1. The difference between the market value of an investment and its cost is the:
2. A) Net present value.
3. B) Internal rate of return.
4. C) Payback period.
5. D) Profitability index.
6. E) Discounted payback period.

Answer: A

 

2. The net present value (NPV) rule can be best stated as:
3. A) An investment should be accepted if, and only if, the NPV is exactly equal to zero.
4. B) An investment should be rejected if the NPV is positive and accepted if it is negative.
5. C) An investment should be accepted if the NPV is positive and rejected if its is negative.
6. D) An investment with greater cash inflows than cash outflows, regardless of when the cash flows occur, will always have a positive NPV and therefore should always be accepted.

Answer: C

 

3. The length of time required for an investment to generate cash flows sufficient to recover its initial cost is the:
4. A) Net present value.
5. B) Internal rate of return.
6. C) Payback period.
7. D) Profitability index.
8. E) Discounted payback period.

Answer: C

 

4. The payback rule can be best stated as:
5. A) An investment is acceptable if its calculated payback period is less than some prespecified number of years.
6. B) An investment should be accepted if the payback is positive and rejected if it is negative.
7. C) An investment should be rejected if the payback is positive and accepted if it is negative.
8. D) An investment is acceptable if its calculated payback period is greater than some prespecified number of years.

Answer: A

 

5. The discount rate that makes the net present value of an investment exactly equal to zero is the:
6. A) Payback period.
7. B) Internal rate of return.
8. C) Average accounting return.
9. D) Profitability index.
10. E) Discounted payback period.

Answer: B

 

6. The internal rate of return (IRR) rule can be best stated as:
7. A) An investment is acceptable if its IRR is exactly equal to its net present value (NPV).
8. B) An investment is acceptable if its IRR is exactly equal to zero.
9. C) An investment is acceptable if its IRR is less than the required return, else it should be rejected.
10. D) An investment is acceptable if its IRR exceeds the required return, else it should be rejected.

Answer: D

 

 

 

7. A situation in which taking one investment prevents the taking of another is called:
8. A) Net present value profiling.
9. B) Operational ambiguity.
10. C) Mutually exclusive investment decisions.
11. D) Issues of scale.
12. E) Multiple rates of return.

Answer: C

 

8. The present value of an investment’s future cash flows divided by its intial cost is the:
9. A) Net present value.
10. B) Internal rate of return.
11. C) Average accounting return.
12. D) Profitability index.
13. E) Payback period.

Answer: D

9. The profitability index (PI) rule can be best stated as:
10. A) An investment is acceptable if its PI is greater than one.
11. B) An investment is acceptable if its PI is less than one.
12. C) An investment is acceptable if its PI is greater than the internal rate of return (IRR).
13. D) An investment is acceptable if its PI is less than the net present value

 

10. Which of the following statements is true?
11. A) NPV should never be used if the project under consideration has nonconventional cash flows.
12. B) NPV is similar to a cost/benefit ratio.
13. C) If the financial manager relies on NPV in making capital budgeting decisions, she acts in the shareholders’ best interests.
14. D) NPV can normally be directly observed in the marketplace.
15. E) IRR is generally preferred to NPV in making correct capital budgeting acceptance decisions.

Answer: C

 

11. Net present value _____________.
12. A) is equal to the initial investment in a project
13. B) is equal to the present value of the project benefits
14. C) is equal to zero when the discount rate used is equal to the IRR
15. D) is simplified by the fact that future cash flows are easy to estimate
16. E) requires the firm set an arbitrary cutoff point for determining whether an investment is acceptable

Answer: C

 

12. The _______ decision rule is considered the “best” in principle.
13. A) internal rate of return
14. B) payback period
15. C) average accounting return
16. D) net present value
17. E) profitability index

Answer: D

 

13. Which of the following decision rules is best for evaluating projects for which cash flows beyond a specified point in time, and the time value of money, can both be ignored?
14. A) Payback
15. B) Net present value
16. C) Average accounting return
17. D) Profitability index
18. E) Internal rate of return

Answer: A

 

14. An investment generates $1.10 in present value benefits for each dollar of invested costs. This conclusion was most likely reached by calculating the project’s:
15. A) Net present value
16. B) Profitability index
17. C) Internal rate of return
18. D) Payback period
19. E) Average accounting return

Answer: B

 

15. The use of which of the following would lead to correct decisions when comparing mutually exclusive investments?

 

1. Profitability index
2. Net present value

III.  Average accounting return

 

1. A) I only
2. B) II only
3. C) III only
4. D) I and II only
5. E) I and III only

Answer: B

 

16. You own some manufacturing equipment that must be replaced. Two different suppliers present a purchase and installation plan for your consideration. This is an example of a business decision involving _____________ projects.
17. A) mutually exclusive
18. B) independent
19. C) working capital
20. D) positive NPV
21. E) crossover

Answer: A

 

17. If a project with conventional cash flows has an IRR less than the required return, then:
18. A) The profitability index is less than one.
19. B) The IRR must be zero.
20. C) The AAR is greater than the required return.
21. D) The payback period is less than the maximum acceptable period.
22. E) The NPV is positive.

Answer: A

 

18. Calculate the NPV of the following project using a discount rate of 10%:

Yr 0 = –$800; Yr 1 = –$80; Yr 2 = $100; Yr 3 = $300; Yr 4 = $500; Yr 5 = $500

8. A) $    04
9. B) $  28
10. C) $208.04
11. D) $459.17
12. E) $887.28

Answer: B

Response: NPV = -$800 – 80 / 1.1 + 100 / 1.12 + 300 / 1.13 + 500 / 1.14 + 500 / 1.15 = $87.28

Using your cashflow keys? CF0= -800, CO1 = -80, FO1=1, CO2 = 100, FO2=1, CO3 = 300, FO3=1, CO4 = 500, FO4=2. Then hit the NPV key, type in 10 for “I,” hit the down arrow to get you back to the NPV display, and hit CPT and you get 87.28.

 

 

 

19. You are considering a project that costs $600 and has expected cash flows of $224, $250.88 and $280.99 over the next three years. If the appropriate discount rate for the project’s cash flows is 12%, what is the net present value of this project?
20. A) The NPV is negative
21. B) $  00
22. C) $  34
23. D) $49.34
24. E) $84.75

Answer: B

CFO = -600, CO1=224, CO2=250.88, CO3=280.99. All the FO’s are equal to one, with each cash flow occurring once. After entering all the Cashflows (the CO1’s, 2’s and 3’s), hit the NPV key, set I equal to 12, hit the down arrow to get back to NPV, hit CPT and you get about zero, or B.

 

20. A project costs $300 and has cash flows of $75 for the first three years and $50 in each of the project’s last three years. What is the payback period of the project?
21. A) The project never pays back
22. B) 75 years
23. C) 50 years
24. D) 25 years
25. E) 50 years

Answer: C

Response: recover $275 in 4 years, need $25 / 50 = 4.50 years

 

21. Suppose a project costs $2,500 and produces cash flows of $400 over each of the following 8 years. What is the IRR of the project?
22. A) There is not enough information; a discount rate is required
23. B) 27%
24. C) 84%
25. D) 61%
26. E) 06%

Answer: C

Response: $2,500 = $400 {[1 – 1/(1 + IRR)8] / IRR}; IRR = 5.84%

-2,500 PV, 400 PMT, 8 N, CPT I/Y = 5.84%

Or you could use your CF keys … but with equally sized cashflows, the TVOM keys are easier.

 

22. A project has an initial investment of $25,000, with $6,500 annual inflows for each of the subsequent 5 years. If the required return is 12%, what is the NPV?
23. A) –$6,500.00
24. B) –$2,447.02
25. C) –$1,568.95
26. D) $   46
27. E) $1,763.81

Answer: C

Response: NPV = -$25,000 + 6,500 [(1 – 1/1.125) / .12] = -$1,568.95

6,500 PMT, 5 N, 12 I/Y, CPT PV = 23,431 the present value of your inflows.

Your NPV = PV(Inflows) – PV (outflows) = 23,431 – 25,000 or a negative 1,569.

 

 

23. What is the NPV of the following set of cash flows if the required return is 15%?

 

 

 

1. A) The NPV is negative
2. B) $   27
3. C) $   44
4. D) $1,247.90
5. E) $4,656.12

Answer: B

CF0 = -10000

CO1 = -1000

FO1 = 1

CO2 = 10000

FO2 = 2

CO3 = -5000

I = 15

NPV = 408.27

 

24. Would you accept a project which is expected to pay $2,500 a year for 6 years if the initial investment is $10,000 and your required return is 8%?
25. A) Yes; the NPV is $1,557
26. B) Yes; the NPV is $928
27. C) Yes; the NPV is $63
28. D) No; the NPV is –$346
29. E) No; the NPV is –$1,221

Answer: A

Response: NPV = + 2,500[(1 – 1/1.086) / .08] = $1,557.20

2,500 PMT, 6 N, 8 I/Y, CPT PV = 11,557, which is greater than the $10,000 cost by $1,557, so you DO THIS DEAL!! You accept.

 

25. What is the payback period of a $15,000 investment with the following cash flows?

 

 

 

2. A) 75 years
3. B) 50 years
4. C) 75 years
5. D) 50 years
6. E) 75 years

Answer: B

Response: recover $12,000 in 3 years, need $3,000 / 6,000 = 3.50 years

 

26. You are considering an investment which has the following cash flows. If you require a 5 year payback period, should you take the investment?

 

3. A) Yes, the payback is 3.000 years.
4. B) Yes, the payback is 3.75 years.
5. C) Yes, the payback is 4.25 years.
6. D) No, the payback is 5.25 years.
7. E) No, the payback is 5.75 years.

Answer: C

Response: recover $27,500 in 4 years, need $2,500 / 10,000 = 4.25 years

 

27. Your required return is 15%. Should you accept a project with the following cash flows?

 

1. A) No, because the IRR is 5%.
2. B) No, because the IRR is 10%.
3. C) Yes, because the IRR is 20%.
4. D) Yes, because the IRR is 30%.
5. E) Yes, because the IRR is 40%.

Answer: D

Response: $25 = $10 / (1 + IRR) + 10 / (1 + IRR)2 + 25 / (1 + IRR)3; IRR = 30%

CF0=-25, CO1=10, FO1=2, CO2=25, FO2=1, IRR, CPT, IRR = 29.97% or about 30%

 

28. You are going to choose between two investments. Both cost $50,000, but investment A pays $25,000 a year for 3 years while investment B pays $20,000 a year for 4 years. If your required return is 12%, which should you choose?
29. A) A because it pays back sooner.
30. B) A because its IRR exceeds 12%.
31. C) A because it has a higher IRR.
32. D) B because its IRR exceeds 12%.
33. E) B because it has a higher NPV.

Answer: E

Response:

A: NPV = + 25,000 [(1 – 1/1.123) / .12] = $10,046

B: NPV = + 20,000 [(1 – 1/1.124) / .12] = $10,747

 

29. Using the profitability index, which of the following projects would you choose if you have limited funds?

 

Project	Initial Investment	NPV
1	$50,000	$10,000
2	75,000	25,000
3	60,000	15,000
4	40,000	17,000
5	90,000	40,000

 

1. A) Project 1
2. B) Project 2
3. C) Project 3
4. D) Project 4
5. E) Project 5

Answer: E

Response:

Project 1: PI = $60,000 / 50,000 = 1.200; Project 2: PI = $100,000 / 75,000 = 1.333

Project 3: PI = $75,000 / 60,000 = 1.250; Project 4: PI = $57,000 / 40,000 = 1.425

Project 5: PI = $130,000 / 90,000 = 1.444

 

 

 

30. You have a choice between 2 mutually exclusive investments. If you require a 15% return, which investment should you choose?

 

 

 

1. A) Project A, because it has a smaller initial investment.
2. B) Project B, because it has a higher NPV.
3. C) Either one, because they have the same profitability indexes.
4. D) Project A, because it has the higher internal rate of return.
5. E) Project B, because it pays back faster.

Answer: B

Response:

A: NPV = + 20,000 / 1.15 + 40,000 / 1.152 + 80,000 / 1.153 = $238

B: NPV = + 75,000 / 1.15 + 45,000 / 1.152 + 40,000 / 1.153 = $545

 

31. For a project with an initial investment of $8,000 and cash inflows of $2,000 each year for 6 years, calculate NPV given a required return of 13%.
32. A) –$846
33. B) –$263
34. C) $    0
35. D) $149
36. E) $552

Answer: C

Response: NPV = -$8,000 + 2,000 [(1 – 1/1.136) / .13] = $0 (actual -$4.90)

Use your TVOM keys with equally-sized cash flows.

Thusly: 2000 PMT, 6 N, 13 I/Y, CPT PV = 7,995, which is less than 8,000, so your NPV would be about a negative five bucks, as with the algebra above.

 

32. What is the IRR of an investment that costs $18,500 and pays $5,250 a year for 5 years?
33. A) 13%
34. B) 15%
35. C) 19%
36. D) 25%
37. E) 28%

Answer: A

Response: $18,500 = $5,250 {[1 – 1/(1 + IRR)5] / IRR}; IRR = 12.92%

Just use your TVOM keys with equal cash flows to calculate IRR. Thusly:

-18,500 PV, 5,250 PMT, 5 N, CPT I/Y = IRR with equally-sized cash-flows or 12.92%

 

33. What is the profitability index of the following investment if the required return = 10%?

 

 

1. A) 94
2. B) 09
3. C) 18
4. D) 27
5. E) 45

Answer: B

Response: PV = $50 / 1.1 + 75 / 1.12 + 75 / 1.13 = $163.79; PI = $163.79 / 150 = 1.09

 

34. What is the payback period for the following investment?

 

1. A) 4 years
2. B) 3 years
3. C) 2 years
4. D) 1 year
5. E) The investment doesn’t payback

Answer: E

Response: recover $10,000 + 8,000 + 4,000 + 2,000 = $24,000; never pays back

 

Use the following to answer questions 35-38:

 

Bill plans to open a do-it-yourself dog bathing center in a storefront. The bathing equipment will cost $50,000. Bill expects the after-tax cash inflows to be $15,000 annually for 8 years, after which he plans to scrap the equipment and retire to the beaches of Jamaica.

 

35. What is the project’s payback period?
36. A) 67 years
37. B) 33 years
38. C) 67 years
39. D) 33 years
40. E) 67 years

Answer: B

Response: payback = $50,000 / 15,000 = 3.33 years

 

36. Assume the required return is 10%. What is the project’s NPV?
37. A) $     887
38. B) $13,322
39. C) $22,759
40. D) $30,024
41. E) $45,001

Answer: D

Response: NPV = + 15,000 [(1 – 1/1.108) / .10] = $30,023.89

Use the CF keys for practice: CF0=-50,000, CO1=15,000, FO1=8, NPV, I=10, NPV = 30,024

Practice these questions using our BA II Plus review sheet problems 18-22.

 

37. Assume the required return is 20%. What is the project’s IRR? Should it be accepted?
38. A) 15%;   yes
39. B) 15%;   no
40. C) 25%;   yes
41. D) 25%;   no
42. E) 20%;   indifferent

Answer: C

Response: $50,000 = $15,000 {[1 – 1/(1 + IRR)8] / IRR}; IRR = 24.95% > 20%; accept

-50,000 PV, 15,000 PMT, 8 N, CPT I/Y = IRR = 24.95%

 

 

38. Assume the required return is 20%. What is the project’s PI? Should it be accepted?
39. A) 85;   yes
40. B) 85;   no
41. C) 00;   indifferent
42. D) 15;   yes
43. E) 15;   no

Answer: D

Response:

PV of inflows = $15,000 [(1 – 1/1.28) / .2] = $57,557; PI = $57,557 / 50,000 = 1.15; accept

At a discount rate of 20%, the PV of the inflows equals the NPV of 7,557  plus the cost of 50,000 or 57,557. (Recall the PV(Inflows) = NPV + PV(Outflows))