has IRR 85% and NPV Rs.15,000; Project B has IRR 25% and NPV Rs.2,00,000. With equal life and financing available, which should be implemented first?

  1. Project A, because its IRR is higher
  2. Project B, because its NPV is higher
  3. Neither, because IRR and NPV disagree
  4. Both must have equal priority
Answer: B) Project B, because its NPV is higher
Confirmed vs Book-1 §7.3 — this is guidebook Ch-7 Objective Q5 with the same numbers, and its answer is B. Reason given by the book: "The net present value method is essentially a comparison tool which enables number of different projects to be compared while the internal rate of return method is designed to assess whether or not a single project will achieve a target rate of return." Also "The higher the net present value, the more attractive is the proposed project" — Rs.2,00,000 versus Rs.15,000, so B is implemented first when financing is available and lives are equal.
Source: AI practice
📖 Book-1 §7.6 Financing Options — True lease

78. Under a 'true lease', which statement is correct?

  1. The lessee owns the asset and claims depreciation
  2. Lease payments are tax-deductible but no depreciation benefit is available
  3. Lease payments are not tax-deductible
  4. The lessee always owns the asset at the end of the lease
Answer: B) Lease payments are tax-deductible but no depreciation benefit is available
Confirmed vs Book-1 §7.6 — "True lease allows use of equipment without ownership risks ... Lease payments are tax deductible. No depreciation tax benefits are available and ownership does not occur even at the end of lease period." So (b) is exactly the book sentence; (a) and (d) contradict "ownership does not occur", and (c) contradicts "lease payments are tax deductible". True lease suits SHORT-term use; debt financing (company owns the equipment) suits long-term use.
Source: AI practice

Short questions (5 marks) — 55

📖 §7.3 Financial Analysis Techniques — Payback Period

1. What are the limitations of the (simple) payback period?

Model answer: 1) It ignores the time value of money — cash inflows in different years are simply added without discounting, violating the principle that cash flows at different times can be combined only after compounding/discounting. 2) It does not consider savings accrued after the payback period has finished, so it favours projects with large early cash inflows and discriminates against projects with substantial inflows in later years (even if more profitable overall). 3) It gives no measure of overall profitability or return on the investment.
'Simple' = ignores time value of money; blind to cash flows after payback.
Source: Guidebook
📖 §7.3 Financial Analysis Techniques — Return on Investment (ROI)

2. What are the limitations of the ROI method?

Model answer: 1) It does not take into account the time value of money. 2) It does not account for the variable nature of annual net cash inflows — it assumes a steady annual return. For example, a 25% ROI would be economically valid only if the investment yields that fixed amount every year in perpetuity, which is not a realistic condition.
ROI = annual return as % of capital, but ignores time value and assumes constant returns.
Source: Guidebook
📖 §7.3 Comparison between Net Present Value and Internal Rate of Return

3. Compare the NPV and IRR methods of financial analysis.

Model answer: In the NPV calculation, the discount rate (cost of capital) is assumed known and the NPV is computed. In the IRR calculation, the NPV is set equal to zero and the discount rate (the IRR) that satisfies this condition is determined. The NPV method is essentially a comparison tool that lets a number of different projects be compared, while the IRR method is designed to assess whether or not a single project will achieve a target rate of return. Both take into account the time value of money and consider the cash flow stream over the entire project life.
NPV = assume rate, compare projects; IRR = set NPV=0, test a single project's return.
Source: Guidebook
📖 §7.7 Energy Performance Contracting and Role of ESCOs

4. Explain briefly the operation of an ESCO.

Model answer: ESCOs are companies that provide a complete energy project service — from assessment to design to construction/installation, along with engineering and project management services, and financing. The ESCO purchases, installs and maintains the equipment, and crucially is paid based on the performance of the installed equipment (payment-on-performance): only after the equipment actually reduces expenses does the contractor get paid. This removes the incentive to cut corners and gives the client energy savings with little up-front money. The ESCO offers contracts as fixed fee, shared savings or guaranteed savings, and the amount of risk assigned to the ESCO is directly related to the percent savings shared with it.
Complete energy service + financing; paid only on verified performance.
Source: Guidebook
📖 §7.3 Simple Payback — worked short question S-1 (CFL retrofit)

5. 100 fused 60 W incandescent lamps are replaced by 100 nos. 12 W CFLs (instead of new 60 W lamps), for 4000 h/yr. Find (i) the annual reduction in electricity cost if energy charge is Rs.4/kWh and demand charge is Rs.250/kVA/month, and (ii) the simple payback if an ILB costs Rs.10 and a CFL costs Rs.100 (lives 1000 h and 4000 h).

Model answer: Connected-load reduction = 100 × (60 − 12) = 4800 W = 4.8 kW. (i) Energy saved = 4.8 × 4000 = 19,200 kWh → energy cost saving = 19,200 × 4 = Rs.76,800/yr. Demand saving = 4.8 kVA × 250 × 12 = Rs.14,400/yr. Total annual reduction ≈ Rs.91,200/yr. (ii) Over 4000 h one CFL (life 4000 h) replaces four ILBs (life 1000 h each); incremental cost per fitting = 100 − 4×10 = Rs.60; for 100 fittings = Rs.6,000. Simple payback = 6,000 / 91,200 ≈ 0.066 yr (≈ 24 days).
Load saving × hours × tariff; payback = incremental cost / annual saving.
Source: Guidebook
📖 §7.3 IRR — affordability/IRR check

6. A firm invests Rs.10 lakh at the start of year 1 in an EE project and expects an IRR of at least 26% on a constant annual net cash flow of Rs.2 lakh over 10 years. Will the project meet the firm's expectation?

Model answer: At the required 26%, the present value of Rs.2 lakh/yr for 10 years (sum of 26% PV factors ≈ 3.465) is about 2 × 3.465 = Rs.6.93 lakh, which is less than the Rs.10 lakh invested → NPV is negative at 26%. The actual IRR (rate making NPV = 0) is far lower (cash flows total only Rs.20 lakh over 10 years on a Rs.10 lakh outlay), so the project does NOT meet the firm's 26% expectation.
PV of inflows at 26% < investment → IRR below 26% → expectation not met.
Source: Guidebook
📖 §7.3 NPV — retrofit appraisal

7. An energy retrofit costs Rs.1,00,000 and yields 6000 kWh/yr at Rs.3/kWh plus Rs.3800/yr demand savings plus Rs.2000/yr maintenance savings, for a 10-year life with no rate change. Calculate the NPV at a 12% discount rate.

Model answer: Annual net saving = energy 6000×3 = 18,000 + demand 3,800 + maintenance 2,000 = Rs.23,800/yr. Sum of 12% PV factors for 10 years ≈ 5.650. PV of savings = 23,800 × 5.650 ≈ Rs.1,34,470. NPV = 1,34,470 − 1,00,000 ≈ +Rs.34,470. NPV > 0, so the upgrade is financially attractive.
Add all annual savings, multiply by Σ PV factors, subtract capital.
Source: Guidebook
📖 §7.3 IRR — Limitations / NPV vs IRR

8. Explain why a project with a high IRR is not necessarily more attractive than a project with lower IRR.

Model answer: The IRR figure cannot distinguish between lending and borrowing, so a high IRR need not be a desirable feature. NPV, by contrast, represents the absolute increase in company/shareholder wealth. A project may have a very high IRR but low NPV, while another has a lower IRR but a much higher NPV; in that case the higher-NPV project should be selected. Hence a high IRR alone does not make a project more attractive — NPV is the better selection criterion when financing is available.
IRR is a % (can't tell lending from borrowing); NPV measures absolute value added.
Source: BEE Book
📖 §7.3 NPV — decision rule (numerical)

9. An industry invests Rs.5,00,000 in an energy-saving project with cash flows Year 1 Rs.2,00,000, Year 2 Rs.3,00,000, Year 3 Rs.2,00,000. Required return 10%. Evaluate the NPV and comment on feasibility.

Model answer: NPV = −5,00,000 + 2,00,000/1.10 + 3,00,000/(1.10)² + 2,00,000/(1.10)³ = −5,00,000 + 1,81,818 + 2,47,934 + 1,50,263 = +Rs.80,015. Since NPV is positive, the project is viable and attractive (accept).
Positive NPV → accept.
Source: 2009
📖 §7.3 IRR — max affordable investment

10. An ESCO invests in a waste-heat recovery project expected to yield Rs.10,00,000/yr for 7 years. If the ESCO expects 30% IRR, calculate the maximum investment that can be made.

Model answer: At the target IRR the investment equals the present value of the savings discounted at 30%. Sum of 30% PV factors for years 1–7 ≈ 2.8021. Investment = 10,00,000 × 2.8021 = Rs.28,02,100. The ESCO can pay up to about Rs.28.0 lakh for the heat exchanger and still keep NPV ≥ 0 (i.e. still achieve at least 30%).
Max investment = annual saving × Σ PV factors at required IRR.
Source: BEE Book
📖 §7.3 NPV — feasibility (numerical)

11. A VFD for a fan needs Rs.3 lakh investment; cash flows at end of years 1, 2, 3 are Rs.1.2 lakh, Rs.1.5 lakh, Rs.1.5 lakh. Calculate NPV at 10% and state whether the project is feasible.

Model answer: NPV = −3,00,000 + 1,20,000/1.10 + 1,50,000/(1.10)² + 1,50,000/(1.10)³ = −3,00,000 + 1,09,090 + 1,23,967 + 1,12,697 = +Rs.45,754. Since NPV is positive, the VFD investment is feasible.
Positive NPV → feasible.
Source: 2023
📖 §7.3 NPV — staggered investment (numerical)

12. Calculate NPV over 4 years for a project with Rs.70,000 invested at the start of year 1 and another Rs.70,000 at the start of year 2, with fuel-cost savings of Rs.65,000 in year 2 and Rs.60,000 each in years 3 and 4. Discount rate 12%.

Model answer: NPV = −70,000 − 70,000/1.12 + 65,000/(1.12)² + 60,000/(1.12)³ + 60,000/(1.12)⁴ = −70,000 − 62,500 + 51,818 + 42,707 + 38,131 ≈ +Rs.156. NPV is marginally positive, so the project is just barely feasible.
Second outlay is discounted one year; barely positive NPV.
Source: 2022
📖 §7.4 Cash Flow + §7.3 NPV (with salvage value)

13. An energy-efficient air compressor costs Rs.6,00,000, saves Rs.1,80,000/yr for 3 years, with annual maintenance of Rs.10,000 from year 2 onward, salvage Rs.50,000 at end of year 3, discount rate 10%. Find (a) net annual cash flow from year 2, (b) NPV, (c) economic acceptability.

Model answer: (a) Net cash flow from year 2 = 1,80,000 − 10,000 = Rs.1,70,000. (b) PV: Yr0 −6,00,000; Yr1 1,80,000×0.909 = 1,63,636; Yr2 1,70,000×0.826 = 1,40,420; Yr3 (1,70,000+50,000)×0.751 = 2,20,000×0.751 = 1,65,220. NPV = (1,63,636+1,40,420+1,65,220) − 6,00,000 = −Rs.1,30,724. (c) NPV is negative, so over 3 years at 10% the project does not recover its cost and is not economically acceptable.
Add salvage to final-year inflow; negative NPV → reject.
Source: 2025
📖 §7.3 IRR — max investment (numerical)

14. Calculate the investment of a project having IRR 16% with annual savings of Rs.15,000, Rs.18,000 and Rs.20,000 at the end of years 1, 2 and 3 respectively.

Model answer: At the IRR the investment equals the PV of savings discounted at 16%: Investment = 15,000×0.862 + 18,000×0.743 + 20,000×0.641 = 12,930 + 13,374 + 12,820 = Rs.39,124 (≈ Rs.39,121).
Investment = Σ(saving × 16% PV factor).
Source: 2024
📖 §7.3 NPV Method — Example 7.4

15. An energy-saving project costs Rs.30,000 and yields net savings of Rs.6,000/yr for 10 years. At an 8% discount rate, calculate the NPV and state whether to accept. (8% PV factors yrs 1–10: 0.926, 0.857, 0.794, 0.735, 0.681, 0.630, 0.583, 0.540, 0.500, 0.463.)

Model answer: Sum of 8% PV factors over 10 years = 6.709. PV of savings = 6,000 × 6.709 = Rs.40,254. NPV = 40,254 − 30,000 = +Rs.10,254. Since NPV > 0, ACCEPT the project. (In the guidebook the comparison Project 2 gives +Rs.10,867, so the higher-NPV Project 2 is preferred.)
Σ(CF × factor) − investment; higher NPV wins when comparing.
Source: Guidebook
📖 §7.3 IRR Method — Example 7.5 (interpolation)

16. A project needs Rs.20,000 and gives cash flows of Rs.6,000, 5,500, 5,000, 4,500, 4,000, 4,000 over years 1–6. Trial NPVs are +Rs.495 at 12% and −Rs.65 at 13%. Estimate the IRR and state whether it is acceptable if the cost of capital is 8%.

Model answer: IRR = r_low + NPV_low × (r_high − r_low) / (NPV_low − NPV_high) = 12 + 495 × (13 − 12) / (495 − (−65)) = 12 + 495/560 = 12.88%. Since IRR (12.88%) > cost of capital (8%), the investment is sound — accept.
Interpolate between a small +ve and small −ve NPV; IRR > k → accept.
Source: Guidebook
📖 Book-1 §7.3 Payback Period — definition and equation

17. Define the simple payback period and state its formula.

Model answer: The simple payback period is the time (number of years) required to recover the initial investment (capital cost), considering only the annual net savings (yearly benefits − yearly costs). Formula: Simple Payback period = Capital cost / Annual net savings. The word 'simple' denotes that the time value of money is NOT considered. The shorter the payback, the more attractive the project; the maximum permissible payback is a matter of company choice.
Confirmed vs Book-1 §7.3 — Simple Payback = Capital cost / Annual net savings; "annual net savings is the cost savings achieved after all the operational costs have been met". The prefix ‘simple’ denotes that time value of money is NOT considered.
Source: AI-practice
📖 Book-1 §7.3 Simple Payback Period — Example 7.1

18. A cogeneration system reduces a company's annual energy bill by Rs.23 lakh. Capital cost is Rs.90 lakh and annual maintenance/operating cost is Rs.5 lakh. What is the payback period?

Model answer: Annual net savings = gross savings − operating cost = 23 − 5 = Rs.18 lakh. Simple payback = Capital cost / Annual net savings = 90 / 18 = 5 years.
Confirmed vs Book-1 §7.3 Example 7.1 — 90/(23−5) = 5 years. Subtract the Rs.5 lakh O&M from the Rs.23 lakh gross saving BEFORE dividing.
Source: AI-practice
📖 Book-1 §7.3 Return on Investment (ROI)

19. Define Return on Investment (ROI), give its formula, and state its relationship to payback period.

Model answer: ROI expresses the annual return expected from a project as a percentage of the capital cost (initial investment): ROI = (Annual net cash flow / Capital cost) × 100. ROI is the inverse of the payback period. For a project to be attractive, ROI must always be higher than the cost of money (interest rate); the greater the ROI, the better the investment. ROI does not require similar project life or capital cost when comparing projects.
Confirmed vs Book-1 §7.3 — ROI = (annual net cash flow / capital cost) × 100, and "ROI is an inverse of payback period". ROI must exceed the cost of money; it needs no equality of project life or capital cost for comparison.
Source: AI-practice
📖 Book-1 §7.3 ROI — Example 7.3

20. An outlay of Rs.1,00,000 for equipment provides an after-tax cash flow of Rs.25,000/yr over six years without significant fluctuation. What is the ROI?

Model answer: ROI = (Average annual operating cash flow / Net investment) × 100 = (25,000 / 1,00,000) × 100 = 25%. (Correspondingly, the payback period = inverse = 4 years.)
Confirmed vs Book-1 §7.3 Example 7.3 — ROI = 25,000/1,00,000 × 100 = 25%; payback = 1/ROI = 4 years.
Source: AI-practice
📖 Book-1 §7.3 Payback Period — Advantages

21. State the advantages of the simple payback period as an appraisal method.

Model answer: 1) It is simple, both in concept and application, and does not require tedious calculations — a shorter payback generally indicates a more attractive investment. 2) It favours projects that generate substantial cash inflows in the earlier years and discriminates against projects whose substantial inflows come only in later years (useful where quick capital recovery matters).
Confirmed vs Book-1 §7.3 (Payback — Advantages) — simple in concept and application with no tedious calculations, and it favours projects with substantial early cash inflows.
Source: AI-practice
📖 Book-1 §7.3 Time Value of Money / NPV Method (compounding vs discounting)

22. What is the time value of money? Differentiate between compounding and discounting.

Model answer: Time value of money means the value of money changes with time, so cash flows occurring at different times must be equated to a common basis before they can be compared or added. Compounding determines the FUTURE value of present cash flows (present → future), e.g. Rs.100 at 10% becomes Rs.110 in one year. Discounting is the opposite process and determines the PRESENT value of future cash flows (future → present), e.g. Rs.100 received in one year is worth only Rs.90.91 today at 10%. The present-value (discounting) concept is the method used to relate these various cash flows.
Confirmed vs Book-1 §7.3 — "Compounding determines the future value of present cash flows, whereas discounting determines the present value of future cash flows." The book’s own example: Rs.100 at 10% → Rs.110 in a year; Rs.100 in a year is worth Rs.90.91 today.
Source: AI-practice
📖 Book-1 §7.3 Time Value of Money — FV/PV relationship

23. Write the equations relating future value and present value of a cash flow, defining each variable.

Model answer: FV = PV × (1 + i)ⁿ (compounding) and PV = FV / (1 + i)ⁿ (discounting). The PV factor (discount factor) = 1 / (1 + i)ⁿ. Where FV = future value of the cash flow, PV (NPV) = present value of the cash flow, i = interest or discount rate, and n = number of years in the future.
Confirmed vs Book-1 §7.3 — the guidebook prints FV = NPV(1+i)ⁿ, or NPV = FV/(1+i)ⁿ, where it uses the symbol NPV for the present value of the cash flow, i = interest/discount rate and n = number of years in the future.
Source: AI-practice
📖 Book-1 §7.3 Net Present Value Method — equation and decision rule

24. Define Net Present Value (NPV) and state its decision rule and formula.

Model answer: The NPV of a project is the sum of the present values of all the cash flows (capital costs and net savings) over the life of the project, discounted at an assumed discount rate k. Formula: NPV = Σ CFₜ / (1 + k)ᵗ for t = 0 to n, where costs/outflows are negative and savings/inflows positive (capital investment at t=0 is negative). Decision rule: accept the project if NPV is positive and reject if NPV is negative; a zero NPV is value-neutral. The higher the NPV, the more attractive the project. NPV considers the time value of money and the entire project life.
Confirmed vs Book-1 §7.3 — NPV = Σ CFₜ/(1+k)ᵗ (t = 0…n), costs negative and savings positive. Decision rule: "Accept the project if the net present value is positive and reject the project if the net present value is negative"; a zero NPV is value-neutral.
Source: AI-practice
📖 Book-1 §7.3 NPV Method — Advantages

25. State the advantages of the Net Present Value (NPV) method.

Model answer: 1) It takes into account the time value of money. 2) It considers the cash flow stream over the entire project life. (As a comparison tool it also directly indicates value added — a positive NPV means an economic gain, and the higher the NPV the more attractive the project.) Its credibility depends on a realistic prediction of the discount rate, which is prudently set slightly above the interest rate at which the project capital is borrowed.
Confirmed vs Book-1 §7.3 (NPV — Advantages) — it takes into account the time value of money and considers the cash flow stream over the whole project life; credibility depends on a realistic discount rate, prudently set slightly above the borrowing rate.
Source: AI-practice
📖 Book-1 §7.3 Internal Rate of Return Method

26. Define the Internal Rate of Return (IRR) and state how it is interpreted.

Model answer: The IRR of a project is the discount rate that makes its Net Present Value equal to zero (the minimum value that would make the investment worthwhile). It is found in the NPV equation by setting NPV = 0 and solving for k. If this discount rate is greater than the current interest rate (cost of capital), the investment is sound. When comparing alternatives, choose the investment with the highest rate of return. Determining IRR is an iterative process of guesses and approximations (or by using a spreadsheet IRR function).
Confirmed vs Book-1 §7.3 — IRR is the discount rate that makes NPV zero; if it exceeds the current interest rate the investment is sound, and among alternatives the highest rate of return is chosen. Determining it is an iterative process of guesses and approximations.
Source: AI-practice
📖 Book-1 §7.3 IRR — interpolation method (Example 7.5)

27. Write the interpolation formula used to estimate the IRR.

Model answer: IRR = Lower rate + [NPV at lower rate × (Higher rate − Lower rate)] / (NPV at lower rate − NPV at higher rate). The two trial rates are chosen so that one gives a small positive NPV and the other a small negative NPV (NPV brackets zero), and the IRR is then interpolated between them.
Confirmed vs Book-1 §7.3 (Example 7.5) — IRR = Lower rate + [NPV at lower rate × (Higher − Lower rate)] / (NPV at lower − NPV at higher). The book applies it as 12 + 495(13−12)/(495−(−65)) = 12.88%.
Source: AI-practice
📖 Book-1 §7.3 IRR — Advantages and Limitations

28. State the advantages and the limitation of the IRR method.

Model answer: Advantages: 1) It takes into account the time value of money. 2) It considers the cash flow stream in its entirety. 3) It makes sense to businessmen who prefer to think in terms of a rate of return and find an absolute quantity like NPV harder to work with. Limitation: the IRR figure cannot distinguish between lending and borrowing, so a high IRR need not necessarily be a desirable feature.
Confirmed vs Book-1 §7.3 — advantages: time value of money, whole cash-flow stream, and a rate of return that businessmen find easier than an absolute NPV. Limitation: "The internal rate of return figure cannot distinguish between lending and borrowing."
Source: AI-practice
📖 Book-1 §7.3 Financial Analysis Techniques — basic criteria for investment appraisal

29. List the basic criteria used for financial investment appraisal and what each measures.

Model answer: 1) Payback period — measures how long before the investment recovers itself (helps decide the financing term). 2) NPV and Cash Flow — allow financial planning by accounting for streams of money inflow and outflow over time; provide all information needed to bring EE projects into the corporate financial system. 3) ROI and IRR — allow comparison with other investment options. Energy-efficiency investment should be judged by exactly the same criteria as any other investment; no faster/more attractive return should be demanded of it.
Confirmed vs Book-1 §7.3 — payback (how long before the investment recovers itself), NPV and cash flow (financial planning of inflow/outflow streams), and ROI and IRR (comparison with other investment options). The book stresses that no faster or more attractive return should be demanded of energy efficiency.
Source: AI-practice
📖 Book-1 §7.4 Cash Flow — Capital Investment Considerations

30. List the four elements considered in judging the attractiveness of any investment (cash-flow elements).

Model answer: 1) Initial capital cost or net investment — all costs to prepare the investment for service (purchase + installation + preparation); non-recurring. 2) Net operating cash inflows — the annual benefits/savings (revenues or savings) after tax and depreciation, summed as a single end-of-year cash flow. 3) Economic life — the time span of benefits, i.e. period between initial cost and the last future cash flow. 4) Salvage value — the terminal value/revenue from disposing of the investment at the end of its useful life.
Confirmed vs Book-1 §7.4 — the four elements are initial capital cost / net investment, net operating cash inflows, economic life, and salvage value.
Source: AI-practice
📖 Book-1 §7.4 Cash Flow — Salvage value

31. What is salvage (terminal) value in investment analysis?

Model answer: The salvage or terminal value of an investment is the revenue (or expense) attributed to disposing of the investment at the end of its useful life. If there is substantial recovery of capital from eventual disposal of assets, these estimated amounts must be made part of the analysis. Such recoveries include proceeds from the sale of facilities and equipment (beyond minor scrap value) as well as the release of any working capital associated with the investment.
Confirmed vs Book-1 §7.4 — salvage (terminal) value is the revenue or expense of disposing of the investment at the end of its useful life, including sale proceeds beyond minor scrap value and the release of working capital.
Source: AI-practice
📖 Book-1 §7.4 Cash Flow Diagrams (Figure 7.2 — rules)

32. What is a cash-flow diagram and what are the conventions/rules for drawing one?

Model answer: A cash-flow diagram is a convenient graphical display of the revenues (savings) and costs of an investment along a time axis, which makes the timing of cash flows clear and improves correct application of time-value-of-money concepts. Rules/convention: the horizontal axis is divided into time periods (usually years); arrows always point away from the time axis; upward arrows = cash inflow (income/savings, +) and downward arrows = cash outflow (costs/expenditure, −); arrows occurring in the same year can be summed. A good diagram should be complete, accurate and legible.
Confirmed vs Book-1 §7.4 (Figure 7.2) — arrows always point away from the time axis; up = income, down = expenses; arrows in the same year can be summed. A good diagram is complete, accurate and legible.
Source: AI-practice
📖 Book-1 §7.5 Sensitivity and Risk Analysis

33. What is sensitivity analysis and why is it carried out?

Model answer: Sensitivity analysis is an assessment of risk. Because many project cash flows (capital cost, energy savings, maintenance, inflation, project life) are based on uncertain estimates, sensitivity analysis tests how sensitive the project's feasibility is to changes in the input parameters — how much a factor would have to vary before the project becomes unviable, and the probability of that happening. It is recommended especially for marginal/borderline projects and projects close to the cut-off rate. It identifies uncertain parameters to which the NPV/IRR decision is sensitive (switching values), leading to improved project design with mitigation against major sources of uncertainty.
Confirmed vs Book-1 §7.5 — "Sensitivity analysis is an assessment of risk", recommended particularly where feasibility is marginal, testing how much a parameter must vary before the project becomes unviable and identifying switching values.
Source: AI-practice
📖 §7.5 Sensitivity Analysis — micro vs macro factors

34. In financial management, what are micro and macro factors? List three of each that influence sensitivity analysis.

Model answer: Micro factors are variables related to the project that the firm CAN influence/change: e.g. operating expenses, capital structure, cost of debt/equity, changing the form of finance (e.g. leasing), changing the project life. Macro factors are macro-economic variables affecting the whole industry that the firm's management CANNOT change: e.g. changes in interest rates, changes in tax rates, changes in accounting standards / depreciation methods and rates, government subsidies, employment/salary trends, environmental & safety regulations, energy price changes, technology changes.
Micro = firm-controllable; Macro = external/uncontrollable.
Source: 2010s
📖 Book-1 §7.6 Financing Options

35. List the conventional financing options for capital investment given in the guidebook.

Model answer: The various conventional financing options are: 1) Debt financing, 2) Equity financing, 3) Retained earnings, 4) Capital lease, 5) True lease, and 6) Performance contracting. Capital investment requires a source of funds; for large companies multiple sources may be employed, and the process of obtaining the funds is called financing.
Confirmed vs Book-1 §7.6 — the conventional financing options listed are debt financing, equity financing, retained earnings, capital lease, true lease and performance contracting.
Source: AI-practice
📖 §7.6 Financing Options — Debt vs Equity

36. Differentiate debt financing from equity financing in terms of ownership, cost and tax treatment.

Model answer: Debt financing: the company borrows money (loans/bonds) to be repaid later with interest; the company OWNS the equipment (good for long-term use), interest payments are tax-deductible, the cost of capital is relatively easy to calculate, but the company takes ALL the risk and must install and manage the project. Equity financing: the lender acquires an ownership (equity) position (stocks) and shares in the organization's financial success; its cost of capital is HIGHER than debt (partly because dividends are NOT tax-deductible, unlike interest).
Debt: own + tax-deductible interest + all risk; Equity: shared ownership, costlier, no tax deduction.
Source: AI-practice
📖 Book-1 §7.6 Financing Options — Retained earnings

37. What are retained earnings as a financing option, and what cost of capital applies to them?

Model answer: Retained earnings are the accumulation of annual earnings surpluses that a company retains within the company rather than paying out to stockholders as dividends. Although held by the company, they truly belong to the stockholders, and hence the same cost of capital as for stock (equity) is applied to them. They are one of the two primary sources of equity financing (stocks and retained earnings).
Confirmed vs Book-1 §7.6 — retained earnings are accumulated annual surpluses kept in the company; "although these earnings are held by the company, they truly belong to the stockholders and hence the same cost of capital for stock is applied".
Source: AI-practice
📖 Book-1 §7.6 Financing Options — Capital lease and True lease

38. Differentiate a capital lease from a true lease, and state why a true lease offers no depreciation benefit.

Model answer: A capital lease allows a lower cost of capital with third-party participation and is a mid-way option between pure debt and pure equity financing (it carries partial ownership characteristics). A true lease allows use of the equipment WITHOUT ownership risks, offers reduced risk of poor performance/service/equipment obsolescence, and is particularly suitable for short-term use; its lease payments are tax-deductible. Because under a true lease ownership never occurs (not even at the end of the lease period), NO depreciation tax benefits are available — only the owner of an asset can claim depreciation.
Confirmed vs Book-1 §7.6 — capital lease is "a mid-way between pure debt and pure equity financing"; the true lease gives use without ownership risks, is suited to short-term use, and "no depreciation tax benefits are available and ownership does not occur even at the end of lease period".
Source: AI-practice
📖 Book-1 §7.6 Financing Options — Debt financing

39. Write short notes on debt financing.

Model answer: Debt financing involves borrowing and using money that is to be repaid later, with interest paid to the lending party for the privilege of using it. The two primary sources of debt capital are loans and bonds (e.g. car loans, mortgage loans). The company owns the equipment, so it suits long-term use. The cost of capital is relatively easy to calculate since interest rates and repayment schedules are clearly documented. A key benefit is that interest payments on debt capital are tax-deductible; however, the company takes all the risk and must install and manage the project itself.
Confirmed vs Book-1 §7.6 — debt financing is borrowing repaid with interest, from loans and bonds; the company owns the equipment (good for long-term use), interest payments are tax deductible, but the company takes all the risk and must install and manage the project.
Source: AI-practice
📖 Book-1 §7.7 Energy Performance Contracting and Role of ESCOs

40. What is an ESCO and what is energy performance contracting?

Model answer: An ESCO (Energy Service Company) is a company that provides a complete energy project service — from assessment to design to construction/installation, along with engineering and project management services, and financing. Energy performance contracting is a unique arrangement allowing industry to make energy-efficiency improvements with very little up-front money: the contractor (usually an ESCO) purchases, installs and maintains the equipment and is paid based on the performance of the installed equipment — only after the equipment actually reduces expenses does the contractor get paid. This payment-on-performance removes the incentive to cut corners and usually entails a facility-wide scope of work.
Confirmed vs Book-1 §7.7 — ESCOs "provide a complete energy project service, from assessment to design to construction or installation, along with engineering and project management services, and financing"; under performance contracting the contractor is paid only after the installed equipment actually reduces expenses.
Source: AI-practice
📖 Book-1 §7.7 Types of Performance Contracting

41. List and explain the three common types of performance contract offered by ESCOs.

Model answer: 1) Fixed fee — the ESCO conducts an audit, designs the project and either helps implement it or simply advises, for a fixed lump-sum fee; the ESCO bears the least risk because its fee does not depend on achieved savings. 2) Shared savings — the ESCO designs, finances and implements the project, verifies the energy savings, and shares an agreed percentage of the actual savings with the customer over a fixed period (more saved → higher revenue to both). 3) Guaranteed savings — the ESCO designs and implements the project but does NOT finance it (though it may facilitate financing), and guarantees the energy savings will be sufficient to cover debt-service payments. A combination of part-fixed-fee and part-shared-savings is also practised.
Confirmed vs Book-1 §7.7 — fixed fee (lump sum; ESCO bears less risk), shared savings (ESCO designs, FINANCES, implements and shares an agreed % of actual savings), guaranteed savings (ESCO does NOT finance but guarantees savings cover debt service). A part-fixed / part-shared combination is also practised.
Source: AI-practice
📖 Book-1 §7.7 Types of Performance Contracting; Ch-7 Objective Q10

42. Which financing arrangement is NOT a type of performance contract, and what are the actual performance-contract types?

Model answer: Hire purchase is NOT a type of performance contract. The three recognised performance-contract types offered by ESCOs are fixed fee, shared savings and guaranteed savings. Hire purchase is simply an instalment-purchase financing arrangement and does not link payment to the verified energy performance of the installed equipment, so it does not qualify as a performance contract.
Confirmed vs Book-1 §7.7 and Ch-7 Objective Q10 — the three performance-contract types are fixed fee, shared savings and guaranteed savings; hire purchase is not one of them because payment is not tied to verified energy performance.
Source: AI-practice
📖 Book-1 §7.7 Drawbacks of ESCOs (Performance Contract: Pros & Cons)

43. What are the drawbacks (cons) of performance contracting with an ESCO?

Model answer: Drawbacks include: the host must share project savings with the ESCO, and the tax benefits of depreciation and other economic benefits must be negotiated. Large contracts raise concern; dealing with an ESCO can be seen as confusing or complicated, and complex potentially-binding contracts leave more margin for error and bring legal expenses and increased administrative costs. Where the ESCO guarantees savings and absorbs shortfalls, there is a risk-management cost, and insurance may be attached at a cost. Hence it is critical to choose an ESCO with a good reputation and relevant experience.
Confirmed vs Book-1 §7.7 (Drawbacks of ESCOs / Pros & Cons box) — the host must share project savings, depreciation and other tax benefits must be negotiated, contracts are potentially binding with legal and administrative costs, and a risk-management (sometimes insurance) cost applies where savings are guaranteed.
Source: AI-practice
📖 Book-1 §7.7 Energy Performance Contracting — risk vs percent savings shared

44. How is the risk assigned to an ESCO related to the savings it shares, with an example?

Model answer: In general, the amount of risk assigned to the ESCO is directly related to the percent of savings that must be shared with the ESCO — the more risk the ESCO carries, the larger its share of savings. For example, a lighting retrofit has a high probability of producing the expected cash flows (low risk), whereas a completely new process does not have the same time-tested reliability (higher risk). If the in-house energy team cannot manage such risk, performance contracting becomes an attractive alternative, with the ESCO taking on more risk in return for a larger savings share.
Confirmed vs Book-1 §7.7 — "the amount of risk assigned to the ESCO is directly related to the percent savings that must be shared with the ESCO", illustrated by a low-risk lighting retrofit versus a completely new process without time-tested reliability.
Source: AI-practice
📖 Book-1 §7.7 Role of ESCOs — Benefits to Industry

45. State the benefits to industry of using an ESCO / performance contracting.

Model answer: Benefits include: immediate upgrade of facilities and reduced operating costs without any initial capital investment; access to the ESCO's energy-efficiency expertise; positive cash flow (most projects generate savings exceeding the guarantee); freeing up the company's own money for core business needs; improved and more energy-efficient O&M; transfer of several normal business risks to the ESCO, including guaranteed equipment performance for the life of the contract; a more comfortable, productive environment; and services paid for out of money the customer would otherwise have paid the utility for wasted energy.
Confirmed vs Book-1 §7.7 (Benefits to Industry) — immediate upgrade with no initial capital investment, access to ESCO expertise, positive cash flow, freed-up capital, better O&M, transfer of business risks including guaranteed equipment performance for the contract life, and services paid from money otherwise wasted on utilities.
Source: AI-practice
📖 Book-1 §7.7 What is Depreciation?

46. What is depreciation, and what three conditions must an asset meet to be depreciable?

Model answer: Most assets used in business decrease in value over time; tax law permits reasonable deductions from taxable income to allow for this, called depreciation allowances. To be depreciable, an asset must meet three conditions: (1) it must be held by the business for the purpose of producing income, (2) it must wear out or be consumed in the course of its use, and (3) it must have a life longer than one year.
Confirmed vs Book-1 §7.7 — depreciation allowances are reasonable deductions from taxable income; the three primary conditions are that the asset is held to produce income, wears out or is consumed in use, and has a life longer than a year.
Source: AI-practice
📖 Book-1 §7.7 What is Depreciation? (with §7.4 salvage value / economic life)

47. Write the straight-line depreciation formula and explain the depreciation tax shield.

Model answer: Straight-line depreciation = (Cost − Salvage value) / Useful life, charging an equal amount each year. Depreciation is a non-cash expense, but it is deductible from taxable income; it therefore reduces the tax payable and so improves the after-tax cash flow — this benefit is called the depreciation tax shield. Note that under a true lease the lessee does not own the asset, so NO depreciation tax benefit is available.
Confirmed vs Book-1 §7.7 / §7.4 — the guidebook defines depreciation allowances and the three depreciability conditions and supplies the terms salvage value and economic life; the straight-line method applies them as (Cost − Salvage)/Useful life. Being a non-cash deduction it cuts tax and so raises after-tax cash flow; §7.6 confirms a true lease gives no depreciation benefit.
Source: AI-practice
📖 Book-1 §7.8 Developing a Typical ESCO Contract — Investment Grade Audit (IGA)

48. What is an Investment Grade Audit (IGA) and its role in ESCO contracting?

Model answer: An investment grade audit (IGA) is the process of conducting an energy audit to identify efficiency opportunities and translating the technical findings into financial terms, so as to present the project as a bankable project capable of securing a loan. An IGA evaluation includes a description of the baseline situation, project design/basic engineering, technical analysis, project financials, baseline calculation, options for monitoring and verification, and an assessment of technical and financial risk with a risk-mitigation plan. The IGA report forms the basis of the energy performance contract between the organization and the ESCO.
Confirmed vs Book-1 §7.8 — an IGA is "the process of conducting an energy audit to identify efficiency opportunities, and translating the technical findings into financial terms to present it as a bankable project capable of securing a loan"; its evaluation covers baseline, design, technical analysis, financials, M&V options and a risk-mitigation plan.
Source: AI-practice
📖 Book-1 §7.8 Developing a Typical ESCO Contract — Calculating savings (M&V)

49. State the formula used to calculate energy saved in measurement & verification (M&V) of an ESCO project, defining each term.

Model answer: Energy Saved = Baseline − Current ± Adjustment. Where: Energy saved is the energy saved over a period from project start to a set point in time; Baseline is the baseline energy consumption (e.g. in kWh); Current is the current energy consumption (from metering or utility bills); Adjustments are any positive or negative corrections needed to bring current energy use to the same set of conditions as the baseline. To get cost savings, the parties must agree how to handle energy-price fluctuations (e.g. a set price), so the result reflects only the efficiency measures, not changing energy costs.
Confirmed vs Book-1 §7.8 (Calculating savings) — Energy Saved = Baseline − Current ± Adjustment, with adjustments bringing current use to the same set of conditions as the baseline. Parties must also agree how to handle energy-price fluctuations (e.g. a set price) so the result reflects efficiency only.
Source: AI-practice
📖 Book-1 §7.2 Investment Need, Appraisal and Criteria

50. Why is financial appraisal of energy conservation projects necessary?

Model answer: Any capital investment project must be justified by a financial appraisal because management invests capital where it will obtain the greatest return, and an energy project is only one of many competing for limited funds. Management normally demands a higher rate of return from energy projects than from core profit-making investments, so energy proposals must show the likely return on the capital invested (how much it will cost and how much it will save). Costs and returns are not easily obtained — equipment loses value and needs more maintenance with age, borrowed money carries interest, and inflation affects future savings — so appraisal techniques are used to make correct, objective decisions and optimize benefits.
Confirmed vs Book-1 §7.2 — "It is the job of senior management to invest capital where it is going to obtain the greatest return" and "management normally demand higher rate of return from energy projects than core or direct profit-making investments"; appraisal techniques exist to make correct and objective decisions.
Source: AI-practice
📖 Book-1 §7.2 Investment Need, Appraisal and Criteria — projecting benefits

51. Besides energy savings, in what terms should the benefits of energy management projects be projected to senior management?

Model answer: Benefits should be projected not only as energy savings but also as: lower operational costs, a low risk/reward ratio, reduced environmental cost, improved productivity, better product quality or enhanced quality of service, and the potential to improve the company's share value. Most importantly, a systematic financial-management approach must be followed to rate the various investment options against the anticipated savings. Before investing, it should also be ensured that existing plant performs at its best, energy charges are at the lowest tariffs, the best fuels/electricity are used efficiently, and good housekeeping is practised.
Confirmed vs Book-1 §7.2 — benefits should be projected as lower operational costs, low risk/reward ratio, reduced environmental cost, improved productivity, better product quality or service, and potential to improve share value, supported by a systematic financial-management approach.
Source: AI-practice
📖 Book-1 §7.3 Payback Period — Limitations, Example 7.2

52. Using two projects A and B (both costing Rs.1,00,000), explain the key drawback of the payback period.

Model answer: Project A pays back in 3 years and Project B in 4 years, so the payback criterion prefers Project A. However, Project B has very substantial cash inflows in years 5 and 6 (e.g. Rs.50,000 and Rs.60,000) which payback completely ignores. This illustrates the drawback: the payback period does not consider savings accrued after the payback period, so it wrongly favours projects with early inflows and discriminates against more profitable projects whose large inflows come later. It also ignores the time value of money, adding cash flows without discounting.
Confirmed vs Book-1 §7.3 Example 7.2 — A pays back in 3 years and B in 4, yet B has cash inflows of Rs.50,000 and Rs.60,000 in years 5 and 6 that payback ignores. The book also notes payback adds cash inflows without suitable discounting.
Source: AI-practice
📖 Book-1 Chapter 7 — §7.3, §7.7, §7.8 (terminology)

53. Expand the following Chapter-7 acronyms: NPV, IRR, ROI, ESCO, IGA, EPC, M&V (PMV).

Model answer: NPV = Net Present Value; IRR = Internal Rate of Return; ROI = Return on Investment; ESCO = Energy Service Company; IGA = Investment Grade Audit; EPC = Energy Performance Contract; M&V (PMV) = Measurement and Verification (Performance Measurement and Verification).
Confirmed vs Book-1 Chapter 7 — all seven expansions appear in the chapter text (§7.3 for NPV/IRR/ROI, §7.7 for ESCO, §7.8 for EPC, IGA and measurement & verification / PMV in the case study).
Source: AI-practice
📖 Book-1 §7.3 Time Value of Money — discounting / present value concept

54. What is meant by 'discounting' or the 'present value concept', and why is it needed?

Model answer: A project involves an initial capital cost and a series of future annual costs and/or savings over its life. To assess feasibility, all these present and future cash flows must be equated to a common basis, but the value of money changes with time. The method by which cash flows occurring at different times are related is called discounting, or the present value concept — it converts future cash flows to their equivalent value today using an assumed interest (discount) rate. For example, at 10% interest Rs.100 received one year from now is worth only Rs.90.91 today.
Confirmed vs Book-1 §7.3 — "To assess project feasibility, all these present and future cash flows must be equated to a common basis. The problem with equating cash flows which occur at different times is that the value of money changes with time. The method by which these various cash flows are related is called discounting, or the present value concept." The book’s own illustration: at 10% interest Rs.100 received one year from now is worth only Rs.90.91 today. Discounting (future → present) is the opposite of compounding (present → future) and underpins both NPV and IRR.
Source: AI-practice
📖 Book-1 §7.3 NPV Method — choice of discount rate

55. How should the discount rate for an NPV calculation be chosen?

Model answer: The discount rate (k) used to evaluate the present value of expected future cash flows should reflect the risk of the project. The whole credibility of the NPV depends on a realistic prediction of this rate, which can often be unpredictable. As a practical rule, it is prudent to set the discount rate slightly above the interest rate at which the capital for the project is borrowed.
Confirmed vs Book-1 §7.3 — "The discount rate (k) employed for evaluating the present value of the expected future cash flows should reflect the risk of the project" and "it is prudent to set the discount rate slightly above the interest rate at which the capital for the project is borrowed".
Source: AI-practice

Long questions (10 marks) — 18

📖 BEE Guidebook Ch.7, Example 7.1 (p.164-165)

1. A cogeneration system installation is expected to reduce a company's annual energy bill by Rs. 23 lakhs. If the capital cost of the new cogeneration installation is Rs. 90 lakhs and the annual maintenance and operating (O&M) costs are Rs. 5 lakhs, what will be the expected simple payback period for the project? State the formula, the advantages and the limitations of the simple payback method.

Model answer: FORMULA: Simple Payback Period = Capital cost / Annual net savings, where Annual net savings = yearly benefits - yearly (operating/maintenance) costs. The prefix 'simple' denotes that the TIME VALUE OF MONEY is NOT considered. STEP 1 - Annual net savings = gross energy saving - O&M cost = 23 - 5 = Rs. 18 lakhs/year. STEP 2 - Simple Payback = Capital cost / Annual net savings = 90 / 18 = 5 YEARS. DECISION: The shorter the payback, the more attractive the project; the maximum permissible payback is a matter of company policy. ADVANTAGES: (i) simple in concept and application, no tedious calculation; (ii) favours projects giving large cash inflows in the early years. LIMITATIONS: (i) ignores all savings accruing AFTER the payback period (discriminates against projects with large later inflows); (ii) ignores the time value of money - cash flows are simply added without discounting.
Classic trap: subtract the O&M cost from the gross saving BEFORE dividing. Net saving 18 (not 23). Answer = exactly 5 years.
Source: unknown
📖 BEE Guidebook Ch.7, Example 7.2 (p.165)

2. Two projects A and B each require an investment of Rs. 1,00,000. Their annual cash inflows are: Project A - Yr1 50,000, Yr2 30,000, Yr3 20,000, Yr4 10,000, Yr5 10,000. Project B - Yr1 20,000, Yr2 20,000, Yr3 20,000, Yr4 40,000, Yr5 50,000, Yr6 60,000. Using the payback criterion, which project is selected, and explain why this exposes the main drawback of the simple payback method.

Model answer: PROJECT A - cumulative cash inflow: end Yr1 50,000; Yr2 80,000; Yr3 1,00,000 -> investment recovered exactly at end of Year 3. Payback A = 3 years. PROJECT B - cumulative: Yr1 20,000; Yr2 40,000; Yr3 60,000; Yr4 1,00,000 -> recovered at end of Year 4. Payback B = 4 years. DECISION BY PAYBACK: A (3 yr) is preferred over B (4 yr). BUT total undiscounted inflows: Project A = 1,20,000 over 5 years; Project B = 2,10,000 over 6 years. Project B is clearly the more profitable project overall, yet payback rejects it because its large inflows (40,000; 50,000; 60,000) come in the LATER years. DRAWBACK ILLUSTRATED: (i) payback ignores all cash flows occurring AFTER the payback period, so it discriminates against projects with substantial later inflows; (ii) it ignores the time value of money - inflows are added without discounting. This is why payback should be supported by NPV/IRR for final selection.
The whole point is: payback picks A but B returns far more (2.10 lakh vs 1.20 lakh). Show cumulative cash flow to prove the 3-yr vs 4-yr result.
Source: unknown
📖 BEE Guidebook Ch.7, Example 7.3 (p.166)

3. An outlay of Rs. 1,00,000 for equipment is expected to provide an after-tax cash flow of Rs. 25,000 per year over a period of six years without significant annual fluctuation. What is the Return on Investment (ROI)? Define ROI, state its relation to payback, and give its advantages and limitations.

Model answer: DEFINITION: ROI expresses the annual return of a project as a percentage of the capital cost. ROI = (Annual net cash flow / Capital cost) x 100. ROI is the INVERSE of the simple payback period. CALCULATION: ROI = (25,000 / 1,00,000) x 100 = 25%. (Check: payback = 1,00,000 / 25,000 = 4 years; ROI = 1/4 = 25% - confirming ROI = inverse of payback.) DECISION RULE: ROI must always exceed the cost of money (interest rate) for the project to be attractive; the higher the ROI the better. ROI does not require projects to have equal life or capital cost to be compared. ADVANTAGES: simple, easy to calculate; being a percentage it is easy to compare with the borrowing interest rate. LIMITATIONS: (i) ignores the time value of money; (ii) ignores the variable nature of annual cash inflows - the 25% figure is strictly valid only if Rs. 25,000/yr continued in perpetuity, which is unrealistic.
ROI = annual net cash flow / capital cost. Remember ROI = 1/payback (a very common objective). Answer = 25%.
Source: unknown
📖 BEE Guidebook Ch.7, Example 7.4 (p.167-168)

4. Using the Net Present Value technique, evaluate the financial merits of the two proposed projects and state which is preferable. Discount rate = 8% for each; both have capital cost Rs. 30,000 and a 10-year life. Net annual savings (Rs.): Project 1 = 6000 every year (Yr1-10). Project 2 = Yr1 6600, Yr2 6600, Yr3 6300, Yr4 6300, Yr5 6000, Yr6 6000, Yr7 5700, Yr8 5700, Yr9 5400, Yr10 5400.

Model answer: METHOD: NPV = Sum of (CF_t x PV factor @8%) - Initial investment, where PV factor = 1/(1.08)^t. Accept if NPV > 0; when comparing, the HIGHER NPV is the better project. PV factors @8%: Yr1 0.926, Yr2 0.857, Yr3 0.794, Yr4 0.735, Yr5 0.681, Yr6 0.630, Yr7 0.583, Yr8 0.540, Yr9 0.500, Yr10 0.463 (sum = 6.709). PROJECT 1 (constant Rs.6000): PV of savings = 6000 x 6.709 = 40,254. NPV1 = 40,254 - 30,000 = +Rs. 10,254. PROJECT 2 (table): Yr1 6600x0.926=6112; Yr2 6600x0.857=5656; Yr3 6300x0.794=5002; Yr4 6300x0.735=4631; Yr5 6000x0.681=4086; Yr6 6000x0.630=3780; Yr7 5700x0.583=3323; Yr8 5700x0.540=3078; Yr9 5400x0.500=2700; Yr10 5400x0.463=2500. Sum of PV = 40,867.8. NPV2 = 40,867.8 - 30,000 = +Rs. 10,867 (the guidebook prints Rs.10,867). DECISION: Both NPVs are positive (both acceptable), but NPV2 (Rs.10,867) > NPV1 (Rs.10,254). Therefore PROJECT 2 is the preferable proposal (higher NPV).
Guaranteed 10-mark template. Lay it out as a Year|CF|DF@8%|PV table; graders reward the table. Higher NPV wins -> Project 2. Both positive so both are individually acceptable.
Source: unknown
📖 BEE Guidebook Ch.7, Example 7.5 (p.169-171)

5. A proposed project requires an initial capital investment of Rs. 20,000. Cash flows: Yr1 6000, Yr2 5500, Yr3 5000, Yr4 4500, Yr5 4000, Yr6 4000. The cost of capital is 8%. Determine the Internal Rate of Return (IRR) by the interpolation method, and state whether the project is sound.

Model answer: IRR = the discount rate at which NPV = 0. Method: try discount rates until NPV brackets zero (one +ve, one -ve), then interpolate. NPV @8% (factors 0.926,0.857,0.794,0.735,0.681,0.630): 6000x0.926 + 5500x0.857 + 5000x0.794 + 4500x0.735 + 4000x0.681 + 4000x0.630 = 5556+4713+3970+3308+2724+2520 = 22,791. NPV = 22,791-20,000 = +2,791. NPV @12% (0.893,0.797,0.712,0.636,0.567,0.507): = 20,495 approx. NPV = +495. NPV @16% (0.862,0.743,0.641,0.552,0.476,0.410): NPV = -1,508. NPV @13% (0.885,0.783,0.693,0.613,0.543,0.480): NPV = -65. NPV crosses zero between 12% (+495) and 13% (-65). INTERPOLATION FORMULA: IRR = Lower rate + [NPV at lower rate / (NPV at lower rate - NPV at higher rate)] x (Higher rate - Lower rate) IRR = 12 + [495 / (495 - (-65))] x (13 - 12) = 12 + (495/560) = 12 + 0.88 = 12.88%. DECISION: IRR (12.88%) > cost of capital (8%), therefore the investment is SOUND and should be accepted.
The other guaranteed 10-mark template. Memorise the interpolation formula EXACTLY. Bracket zero with a small +ve (12%, +495) and small -ve (13%, -65). Answer = 12.88%.
Source: unknown
📖 BEE Guidebook Ch.7, Solved Example (p.185-186)

6. An oil-fired reheating furnace heats steel billets from 40 C to 1220 C at a furnace efficiency of 28%. It operates 4700 hours/annum. GCV of furnace oil = 10,000 kcal/kg, density 0.94 kg/litre, cost Rs.45/litre. Specific heat of billets = 0.12 kcal/kg C. (a) Energy needed to heat 12 tons of billets/hr. (b) Litres of furnace oil per ton of billet. (c) If efficiency improves 28% -> 30% by ceramic-fibre insulation, the hourly oil cost saving. (d) Simple payback if investment is Rs.20 lakhs. (e) How large an investment is justified for the efficiency improvement at an IRR of 16% per year over 6 years?

Model answer: (a) Heat = m x Cp x dT = 12000 kg x 0.12 x (1220-40) = 12000 x 0.12 x 1180 = 16,99,200 kcal/hr. (b) Useful heat per ton = 16,99,200/12 = 1,41,600 kcal/ton. Input (at 28% eff) = 1,41,600/0.28 = 5,05,714 kcal/ton. Oil = 5,05,714/10,000 = 50.57 kg/ton = 50.57/0.94 = 53.79 litres/ton. (c) Cost saving per ton = 53.79 x [1 - (0.28/0.30)] x Rs.45 = 53.79 x 0.0667 x 45 = Rs.161.37/ton. For 12 ton/hr: 161.37 x 12 = Rs.1936/hr. (d) Annual saving = 1936 x 4700 = Rs.90,99,200 (approx Rs.91 lakh/yr). Simple payback = 20,00,000 / 90,99,200 = 0.22 year (approx 2.6 months). (The guidebook prints approx 0.35 yr; the arithmetically correct figure from 20 lakh / 91 lakh is 0.22 yr.) (e) Max justifiable investment = annual net inflow x (sum of PV factors @16% for Yr1-6). PV factors @16%: 0.862+0.743+0.641+0.552+0.476+0.410 = 3.684. Max investment = 91 x 3.684 = 335.2 lakh = approx Rs. 3.35 CRORE. Invest up to Rs.3.35 crore and still earn the 16% target return.
Part (e) is the 'maximum affordable investment at a given IRR' technique: annual inflow x sum-of-PV-factors. 91 x 3.684 = 3.35 crore. Note the guidebook's printed 0.35-yr payback in (d) is a book slip; correct value is 0.22 yr.
Source: unknown
📖 BEE Guidebook Ch.7, Long Question L-1 (p.187)

7. A company invests Rs. 10 lakhs and completes an energy efficiency project at the beginning of year 1. The firm is investing its own money and expects an IRR of at least 26% on a constant positive annual net cash flow of Rs. 2 lakhs over 10 years. (1) Will the project meet the firm's expectations? (2) What is the IRR of this measure?

Model answer: The cash flow is a level annuity of Rs.2 lakh/yr for 10 years against Rs.10 lakh invested. IRR is the rate at which the 10-year present-worth annuity factor equals Investment / Annual cash flow = 10 / 2 = 5.0. Look up the annuity present-worth factor A = [1 - (1+r)^-10] / r for 10 years: at r = 15%: A = 5.019 at r = 16%: A = 4.833 We need A = 5.0, which lies just below 15%. Interpolating: IRR = 15 + (5.019 - 5.0)/(5.019 - 4.833) = 15 + 0.019/0.186 = 15.1%. (2) IRR is approximately 15% (about 15.1%). (1) Since the IRR (approx 15%) is LESS than the required 26%, the project does NOT meet the firm's expectations and would be rejected on the firm's own hurdle rate. (Equivalently, NPV at 26% is negative.)
For a level annuity, IRR is where annuity factor = investment/annual CF = 5.0, giving ~15%. Because 15% < 26% hurdle, the answer is NO - it fails the firm's expectation.
Source: unknown
📖 BEE Guidebook Ch.7, Long Question L-2 (p.187-188)

8. An energy-saving retrofit costs Rs. 1,00,000 and yields: energy & demand savings of 6000 kWh/year plus Rs. 3800/year in demand charges, and maintenance cost savings of Rs. 2000/year. Energy savings are valued at Rs. 3.00/kWh with no change in energy rates, and the project life is 10 years. Calculate the NPV against a 12% discount rate and give the decision.

Model answer: STEP 1 - Total annual saving = energy + demand + maintenance = (6000 kWh x Rs.3.00) + Rs.3800 + Rs.2000 = 18,000 + 3,800 + 2,000 = Rs. 23,800/year (a level 10-year annuity). STEP 2 - 12% present-worth annuity factor for 10 years = sum of PV factors @12% (Yr1-10): 0.893+0.797+0.712+0.636+0.567+0.507+0.452+0.404+0.361+0.322 = 5.651. (Check: [1-(1.12)^-10]/0.12 = 5.650.) STEP 3 - PV of savings = 23,800 x 5.651 = Rs. 1,34,494. NPV = PV of savings - initial cost = 1,34,494 - 1,00,000 = +Rs. 34,494 (approx Rs. 34,500). DECISION: NPV is positive (> 0), so the retrofit is financially VIABLE and should be accepted.
Add all three savings streams first (23,800/yr). Then multiply by the 10-year @12% annuity factor (5.651). NPV approx +34,500 -> accept.
Source: unknown
📖 BEE Guidebook Ch.7, Short Question S-1 (p.187)

9. 100 fused 60 W incandescent lamps (ILB) are replaced by 100 nos. of 12 W CFL (instead of new ILBs). For 4000 hours of operation per year, calculate: (i) the annual reduction in electricity cost if the energy charge is Rs.4/kWh and the demand charge is Rs.250/kVA/month; (ii) the simple payback period, given ILB costs Rs.10 (life 1000 h) and CFL costs Rs.100 (life 4000 h).

Model answer: (i) ANNUAL ELECTRICITY SAVING: Connected-load reduction = 100 x (60 - 12) = 100 x 48 = 4800 W = 4.8 kW (approx 4.8 kVA at unity PF for lamps). Energy saving = 4.8 kW x 4000 h = 19,200 kWh/yr -> energy cost saving = 19,200 x Rs.4 = Rs. 76,800/yr. Demand saving = 4.8 kVA x Rs.250/kVA/month x 12 months = Rs. 14,400/yr. Total annual reduction = 76,800 + 14,400 = Rs. 91,200/year. (ii) SIMPLE PAYBACK: Over the 4000-h CFL life, one CFL (Rs.100) replaces four ILBs (4 x Rs.10 = Rs.40, since ILB life is only 1000 h). Incremental cost per point = 100 - 40 = Rs.60; for 100 points = Rs. 6,000. Simple payback = incremental investment / annual saving = 6,000 / 91,200 = 0.066 year (approx 0.8 month, under 25 days). (If only the energy saving Rs.76,800 is credited, payback = 6,000/76,800 = 0.078 yr - still under 1 month.) The retrofit pays back almost immediately.
Two savings: energy (Rs.76,800) + demand (Rs.14,400) = Rs.91,200/yr. For the payback denominator, compare 1 CFL vs 4 ILBs over the 4000-h life (incremental Rs.6,000, not Rs.9,000).
Source: unknown
📖 BEE Guidebook Ch.7, Sec 7.7-7.8 and Short Question S-2 (p.177-181)

10. Explain the operation of an Energy Service Company (ESCO) and energy performance contracting. Describe the three common types of performance contract, the services an ESCO offers, and the benefits and drawbacks of the ESCO route.

Model answer: WHAT AN ESCO IS: An ESCO provides a COMPLETE energy-project service - from assessment, to design, to construction/installation, together with engineering and project-management services AND financing. PERFORMANCE CONTRACTING - 'PAYMENT ON PERFORMANCE': The contractor assumes responsibility for purchasing, installing and maintaining the equipment, but is PAID ONLY AFTER the installed equipment actually reduces the client's expenses. This removes any incentive to cut corners and often creates an incentive to EXCEED the savings estimate; scope is usually facility-wide to capture extra savings. The more risk assigned to the ESCO, the larger the share of savings it must be given. THREE TYPES OF PERFORMANCE CONTRACT: 1. FIXED FEE - ESCO audits, designs and either helps implement or merely advises, for a fixed lump-sum fee. The ESCO bears the LEAST risk because its fee does not depend on the savings achieved. 2. SHARED SAVINGS - ESCO designs, FINANCES and implements the project, verifies the savings, and shares an agreed percentage of the actual energy savings with the host over a fixed period. The more energy saved, the higher the revenue to both parties. 3. GUARANTEED SAVINGS - ESCO designs and implements but does NOT finance the project (though it may arrange financing); it GUARANTEES that savings will be enough to cover the debt-service payments. Energy managers prefer this (most secure) but the extra security costs more. (A combination of part-fixed-fee and part-shared-savings is also used.) SERVICES OFFERED: investment-grade energy audit (IGA); financing from own/arranged sources; purchase, installation and maintenance of efficient equipment; O&M training; monitoring; measurement & verification; and a guarantee of savings. BENEFITS TO INDUSTRY: immediate facility upgrade with little/no up-front capital; access to ESCO expertise; positive cash flow; frees the firm's capital for core business; ESCO assumes several business risks including guaranteed performance. DRAWBACKS: savings must be shared with the ESCO; depreciation/tax benefits must be negotiated; complex, potentially binding contracts, legal and administrative costs; risk-management/insurance cost when savings are guaranteed. Choose an ESCO with a good reputation and relevant experience.
Remember the THREE types (fixed fee / shared savings / guaranteed savings) and the key differentiator - who bears risk and who finances. Hire-purchase is NOT a performance contract (common objective trap).
Source: unknown
📖 BEE Guidebook Ch.7, Sec 7.5 (p.174-175); recurring exam short note

11. What is sensitivity and risk analysis in the appraisal of energy-conservation projects? Why is it carried out, and list the micro and macro factors that are considered.

Model answer: DEFINITION: Sensitivity analysis is an ASSESSMENT OF RISK. Many project cash flows (capital cost, energy-cost savings, maintenance costs) are only estimates and future flows contain inflation, while project life itself can vary. Sensitivity analysis asks: how sensitive is the project's feasibility to changes in the input parameters? What if a factor is less favourable than predicted? By how much can a variable change before the project becomes unviable, and how likely is that? WHY / WHEN: It is recommended particularly for MARGINAL (borderline) projects and for large projects near the cut-off rate. Example: if a project is feasible only while energy-cost escalation stays above 9% and the assumed escalation is 10%, the break-even is close - a HIGH-RISK project. Spreadsheets perform it easily with built-in 'what-if' functions; manually it is laborious (re-working the analysis many times). It identifies parameters that are both uncertain and to which the NPV/IRR decision is sensitive; 'switching values' (the change needed to flip accept/reject) are found. It leads to improved project design with mitigation of major uncertainties. MICRO FACTORS (the firm CAN change): operating expenses; capital structure; costs of debt and equity; changing the form of finance (e.g. leasing); changing the project life. MACRO FACTORS (the firm CANNOT change): changes in interest rates; changes in tax rates; changes in accounting standards (e.g. depreciation method); changes in depreciation rates; extension of government-subsidised schemes (e.g. rural electrification); general employment/salary trends; imposition of environmental and safety regulations; energy price change; technology changes.
Sensitivity analysis = 'assessment of risk' - used mainly on marginal projects. The clean split is Micro = things the firm controls (finance, project life, costs), Macro = external economy (interest/tax rates, depreciation rules, energy price, regulation).
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📖 BEE Guidebook Ch.7, Sec 7.3 and Short Questions S-3, S-4, S-5 (p.165-172)

12. Compare the Net Present Value (NPV) and Internal Rate of Return (IRR) methods of investment appraisal, and state the limitations of the simple payback period method and of the ROI method.

Model answer: NPV vs IRR: - In the NPV method the discount rate (cost of capital) is ASSUMED KNOWN, and the NPV of the project is calculated; accept if NPV > 0, and the higher-NPV project is better. NPV is essentially a COMPARISON tool that lets a number of different projects be compared, and it gives the result as an absolute money value. - In the IRR method the NPV is SET EQUAL TO ZERO and the discount rate that satisfies this is found (the IRR); accept if IRR > the cost of capital. IRR is designed to assess whether a SINGLE project will achieve a target rate of return, and it expresses the result as a percentage rate, which businessmen often find easier to grasp. - Both account for the time value of money and consider the whole cash-flow stream. A limitation of IRR is that it cannot distinguish between lending and borrowing, so a high IRR is not always desirable. LIMITATIONS OF SIMPLE PAYBACK: (i) it ignores all savings that accrue AFTER the payback period (it favours early-inflow projects and discriminates against later-inflow projects); (ii) it does NOT consider the time value of money - cash inflows are simply added without discounting, violating the principle that flows at different times must be discounted before being combined. LIMITATIONS OF ROI: (i) it does not take into account the time value of money; (ii) it does not account for the variable nature of annual cash inflows - the ROI figure is strictly valid only if the annual return continued in perpetuity, which is unrealistic.
Key one-liner examiners want: NPV assumes the discount rate and gives an absolute value for COMPARING projects; IRR solves for the rate that makes NPV=0 to test a SINGLE project against a hurdle. Both use time value of money; payback and ROI do not.
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📖 Book-1 §7.6 Financing Options (with §7.7 Performance contracting)

13. Describe the conventional financing options available for capital investment in energy-efficiency projects, bringing out the ownership and tax implications of each.

Model answer: Capital investment requires a source of funds; obtaining them is called FINANCING. The conventional options are: 1. DEBT FINANCING - borrowing money (loans, bonds) that is repaid later with interest. The company OWNS the equipment, so this suits long-term use. Cost of capital is easy to calculate (rates and schedules are documented), and interest payments are TAX-DEDUCTIBLE. However, the company takes ALL the risk and must install and manage the project itself. 2. EQUITY FINANCING - the lender acquires an ownership (equity) stake (via stocks) and shares in the firm's success. Its cost of capital is HIGHER than debt, partly because stock DIVIDENDS are NOT tax-deductible (unlike interest). 3. RETAINED EARNINGS - accumulated annual surpluses kept within the company instead of paid out as dividends. They belong to the stockholders, so the SAME cost of capital as stock applies. 4. CAPITAL LEASE - a mid-way arrangement between pure debt and pure equity that allows a lower cost of capital with third-party participation; it has partial-ownership characteristics. 5. TRUE LEASE - use of equipment WITHOUT ownership risks; reduces the risk of poor performance, service and obsolescence and suits SHORT-TERM use. Lease payments are tax-deductible, but NO depreciation tax benefit is available and ownership does NOT pass, even at the end of the lease. 6. PERFORMANCE CONTRACTING (ESCO) - 'pay on performance' with little or no up-front money; the ESCO carries much of the risk and shares in the savings. Attractive when the project is financed externally.
Confirmed vs Book-1 §7.6 (with §7.7) — tabulate option | ownership | tax treatment. Book traps: interest on debt IS tax-deductible but stock dividends are NOT; a capital lease is mid-way between pure debt and pure equity; a true lease gives NO depreciation benefit and NO ownership even at the end of the lease.
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📖 Book-1 §7.7 What is Depreciation? (with §7.4 salvage value / economic life)

14. What is depreciation? State the conditions for an asset to be depreciable, explain the straight-line method, and describe how depreciation acts as a 'tax shield' in the cash-flow analysis of an energy project.

Model answer: WHAT IT IS: Most assets used in a business decrease in value over time. Tax law permits reasonable deductions from taxable income to allow for this - these deductions are called DEPRECIATION ALLOWANCES. CONDITIONS TO BE DEPRECIABLE (all three): (1) the asset must be held by the business for the purpose of PRODUCING INCOME; (2) it must WEAR OUT or be consumed in the course of its use; (3) it must have a life LONGER THAN ONE YEAR. STRAIGHT-LINE METHOD: an equal amount is written off each year: Annual depreciation = (Capital cost - Salvage value) / Useful life (years). Example: equipment Rs.5,00,000, salvage Rs.50,000, life 10 yr -> (500000-50000)/10 = Rs.45,000/yr. DEPRECIATION 'TAX SHIELD': depreciation is a NON-CASH expense, yet it is deductible from taxable income. By reducing taxable income it reduces the tax payable, which INCREASES the after-tax cash flow of the project. The cash benefit each year = Depreciation x Tax rate (the 'tax shield'). This is why after-tax NPV/IRR are more favourable than a simple pre-tax payback would suggest. NOTE: under a TRUE LEASE the lessee does not own the asset, so NO depreciation tax benefit is available - a key point when comparing leasing against ownership.
Confirmed vs Book-1 §7.7 / §7.4 — quote the definition of depreciation allowances and the three depreciability conditions verbatim, then apply the straight-line method with the book’s salvage-value and economic-life terms. Depreciation is a non-cash charge that lowers taxable income → lowers tax → raises after-tax cash inflow; a true lease (§7.6) gives no such benefit.
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📖 21st National Certification Exam, Paper-1, Sep 2021 (25.09.2021)

15. A company invests Rs. 12 lakhs and completes an energy-efficiency project at the beginning of year 1, expecting an IRR of at least 8% on the investment. The project savings are: end of Year 1 = Rs.1.20 lakh, Year 2 = Rs.3 lakh, Year 3 = Rs.4 lakh, Year 4 = Rs.6 lakh, Year 5 = Rs.9 lakh. Will the project meet the firm's expectations? Justify using NPV at the firm's required rate.

Model answer: Test by computing NPV at the required 8% rate; if NPV > 0 the IRR exceeds 8% and the project meets expectations. PV factors @8%: Yr1 0.926, Yr2 0.857, Yr3 0.794, Yr4 0.735, Yr5 0.681. Yr1 1.20 x 0.926 = 1.111 Yr2 3.00 x 0.857 = 2.571 Yr3 4.00 x 0.794 = 3.176 Yr4 6.00 x 0.735 = 4.410 Yr5 9.00 x 0.681 = 6.129 Sum of PV of inflows = Rs. 17.397 lakh. NPV = 17.397 - 12.00 = +Rs. 5.40 lakh (all figures in lakh). DECISION: NPV is strongly positive at 8%, so the IRR is well above 8%. YES - the project comfortably meets the firm's expectations and should be accepted.
NPV at the hurdle rate is positive (+5.4 lakh), so IRR > 8% -> accept. Watch the rising cash-flow profile (1.2, 3, 4, 6, 9).
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📖 BEE Paper-1, Last-10-years compilation (Sep 2016 pattern)

16. A company will invest in only ONE of two energy-conservation projects and requires a minimum return of 18%. Project A: investment Rs.17,50,000; net annual inflows Yr1-4 = Rs.4,00,000 each, Yr5 = Rs.5,00,000 (6,00,000 saving less 1,00,000 expense), Yr6 = Rs.6,00,000, Yr7 = Rs.6,00,000, Yr8 = Rs.3,80,300. Project B: investment Rs.12,00,000; net annual inflows Yr1 4,50,000, Yr2 4,00,000, Yr3 3,50,000, Yr4 3,00,000, Yr5 2,50,000, Yr6 2,00,000, Yr7 1,16,650. Using NPV, justify which project to choose.

Model answer: Because the two projects have different investments and lives, compare them on NPV (not payback). NPV @18% (factors 0.847, 0.718, 0.609, 0.516, 0.437, 0.370, 0.314, 0.266): Project A: 400000x0.847 + 400000x0.718 + 400000x0.609 + 400000x0.516 + 500000x0.437 + 600000x0.370 + 600000x0.314 + 380300x0.266 = 18,06,060; NPV_A = 18,06,060 - 17,50,000 = +Rs. 56,060. Project B: 450000x0.847 + 400000x0.718 + 350000x0.609 + 300000x0.516 + 250000x0.437 + 200000x0.370 + 116650x0.314 = 12,56,178; NPV_B = 12,56,178 - 12,00,000 = +Rs. 56,178. At 18% both NPVs are essentially EQUAL (approx Rs.56-57 thousand), so both are acceptable and the tie must be broken. BREAK THE TIE at 20% (factors 0.833, 0.694, 0.579, 0.482, 0.402, 0.335, 0.279, 0.233): Project A NPV @20% = 16,93,210 - 17,50,000 = -Rs. 56,790 (negative). Project B NPV @20% = 11,99,745 - 12,00,000 = approx -Rs. 250 (about zero). DECISION: At the higher 20% rate Project B (approx breakeven) clearly outperforms Project A (strongly negative). Project B holds its value better, so PROJECT B is recommended.
Both projects have nearly identical NPV at 18%, so you MUST raise the rate (to 20%) to break the tie. B stays near zero while A goes sharply negative -> choose B.
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📖 24th National Certification Exam, Paper-1, Sep 2024

17. Evaluate a multi-phase project over 5 years: initial investment Rs.20 lakhs; an additional investment of Rs.5 lakhs in Year 3; salvage value Rs.3 lakhs at end of Year 5. Yearly savings (Rs. lakhs): Y1 6, Y2 7, Y3 4, Y4 9, Y5 12. Calculate the Internal Rate of Return (IRR) by interpolation.

Model answer: STEP 1 - Net cash flows (Rs. lakhs): Year 0 = -20; Y1 = +6; Y2 = +7; Y3 = 4 - 5 = -1 (saving less the extra investment); Y4 = +9; Y5 = 12 + 3 = +15 (saving plus salvage). STEP 2 - Find rates that bracket NPV = 0. NPV @19% (factors 0.840, 0.706, 0.593, 0.499, 0.419): 6x0.840 + 7x0.706 - 1x0.593 + 9x0.499 + 15x0.419 = 5.04 + 4.94 - 0.59 + 4.49 + 6.29 = 20.17; NPV = 20.17 - 20 = +0.17. NPV @20% (factors 0.833, 0.694, 0.579, 0.482, 0.402): 5.00 + 4.86 - 0.58 + 4.34 + 6.03 = 19.65; NPV = -0.35. STEP 3 - Interpolate between 19% (+0.17) and 20% (-0.35): IRR = 19 + [0.17 / (0.17 - (-0.35))] x (20 - 19) = 19 + 0.17/0.52 = 19 + 0.32 = 19.32%. DECISION: IRR approx 19.3%; accept if this exceeds the firm's cost of capital.
The trick is building the net cash-flow column: Y3 nets to -1 (extra 5-lakh outlay), Y5 to +15 (add salvage). Then bracket zero at 19%/20% and interpolate to 19.32%.
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📖 25th National Certification Exam, Paper-1, Sep 2025

18. An industry is exploring two options for its energy-efficiency strategy; only one will be chosen. Discount rate 10%, project life 5 years. Project A: capital Rs.80,000, annual saving Rs.25,000/yr. Project B: capital Rs.1,00,000, annual saving Rs.35,000/yr. Using NPV, find the better option.

Model answer: PV factors @10% (Yr1-5): 0.909, 0.826, 0.751, 0.683, 0.621; sum = 3.790. Project A: NPV = -80,000 + 25,000 x 3.790 = -80,000 + 94,750 = +Rs. 14,750. Project B: NPV = -1,00,000 + 35,000 x 3.790 = -1,00,000 + 1,32,650 = +Rs. 32,650. DECISION: Both NPVs are positive (both viable), but Project B (Rs.32,650) has the higher NPV. Therefore PROJECT B is the better option.
Level annuity, so use the summed 5-year @10% factor (3.790) x annual saving. Higher NPV wins -> Project B.
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