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The internal rate of return is that discount rate that equates the present value of the cash outflows (or costs) with the present value of the cash inflows.

A) True
B) False

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Which of the following statements is CORRECT?


A) If a project has "normal" cash flows, then its MIRR must be positive.
B) If a project has "normal" cash flows, then it will have exactly two real IRRs.
C) The definition of "normal" cash flows is that the cash flow stream has one or more negative cash flows followed by a stream of positive cash flows and then one negative cash flow at the end of the project's life.
D) If a project has "normal" cash flows, then it can have only one real IRR, whereas a project with "nonnormal" cash flows might have more than one real IRR.
E) If a project has "normal" cash flows, then its IRR must be positive.

F) B) and E)
G) C) and E)

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Projects S and L are equally risky, mutually exclusive, and have normal cash flows.Project S has an IRR of 15%, while Project L's IRR is 12%.The two projects have the same NPV when the cost of capital is 7%.Which of the following statements is CORRECT?


A) If the cost of capital is 6%, Project S will have the higher NPV.
B) If the cost of capital is 13%, Project S will have the lower NPV.
C) If the cost of capital is 10%, both projects will have a negative NPV.
D) Project S's NPV is more sensitive to changes in cost of capital than Project L's.
E) If the cost of capital is 10%, both projects will have positive NPVs.

F) A) and B)
G) B) and D)

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Projects A and B are mutually exclusive and have normal cash flows.Project A has an IRR of 15% and B's IRR is 20%.The company's cost of capital is 12%, and at that rate Project A has the higher NPV.Which of the following statements is CORRECT?


A) Assuming the timing pattern of the two projects' cash flows is the same, Project B probably has a higher cost (and larger scale) .
B) Assuming the two projects have the same scale, Project B probably has a faster payback than Project A.
C) The crossover rate for the two projects must be 12%.
D) Since B has the higher IRR, then it must also have the higher NPV if the crossover rate is less than the cost of capital of 12%.
E) The crossover rate for the two projects must be less than 12%.

F) A) and C)
G) A) and E)

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Projects C and D both have normal cash flows and are mutually exclusive.Project C has a higher NPV if the cost of capital is less than 12%, whereas Project D has a higher NPV if the cost of capital exceeds 12%.Which of the following statements is CORRECT?


A) Project D is probably larger in scale than Project C.
B) Project C probably has a faster payback.
C) Project C probably has a higher IRR.
D) The crossover rate between the two projects is below 12%.
E) Project D probably has a higher IRR.

F) A) and B)
G) None of the above

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E

Conflicts between two mutually exclusive projects occasionally occur, where the NPV method ranks one project higher but the IRR method ranks the other one first.In theory, such conflicts should be resolved in favor of the project with the higher positive IRR.

A) True
B) False

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False

Consider two projects, X and Y.Project X's IRR is 19% and Project Y's IRR is 17%.The projects have the same risk and the same lives, and each has constant cash flows during each year of their lives.If the cost of capital is 10%, Project Y has a higher NPV than X.Given this information, which of the following statements is CORRECT?


A) The crossover rate must be greater than 10%.
B) If the cost of capital is 8%, Project X will have the higher NPV.
C) If the cost of capital is 18%, Project Y will have the higher NPV.
D) Project X is larger in the sense that it has the higher initial cost.
E) The crossover rate must be less than 10%.

F) None of the above
G) B) and E)

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The cost of capital for two mutually exclusive projects that are being considered is 12%.Project K has an IRR of 20% while Project R's IRR is 15%.The projects have the same NPV at the 12% current cost of capital.Interest rates are currently high.However, you believe that money costs and thus your cost of capital will soon decline.You also think that the projects will not be funded until the cost of capital has decreased, and their cash flows will not be affected by the change in economic conditions.Under these conditions, which of the following statements is CORRECT?


A) You should delay a decision until you have more information on the projects, even if this means that a competitor might come in and capture this market.
B) You should recommend Project R, because at the new cost of capital it will have the higher NPV.
C) You should recommend Project K, because at the new cost of capital it will have the higher NPV.
D) You should recommend Project R because it will have both a higher IRR and a higher NPV under the new conditions.
E) You should reject both projects because they will both have negative NPVs under the new conditions.

F) A) and B)
G) C) and D)

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Langton Inc.is considering Projects S and L, whose cash flows are shown below.These projects are mutually exclusive, equally risky, and not repeatable.The CEO believes the IRR is the best selection criterion, while the CFO advocates the MIRR.If the decision is made by choosing the project with the higher IRR rather than the one with the higher MIRR, how much, if any, value will be forgone.In other words, what's the NPV of the chosen project versus the maximum possible NPV? Note that (1) "true value" is measured by NPV, and (2) under some conditions the choice of IRR vs.MIRR will have no effect on the value lost. r=7.00% Year 01234CFS$1,100$550$600$100$100CFL$2,750$725$725$800$1,400\begin{array} { c c c c c c } & \mathrm { r } = 7.00 \% & & & \\\text { Year } & 0 & 1 & 2 & 3 & 4 \\\hline \mathrm { CF } _ { \mathrm { S } }& - \$ 1,100 & \$ 550 & \$ 600 & \$ 100 & \$ 100 \\\mathrm { CF } _ { \mathrm { L } } & - \$ 2,750 & \$ 725 & \$ 725 & \$ 800 & \$ 1,400\end{array}


A) $185.90
B) $197.01
C) $208.11
D) $219.22
E) $230.32

F) C) and D)
G) A) and E)

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Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows.


A) A project's regular IRR is found by compounding the cash inflows at the cost of capital to find the present value (PV) , then discounting the TV to find the IRR.
B) If a project's IRR is smaller than the cost of capital, then its NPV will be positive.
C) A project's IRR is the discount rate that causes the PV of the inflows to equal the project's cost.
D) If a project's IRR is positive, then its NPV must also be positive.
E) A project's regular IRR is found by compounding the initial cost at the cost of capital to find the terminal value (TV) , then discounting the TV at the cost of capital.

F) A) and B)
G) B) and E)

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A project's IRR is independent of the firm's cost of capital.In other words, a project's IRR doesn't change with a change in the firm's cost of capital.

A) True
B) False

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Computer Consultants Inc.is considering a project that has the following cash flow and cost of capital (r) data.What is the project's MIRR? Note that a project's MIRR can be less than the cost of capital (and even negative) , in which case it will be rejected. r=10.00% Year 0123 Cash flows $1,000$450$450$450\begin{array} { l c c c c } \mathrm { r } = 10.00 \% \\\text { Year } & 0 & 1 & 2 & 3 \\\hline \text { Cash flows } & - \$ 1,000 & \$ 450 & \$ 450 & \$ 450\end{array}


A) 9.32%
B) 10.35%
C) 11.50%
D) 12.78%
E) 14.20%

F) A) and C)
G) A) and E)

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Because "present value" refers to the value of cash flows that occur at different points in time, a series of present values of cash flows should not be summed to determine the value of a capital budgeting project.

A) True
B) False

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When evaluating mutually exclusive projects, the modified IRR (MIRR) always leads to the same capital budgeting decisions as the NPV method, regardless of the relative lives or sizes of the projects being evaluated.

A) True
B) False

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Westwood Painting Co.is considering a project that has the following cash flow and cost of capital (r) data.What is the project's MIRR? Note that a project's MIRR can be less than the cost of capital (and even negative) , in which case it will be rejected. r=12.25% Year 01234 Cash flows $850$300$320$340$360\begin{array} { l c c c c c } & r = 12.25 \% \\\text { Year } & 0 & 1 & 2 & 3 & 4 \\\hline \text { Cash flows } & - \$ 850 & \$ 300 & \$ 320 & \$ 340 & \$ 360\end{array}


A) 13.42%
B) 14.91%
C) 16.56%
D) 18.22%
E) 20.04%

F) A) and E)
G) B) and E)

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Patterson Co.is considering a project that has the following cash flow and cost of capital (r) data.What is the project's NPV? Note that a project's expected NPV can be negative, in which case it will be rejected. r:10.00% Year 0123 Cash flows $950$500$400$300\begin{array} { l c c c c } r:& 10.00 \% & & & \\\text { Year } & 0 & 1 & 2 & 3 \\\hline \text { Cash flows } & - \$ 950 & \$ 500 & \$ 400 & \$ 300\end{array}


A) $54.62
B) $57.49
C) $60.52
D) $63.54
E) $66.72

F) A) and C)
G) A) and E)

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Dickson Co.is considering a project that has the following cash flow and cost of capital (r) data.What is the project's NPV? Note that a project's expected NPV can be negative, in which case it will be rejected.  r: 12.00% Year 012345 Cash flows $1,100$400$390$380$370$360\begin{array} { l c c c c c c } \text { r: } & 12.00 \% & & & & \\\text { Year } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Cash flows } & - \$ 1,100 & \$ 400 & \$ 390 & \$ 380 & \$ 370 & \$ 360\end{array}


A) $250.15
B) $277.94
C) $305.73
D) $336.31
E) $369.94

F) A) and D)
G) A) and C)

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In theory, capital budgeting decisions should depend solely on forecasted cash flows and the opportunity cost of capital.The decision criterion should not be affected by managers' tastes, choice of accounting method, or the profitability of other independent projects.

A) True
B) False

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You are on the staff of O'Hara Inc.The CFO believes project acceptance should be based on the NPV, but Andrew O'Hara, the president, insists that no project should be accepted unless its IRR exceeds the project's risk-adjusted cost of capital.Now you must make a recommendation on a project that has a cost of $15,000 and two cash flows: $110,000 at the end of Year 1 and −$100,000 at the end of Year 2.The president and the CFO both agree that the appropriate cost of capital for this project is 10%.At 10%, the NPV is $2,355.37, but you find two IRRs, one at 6.33% and one at 527%, and a MIRR of 11.32%.Which of the following statements best describes your optimal recommendation, i.e., the analysis and recommendation that is best for the company and least likely to get you in trouble with either the CFO or the president?


A) You should recommend that the project be rejected because, although its NPV is positive, it has an IRR that is less than the cost of capital.
B) You should recommend that the project be accepted because (1) its NPV is positive and (2) although it has two IRRs, in this case it would be better to focus on the MIRR, which exceeds the cost of capital.You should explain this to the president and tell him that the firm's value will increase if the project is accepted.
C) You should recommend that the project be rejected.Although its NPV is positive it has two IRRs, one of which is less than the cost of capital, which indicates that the firm's value will decline if the project is accepted.
D) You should recommend that the project be rejected because, although its NPV is positive, its MIRR is less than the cost of capital, and that indicates that the firm's value will decline if it is accepted.
E) You should recommend that the project be rejected because its NPV is negative and its IRR is less than the cost of capital.

F) B) and C)
G) C) and E)

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B

Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one cash outflow at t = 0 followed by a series of positive cash flows.


A) A project's MIRR is always less than its regular IRR.
B) If a project's IRR is greater than its cost of capital, then its MIRR will be greater than the IRR.
C) To find a project's MIRR, we compound cash inflows at the regular IRR and then find the discount rate that causes the PV of the terminal value to equal the initial cost.
D) To find a project's MIRR, the textbook procedure compounds cash inflows at the cost of capital and then finds the discount rate that causes the PV of the terminal value to equal the initial cost.
E) A project's MIRR is always greater than its regular IRR.

F) B) and E)
G) A) and D)

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