1. A project costs CU 120,000 and returns cash flows of CU 40,000, CU 50,000, CU 60,000 and CU 30,000 in years 1 to 4, evenly through each year. What is the payback period?

A) 2.0 years
B) 2.5 years
C) 3.0 years
D) 3.5 years

Correct: B difficult Investment appraisal

After two years CU 90,000 has been recovered. The remaining CU 30,000 is recovered in year 3: 30,000 / 60,000 = 0.5 of the year. Payback = 2.5 years. If you answered 2.0 you ignored the part year. If you answered 3.0 you rounded up to the full year of recovery. If you answered 3.5 you added half a year to the full third year.

2. A project costs CU 100,000 and returns CU 50,000 a year for four years. The cost of capital is 10% with discount factors of 0.909, 0.826, 0.751 and 0.683. What is the discounted payback period?

A) 2.35 years
B) 2.00 years
C) 3.00 years
D) 3.35 years

Correct: A difficult Investment appraisal

Discounted cash flows: year 1 = 45,450, year 2 = 41,300 (cumulative 86,750), year 3 = 37,550. The remaining 13,250 is recovered in year 3: 13,250 / 37,550 = 0.35. Discounted payback = 2.35 years. If you answered 2.00 you ignored the discounted flow of year 3. If you answered 3.00 you rounded up. If you answered 3.35 you added one year too many.

3. A machine costs CU 200,000 and has a residual value of CU 20,000 after four years. The average annual accounting profit is CU 27,000. What is the accounting rate of return based on the average investment?

A) 13.5%
B) 24.5%
C) 15.0%
D) 27.0%

Correct: B difficult Investment appraisal

Average investment = (200,000 + 20,000) / 2 = CU 110,000. ARR = 27,000 / 110,000 = 24.5%. If you answered 13.5% you used the initial investment (27,000 / 200,000). If you answered 15.0% you used the investment less the residual value (27,000 / 180,000). If you answered 27.0% you gave the profit in thousands.

4. A project costs CU 100,000 now and returns CU 45,000 at the end of each of the next three years. The annuity factor for three years at 10% is 2.487. What is the NPV?

A) CU 11,915
B) CU 35,000
C) CU 45,000
D) CU 111,915

Correct: A difficult Investment appraisal

PV of inflows = 45,000 x 2.487 = CU 111,915. NPV = 111,915 - 100,000 = CU 11,915. If you answered CU 111,915 you did not deduct the outlay. If you answered CU 35,000 you used undiscounted inflows (135,000 - 100,000). If you answered CU 45,000 you gave the annual inflow.

5. A project has a positive NPV of CU 8,400 at a 12% discount rate and a negative NPV of CU 5,600 at 16%. Using linear interpolation, what is the IRR?

A) 13.2%
B) 14.0%
C) 15.6%
D) 14.4%

Correct: D difficult Investment appraisal

IRR = 12% + [8,400 / (8,400 + 5,600)] x (16% - 12%) = 12% + 0.6 x 4% = 14.4%. If you answered 14.0% you took the midpoint of 12% and 16%. If you answered 15.6% you interpolated from 16% using the wrong proportion (16 - 0.4 x 4). If you answered 13.2% you used a proportion of 0.3 (12 + 0.3 x 4).

6. An investment of CU 230,000 produces cash flows of CU 20,000 a year in perpetuity. The cost of capital is 8%. What is the NPV?

A) CU 20,000
B) CU 160,000
C) CU 230,000
D) CU 250,000

Correct: A difficult Investment appraisal

PV of a perpetuity = 20,000 / 0.08 = CU 250,000. NPV = 250,000 - 230,000 = CU 20,000. If you answered CU 250,000 you did not deduct the outlay. If you answered CU 160,000 you multiplied the cash flow by 8. If you answered CU 230,000 you gave the outlay.

7. The real cost of capital is 5% and the expected inflation rate is 3%. What is the money (nominal) cost of capital?

A) 2.0%
B) 8.00%
C) 8.15%
D) 8.50%

Correct: C difficult Investment appraisal

(1 + money rate) = (1 + real rate) x (1 + inflation) = 1.05 x 1.03 = 1.0815, so the money rate is 8.15%. If you answered 8.00% you added the rates. If you answered 2.0% you took the difference. If you answered 8.50% you added 3.5% for inflation.

8. A project's cash flow is CU 50,000 a year in today's prices. Cash flows inflate at 4% a year. What is the money cash flow in year 2?

A) CU 50,000
B) CU 52,000
C) CU 54,000
D) CU 54,080

Correct: D difficult Investment appraisal

Money cash flow = 50,000 x 1.04 squared = CU 54,080. If you answered CU 52,000 you inflated for one year only. If you answered CU 54,000 you used simple interest (8%). If you answered CU 50,000 you did not inflate.

9. Which of the following are relevant cash flows in a project appraisal? (1) Depreciation of the new equipment (2) The opportunity cost of land owned by the company that will be used (3) Research costs already spent (4) Additional working capital needed

A) (1) and (3) only
B) (1), (2) and (4) only
C) (2) and (4) only
D) (2), (3) and (4) only

Correct: C difficult Investment appraisal

Relevant cash flows are future, incremental cash flows. The opportunity cost of the land and the working capital are relevant. Depreciation is not a cash flow and research costs already spent are sunk.

10. Which of the following statements about appraisal methods are correct? (1) NPV takes account of the time value of money. (2) Payback ignores cash flows after the payback period. (3) The accounting rate of return is based on cash flows.

A) (1) and (3) only
B) (2) and (3) only
C) (1) and (2) only
D) (1), (2) and (3)

Correct: C difficult Investment appraisal

NPV discounts cash flows (1). Payback ignores cash flows after the period in which the investment is recovered (2). ARR is based on accounting profit, not cash flows (3).

11. Cash flows of CU 30,000 a year arise at the end of years 3 to 6. The cost of capital is 10%. Cumulative annuity factors at 10% are: 2 years 1.736, 4 years 3.170, 6 years 4.355. What is the present value?

A) CU 52,080
B) CU 95,100
C) CU 78,570
D) CU 130,650

Correct: C difficult Investment appraisal

The annuity factor for years 3 to 6 = 4.355 - 1.736 = 2.619. PV = 30,000 x 2.619 = CU 78,570. If you answered CU 130,650 you used the six-year factor (as if cash flows began in year 1). If you answered CU 95,100 you used the four-year factor. If you answered CU 52,080 you used the two-year factor.

12. An energy-saving investment cuts emissions by 1,000 tonnes of CO2e a year for five years. The carbon price is CU 40 per tonne and the cost of capital 10%. The five-year annuity factor is 3.791. What is the present value of the carbon cost saved?

A) CU 151,640
B) CU 40,000
C) CU 200,000
D) CU 379,100

Correct: A difficult Sustainability

Annual saving = 1,000 x 40 = CU 40,000. PV = 40,000 x 3.791 = CU 151,640. Environmental costs such as carbon prices should be included in the appraisal, as they are real cash flows. If you answered CU 40,000 you gave one year's saving. If you answered CU 200,000 you did not discount. If you answered CU 379,100 you used 10,000 tonnes by mistake.

13. A project needs CU 10,000 of working capital at the start, recovered in full at the end of year 3. The cost of capital is 10% and the year 3 discount factor is 0.751. What is the net present value effect of the working capital?

A) CU 2,490 positive
B) CU 2,490 negative
C) CU 7,510 negative
D) CU 10,000 negative

Correct: B difficult Investment appraisal

The outlay of CU 10,000 is at time 0. The recovery is 10,000 x 0.751 = CU 7,510. Net PV = -10,000 + 7,510 = -CU 2,490. If you answered CU 10,000 negative you ignored the recovery. If you answered CU 7,510 you took the present value of the recovery as the net effect. If you answered CU 2,490 positive you reversed the sign.

14. Why might a company include environmental costs such as waste disposal and regulatory compliance in an investment appraisal?

A) Because they are non-cash, so they do not affect the decision
B) Because they always make a project unprofitable
C) Because the standards require them to be capitalised in the cost of the asset
D) Because they are often hidden in overheads, and omitting them overstates the project's financial return

Correct: D difficult Sustainability

Environmental costing aims to identify costs that are normally hidden in general overheads. These are real cash costs and should be included in the incremental cash flows. They do not always make a project unprofitable.

15. A project has an NPV of CU 5,000 at 10% and an NPV of -CU 10,000 at 20%. The required return is 12%. What should the company do, using the IRR?

A) Reject, because the IRR of about 13.3% is below the required return
B) Accept, because the IRR of about 13.3% exceeds the 12% required return
C) Accept, because the IRR of 15% is above the required return
D) Reject, because the NPV at 20% is negative

Correct: B difficult Investment appraisal

IRR = 10% + [5,000 / (5,000 + 10,000)] x 10% = 13.3%. As the IRR exceeds the 12% required return, the project should be accepted. A negative NPV at 20% does not mean the project should be rejected: it only shows that the IRR is below 20%.

16. A project costs CU 100,000 now and returns CU 40,000, CU 50,000 and CU 45,000 at the end of Years 1 to 3. The cost of capital is 10%. What is the NPV (to the nearest CU 100)?

A) CU 22,600
B) CU 1,400
C) CU 11,500
D) CU 35,000

Correct: C difficult Investment appraisal: NPV

PV of inflows = 40,000 x 0.909 + 50,000 x 0.826 + 45,000 x 0.751 = CU 111,500. NPV = CU 11,500. If you answered CU 22,600 you discounted each flow one year too little (treating Year 1 as Year 0). If you answered CU 1,400 you discounted each flow one year too much. If you answered CU 35,000 you did not discount.

17. A project has NPV of +CU 5,100 at 10% and -CU 13,500 at 20%. What is the IRR using linear interpolation?

A) 12.7%
B) 15.0%
C) 17.3%
D) 12.0%

Correct: A difficult Investment appraisal: IRR

IRR = 10% + [5,100 / (5,100 + 13,500)] x 10% = 12.7%. If you answered 15.0% you took the midpoint. If you answered 17.3% you used the negative NPV as the numerator. If you answered 12.0% you chose a rounded trial rate without interpolating.

18. A project costs CU 100,000 and produces CU 40,000, CU 50,000, CU 45,000 and CU 30,000 in Years 1 to 4. What is the payback period?

A) 2.22 years
B) 2.50 years
C) 3.00 years
D) 2.66 years

Correct: A difficult Investment appraisal: payback

Cumulative cash after Year 2 = 90,000. The remaining CU 10,000 is recovered in Year 3: 10,000 / 45,000 = 0.22. Payback = 2.22 years. If you answered 2.50 you assumed Year 3 was half recovered. If you answered 3.00 you rounded up to full years. If you answered 2.66 you gave the discounted payback.

19. Using the same cash flows (CU 100,000 outlay; CU 40,000, 50,000, 45,000 and 30,000 in Years 1 to 4) and a 10% cost of capital, what is the discounted payback period?

A) 2.66 years
B) 2.22 years
C) 3.00 years
D) 3.66 years

Correct: A difficult Investment appraisal: payback

Discounted cumulative cash after Year 2 = -22,314. Year 3's discounted flow is 45,000 / 1.331 = 33,809. Fraction = 22,314 / 33,809 = 0.66. Discounted payback = 2.66 years. If you answered 2.22 you did not discount. If you answered 3.00 you rounded up. If you answered 3.66 you added a year in error.

20. A machine costs CU 200,000, has a scrap value of CU 20,000 after 4 years, and generates cash inflows totalling CU 260,000. Depreciation is straight line. What is the ARR based on average investment?

A) 18.2%
B) 10.0%
C) 11.1%
D) 59.1%

Correct: A difficult Investment appraisal: ARR

Depreciation = 180,000 / 4 = 45,000 a year. Average profit = (260,000 - 180,000) / 4 = 20,000. Average investment = (200,000 + 20,000) / 2 = 110,000. ARR = 18.2%. If you answered 10.0% you used the initial investment. If you answered 11.1% you used cost less scrap (180,000). If you answered 59.1% you used average cash flow (65,000) instead of profit.

21. An asset produces CU 15,000 a year for 5 years (first receipt in one year) and the cost of capital is 8%. The 5-year annuity factor is 3.993. What is the present value?

A) CU 187,500
B) CU 59,895
C) CU 75,000
D) CU 49,680

Correct: B difficult Investment appraisal: NPV

PV = 15,000 x 3.993 = CU 59,895. If you answered CU 187,500 you treated it as a perpetuity (15,000 / 0.08). If you answered CU 75,000 you did not discount. If you answered CU 49,680 you used the four-year annuity factor (3.312).

22. The money cost of capital is 10% and expected inflation is 4%. What is the real cost of capital?

A) 6.00%
B) 5.77%
C) 14.4%
D) 10.0%

Correct: B difficult Investment appraisal: inflation

(1 + money rate) = (1 + real rate)(1 + inflation), so real = 1.10 / 1.04 - 1 = 5.77%. If you answered 6.00% you subtracted the rates. If you answered 14.4% you multiplied the factors. If you answered 10.0% you ignored inflation.

23. A project needs CU 100,000 of equipment and CU 20,000 of working capital now. Cash inflows are CU 45,000 a year for 4 years, and the working capital is recovered at the end of Year 4. The cost of capital is 10%. What is the NPV (nearest CU 100)?

A) CU 42,600
B) CU 22,600
C) CU 62,600
D) CU 36,300

Correct: D difficult Investment appraisal: NPV

PV of operating inflows = 45,000 x 3.170 = 142,650. PV of working capital recovery = 20,000 x 0.683 = 13,660. Outlay = 120,000. NPV = 36,300. If you answered CU 42,600 you ignored working capital. If you answered CU 22,600 you did not recover the working capital. If you answered CU 62,600 you added the working capital to the NPV instead of treating it as an outflow.

24. Which TWO of the following are relevant cash flows in an investment appraisal? (1) A feasibility study fee already paid. (2) An annual incremental cost saving. (3) Sale proceeds of an old machine that would be forgone if the project goes ahead.

A) (1) and (2)
B) (1) and (3)
C) (2) and (3)
D) (2) only

Correct: C difficult Investment appraisal: NPV

Relevant cash flows are future and incremental. The fee already paid is a sunk cost. The forgone sale proceeds are an opportunity cost.

25. Mutually exclusive Project A has NPV of CU 20,000 and IRR of 14%. Project B has NPV of CU 15,000 and IRR of 18%. The cost of capital is 10%. Which should be chosen and why?

A) Project B, because its IRR is higher
B) Project A, because the higher NPV increases shareholder wealth more
C) Project B, because its NPV per CU invested must be higher
D) Neither, because both IRRs exceed the cost of capital

Correct: B difficult Investment appraisal: NPV

For mutually exclusive projects the NPV rule is followed because it measures the absolute increase in wealth. IRR conflicts can arise because of scale or timing of cash flows. Both projects should not be rejected: both add value.