chp 7

Question 1

A project has an initial cost of $15,000. The future cash flows are $3,200, $6,100, -$1,100, and $18,200 for Years 1 to 4, respectively. How many IRRs will this project have?

Answer 1

3

Question 2

The length of time required for an investment to generate cash flows sufficient to recover the initial cost of the investment is called the

Answer 2

payback period.

Question 3

The discount rate that makes the NPV of an investment exactly equal to zero is called the

Answer 3

IRR

Question 4

What is the primary shortcoming of the average accounting rate of return from a financial perspective?

Answer 4

The use of net income rather than cash flows

Question 5

If the discounted payback method is preferable to the payback method, then why is the payback method ever used?

Answer 5

Payback is easier to compute than discounted payback.

Question 6

An investment is acceptable if the profitability index of the investment is

Answer 6

greater than one.

Question 7

A firm should accept projects with positive NPVs primarily because those projects will

Answer 7

create value for the firm’s current stockholders.

Question 8

Analysis using the profitability index

Answer 8

is useful as a decision tool when investment funds are limited.

Question 9

The discounted payback method

Answer 9

uses an arbitrary cutoff period.

Question 10

All else constant, the NPV of a typical investment project increases when

Answer 10

the rate of return decreases.

Question 11

All else equal, the payback period for a project will decrease whenever the

Answer 11

cash inflows are moved earlier in time.

Question 12

Which methods of project analysis are most biased towards short-term projects?

Answer 12

Payback and discounted payback

Question 13

A project with conventional cash flows has an NPV of -$500, an IRR of 9.5%, and a payback period of 4.2 years. Given this information, an analyst would be justified in concluding that

Answer 13

the required rate of return is greater than 9.5 percent.

Question 14

The payback method

Answer 14

ignores the time value of money.

Question 15

What is the IRR on an investment that has an initial cost of $63,100 and projected cash inflows of $18,700, $38,600, and $34,100 for Years 1 to 3, respectively?

Answer 15

19.10
NPV = $0 = –$63,100 + $18,700 / (1 + IRR) + $38,600 / (1 + IRR)2 + $34,100 / (1 + IRR)3
IRR = .1910 or 19.10%

Question 16

A project has an initial cost of $240,000 and cash flows of $78,000, –$22,000, and $164,000 for Years 1 to 3, respectively. If the required rate of return for this investment is 17 percent, should you accept it based solely on the IRR rule? Why or why not?

Answer 16

You cannot apply the IRR rule in this case because there are multiple IRRs.

Since the cash flow in Year 2 is a negative value, there are multiple IRRs. Thus, the IRR rule does not apply.

Question 17

A project is expected to have annual cash flows of $36,800, $24,600, and –$9,200 for Years 1 to 3, respectively. The initial cash outlay is $44,500 and the discount rate is 11 percent. What is the modified IRR using the discounting approach?

Answer 17

13.97%
Modified Year 0 cash flow = –$44,500 + (–$9,200/1.113) = –$51,226.96

$0 = –$51,226.96 + $36,800/(1 + MIRR) + $24,600/(1 + MIRR)2
MIRR = .1397, or 13.97%

Question 18

A project requires an initial investment of $135,000 and will produce cash inflows of $120,000, $175,000, and $340,000 over the next 3 years, respectively. What is the project’s NPV at a required return of 14 percent?

Answer 18

$334,410
Using a financial calculator CF0 = –135,000, CF1 = 120,00, CF2 = 175,000, CF3 = 340,000 , I/YR = 14, Solve for NPV = $334,410. Or: $120,000/(1 + .14) + $175,000/(1 + .14)2 + $340,000/(1 + .14)3 – $135,000 = $334,410.

Question 19

Project Q has an initial cost of $257,412 and projected cash flows of $123,300 in Year 1 and $180,300 in Year 2. Project R has an initial cost of $345,000 and projected cash flows of $184,500 in Year 1 and $230,600 in Year 2. The discount rate is 12.2 percent and the projects are independent. Which project(s), if either, should be accepted based on its profitability index value?

Answer 19

Accept Project R and reject Project Q

PIQ = ($123,300 / 1.122 + $180,300 / 1.1222) / $257,412 = .98; Reject

PIR = ($184,500 / 1.122 + $230,600 / 1.1222) / $345,000 = 1.01; Accept

Question 20

The Walk-Up Window is considering two mutually exclusive projects. Project A has an initial cost of $64,230 and annual cash flows of $25,200 for 3 years. Project B has an initial cost of $45,400 and annual cash flows of $21,400, $21,900, and $10,200 for Years 1 to 3, respectively. What is the incremental IRRA–B? Which project should be accepted if the discount rate is 9 percent? Which project should be accepted if the discount rate is 6 percent?

Answer 20

6.65%; Project B; Project A

Incremental cash flows:
Time 0: –$64,230 – (–$45,400) = –$18,830
Year 1: $25,200 – $21,400 = $3,800
Year 2: $25,200 – $21,900 = $3,300
Year 3: $25,200 – $10,200 = $15,000

Incremental IRRA–B = –$18,830 + $3,800 / (1 + IRR) + $3,300 / (1 + IRR)2 + $15,000 / (1 + IRR)3
Incremental IRRA–B = 0.0665, or 6.65%

NPVA = –$64,230 + $25,200 / 1.09 + $25,200 / 1.092 + $25,200 / 1.093 = –$441.37
NPVB = –$45,400 + $21,400 / 1.09 + $21,900 / 1.092 + $10,200 / 1.093 = $542.09
NPVA = –$64,230 + $25,200 / 1.06 + $25,200 / 1.062 + $25,200 / 1.063 = $3,129.90
NPVB = –$45,400 + $21,400 / 1.06 + $21,900 / 1.062 + $10,200 / 1.063 = $2,843.72

Question 21

Turner Enterprises is analyzing a project that is expected to have annual cash flows of $46,400, $51,300 and –$15,200 for Years 1 to 3, respectively. The initial cash outlay is $65,900 and the discount rate is 12 percent. What is the MIRR using the discounting approach?

Answer 21

17.43%
Modified Year 0 cash flow = –$65,900 – $15,200/1.123 = –$76,719.10

$0 = –$76,719.10 + $46,400/(1 + MIRR) + $51,300/(1 + MIRR)2
MIRR = .1743, or 17.43%

Question 22

Project A has an initial cost of $211,400 and projected cash flows of $46,200, $64,900, and $135,800 for Years 1 to 3, respectively. Project B has an initial cost of $187,900 and projected cash flows of $43,200, $59,700, and $125,600 for Years 1 to 3, respectively. What is the incremental IRRA–B of these two mutually exclusive projects?

Answer 22

−9.62%
Incremental cash flows:
Time 0: –$211,400 – (–$187,900) = –$23,500
Year 1: $46,200 – $43,200 = $3,000
Year 2: $64,900 – $59,700 = $5,200
Year 3: $135,800 – $125,600 = $10,200

Incremental IRRA–B = –$23,500 + $3,000 / (1 + IRR) + $5,200 / (1 + IRR)2 + $10,200 / (1 + IRR)3
IRR = –.0962, or –9.62%

Question 23

You are considering two independent projects that each have a required return of 15 percent. Project A has an initial cost of $198,700 and cash inflows of $67,200, $109,600, and $88,700 for Years 1 to 3, respectively. Project B has an initial cost of $102,000 and cash inflows of $37,600 and $91,200 for Years 1 and 2, respectively. Given this information, which one of the following statements is correct based on the NPV and IRR methods of analysis?

Answer 23

You should accept Project A and reject Project B.
NPVA = –$198,700 + $67,200 / 1.15 + $109,600 / 1.152 + $88,700 / 1.153
NPVA = $929.82; Accept

$0 = –$198,700 + $67,200 / (1 + IRR) + $109,600 / (1 + IRR)2 + $88,700 / (1 + IRR)3
IRR = .1527, or 15.27%; Accept

NPVB = –$102,000 + $37,600 / 1.15 + $91,200 / 1.152
NPVB = –$344.05; Reject

$0 = –$102,000 + $37,600 / (1 + IRR) + $91,200 / (1 + IRR)2
IRR = .1477, or 14.77%; Reject

Question 24

Dorian International has $75,000 that it can invest for two and half years. After that, the funds are needed to repay an outstanding bond issue. The company has two potential projects that are within the funding limit. Project A has an initial cost of $40,000 and cash flows of $24,000 a year for two years. Project B has an initial cost of $75,000 and cash flows of $27,000 a year for four years. If the required rate of return on both projects is 12 percent, what is your recommendation?

Answer 24

Accept Project A and reject Project B
Because the company must have the funds returned within two and a half years, any project that can be accepted must pay back within two and half years and also have a positive NPV.

PaybackA = 1 + ($40,000 – $24,000) / $24,000 = 1.67 years; Project A meets the payback requirement.

PaybackB = 2 + ($75,000 – $27,000 – $27,000) / $27,000 = 2.78 years; Project B must be rejected because it does not meet the mandatory payback period of 2.5 years.

NPVA = –$40,000 + $24,000 / 1.12 + $24,000 / 1.12 = $561.22; Project A passes the NPV test.

Question 25

One advantage of the payback method of project analysis is the method’s

Answer 25

simplicity.

Question 26

The Bees Knees is considering two projects. Project A consists of building a bee sanctuary on the firm’s small parcel of land. Project B consists of building a retail store on on that same parcel. The parcel can accommodate only one of the projects. Which method of analysis is most appropriate for an analyst to employ?

Answer 26

NPV

Question 27

Assume a project has normal cash flows. According to the accept/reject rules, the project should be accepted if the

Answer 27

IRR exceeds the required return.

Question 28

A firm should accept projects with positive NPVs primarily because those projects will

Answer 28

create value for the firm’s current stockholders.

Question 29

What is the primary shortcoming of the average accounting rate of return from a financial perspective?

Answer 29

The use of net income rather than cash flows

Question 30

When the acceptance or rejection of one project impacts the ability to accept or reject another project, the projects are generally considered to be

Answer 30

mutually exclusive.

Question 31

NPV

Answer 31

calculations consider the risk of each project.

Question 32

Using a discount rate of 17 percent, you found that two mutually exclusive projects produce the same positive NVP. Both projects have 7-year lives. During Year 1 and Year 2, Project A has larger cash flows than Project B. Given this information, you can reasonably conclude that

Answer 32

one project will be preferred at rates less than 17 percent and the other will be preferred at rates higher than 17 percent.

Question 33

Assume a project has normal cash flows and a positive (non-zero) NPV. The project’s

Answer 33

IRR will exceed its required rate of return.

Question 34

You know that two mutually exclusive projects are of different sizes. The smaller project is known to have a positive NPV. Which one of these accurately describes a method of properly determining which one, if either, project should be accepted?

Answer 34

Accept the larger project if the incremental IRR exceeds the discount rate

Question 35

The discounted payback period of a project will decrease whenever the

Answer 35

discount rate applied to the project is decreased.

Question 36

Rodriquez’s Hot Rods is considering a new project with an initial cost of $54,780 and a discount rate of 14 percent. The project is expected to have cash inflows of $27,000 a year for three years. What is the discounted payback period?

Answer 36

2.57 years

Discounted Year 1 cash flow = $27,000 / 1.14 = $23,684.21

Discounted Year 2 cash flow = $27,000 / 1.142 = $20,775.62
Discounted Year 3 cash flow = $27,000 / 1.143 = $18,224.23

Discounted payback period = 2 + ($54,780 – $23,684.21 – $20,775.62) / $18,224.23 = 2.57 years

Question 37

You are considering two independent projects. The required rate of return is 13.75 percent for Project A and 14.25 percent for Project B. Project A has an initial cost of $51,400 and cash inflows of $21,400, $24,900, and $22,200 for Years 1 to 3, respectively. Project B has an initial cost of $38,300 and cash inflows of $23,000 a year for two years. Which project(s), if either, should you accept?

Answer 37

Accept A and reject B

NPVA = –$51,400 + $21,400 / 1.1375 + $24,900 / 1.13752 + $22,200 / 1.13753 = $1,740.62; Accept

NPVB = –$38,300 + $23,000 / 1.1425 + $23,000 / 1.14252 = –$548.32; Reject

Question 38

Motor Sales is considering a project that costs $15,900 and will produce cash inflows of $5,500 a year for four years. The project has a required rate of return of 11.25 percent. What is the discounted payback period?

Answer 38

3.70 years

Discounted Year 1 cash flow = $5,500 / 1.1125 = $4,943.82

Discounted Year 2 cash flow = $5,500 / 1.11252 = $4,443.88
Discounted Year 3 cash flow = $5,500 / 1.11253 = $3,994.50
Discounted Year 4 cash flow = $5,500 / 1.11254 = $3,590.56

Discounted payback period = 3 + ($15,900 – $4,943.82 – $4,443.88 – $3,994.50) / $3,590.56 = 3.70 years

Question 39

A project is expected to have annual cash flows of $36,800, $24,600, and –$9,200 for Years 1 to 3, respectively. The initial cash outlay is $44,500 and the discount rate is 11 percent. What is the modified IRR using the discounting approach?

Answer 39

13.97%

Modified Year 0 cash flow = –$44,500 + (–$9,200/1.113) = –$51,226.96

$0 = –$51,226.96 + $36,800/(1 + MIRR) + $24,600/(1 + MIRR)2
MIRR = .1397, or 13.97%

Question 40

A project has an initial cost of $48,900 and cash flows of $31,300, –$11,600, and $40,300 for Years 1 to 3, respectively. The discount rate is 14 percent. What is the modified IRR using the discounting approach?

Answer 40

10.85%

Modified Year 0 cash flow = –$49,900 – $11,600/1.142 = –$57,825.80
$0 = –$57,825.80 + $31,300/(1 + MIRR) + $40,300/(1 + MIRR)3
MIRR = .1085, or 10.85%

Question 41

Project A has an initial cost of $16,400 and cash flows of $5,100, $6,800, and $6,900 for Years 1 to 3, respectively. Project B has an initial cost of $21,200 and cash flows of $8,300, $7,900, and $7,700 for Years 1 to 3, respectively. What is the incremental IRRB–A?

Answer 41

4.07%

Incremental cash flows:
Time 0: –$21,200 – (–$16,400) = –$4,800
Year 1: $8,300 – $5,100 = $3,200
Year 2: $7,900 – $6,800 = $1,100
Year 3: $7,700 – $6,900 = $800

Incremental IRRB–A = –$4,800 + $3,200 / (1 + IRR) + $1,100 / (1 + IRR)2 + $800 / (1 + IRR)3
IRR = 0.0407, or 4.07%

Question 42

Project I has an initial cash outflow of $18,300 and annual cash flows of $8,700 for Years 1 to 3. Project II has an initial cash outflow of $25,400 and annual cash flows of $10,500 for Years 1 to 3. These projects are mutually exclusive. The required rate of return is 11 percent. Based on the incremental NPV(II – I) which project(s) should be accepted and why?

Answer 42

Project I; because both the incremental NPV(II – I)and NPVI are positive.

Incremental cash flows:
Time 0: –$25,400 – (–$18,300) = –$7,100
Years 1 to 3: $10,500 – $8,700 = $1,800

Incremental NPV(II – I) = –$7,100 + $1,800 / 1.11 + $1,800 / 1.112 + $1,800 / 1.113 = –$2,701.31

NPVI = –$18,300 + $8,700 / 1.11 + $8,700 / 1.112 + $8,700 / 1.113 = $2,960.32