Question 1

A currently used machine costs $10,000 annually to run.What is the maximum that should be paid to replace the machine with one that will last 3 years and cost only $4,000 annually to run? The opportunity cost of capital is 12%.
A) $15,209.84
B) $9,607.33
C) $14,410.99
D) $10,338.56

Accepted Answer

NPV = [−$10,000 − (−$4,000)][(1 / 0.12) − 1 / 0.12(1.12)³] = $14,410.99

Question 2

According to the NPV rule,all projects should be accepted if NPV is positive when discounted at the:
A) internal rate of return.
B) opportunity cost of capital.
C) risk-free interest rate.
D) accounting rate of return.

Accepted Answer

The NPV rule states that a project should be accepted if its NPV is positive when discounted at the opportunity cost of capital. This is because the opportunity cost of capital represents the minimum rate of return that investors could earn by investing in a similar project with similar risk. Therefore, accepting projects with a positive NPV at this rate ensures that the project will generate returns higher than the cost of capital and create value for the company. Discounting at the internal rate of return or risk-free interest rate does not necessarily reflect the cost of capital, and using the accounting rate of return as a decision-making tool has several drawbacks.

Question 3

What is the decision rule in the case of sign changes that produce multiple IRRs for a project?
A) Select the lowest IRR to be conservative
B) Select the highest IRR to maximize the benefits
C) Any or all of the IRRs are justified to use
D) Calculate the modified internal rate of return.

Accepted Answer

When sign changes result in multiple IRRs, the best choice is to calculate the modified internal rate of return (MIRR), which eliminates the issue of multiple IRRs by assuming that all cash flows are reinvested at a predetermined rate. Using MIRR allows for a more accurate comparison of the profitability of different projects.

Question 4

The investment timing problem arises when:
A) cash flows may occur at the beginning or end of each time period.
B) there is a choice between using the payback or NPV rules.
C) the project has a positive initial cash flow.
D) investment can occur now or at some future point.

Accepted Answer

The investment timing problem refers to the decision of whether to invest now or defer investment to a later time. Therefore, the best choice for this problem is option D, which specifically addresses this issue. The other options are not relevant to the investment timing problem.

Question 5

A firm is considering a project with the following cash flows: Time 0 = +$20,000,Years 1-5 = −$4,500.Should the project be accepted if the cost of capital is 10%?
A) Yes; The IRR of the project is 4.06%.
B) Yes; The IRR of the project is 12.5%.
C) No; The IRR of the project is 4.06%.
D) No; The IRR of the project is 12.5%.

Accepted Answer

Using a financial calculator: n = 5; PV = $20,000; PMT = −$4,500; FV = 0; CPT i = 4.06%Given the cash flow signs, it resembles borrowing at 4.06% and, therefore, it is acceptable if this is less than the cost of capital.

Question 6

What is the equivalent annual cost for a project that requires a $40,000 investment at time zero,and a $10,000 annual expense during each of the next 4 years,if the opportunity cost of capital is 10%?
A) $20,000.00
B) $21,356.95
C) $22,618.83
D) $25,237.66

Accepted Answer

NPV = −$40,000 − $10,000[(1 / 0.1) − 1 / 0.1(1.1)⁴] = −$71,698.65The EAC is the payment that has the same NPV given 4 years and a 10% discount rate.So, using a financial calculator:n = 4; i = 10%; PV = −$71,698.65; FV = 0; CPT PMT = $22,618.83

Question 7

A polisher costs $10,000 and will cost $20,000 a year to operate and maintain.If the discount rate is 10% and the polisher will last for 5 years,what is the equivalent annual cost of the tool?
A) $17,163.04
B) $22,187.84
C) $22,637.98
D) $19,411.15

Accepted Answer

PV = −$10,000 + −$20,000[(1 / 0.1) − 1 / 0.1(1.1)⁵] = −$85,815.74 The equivalent annual cost is the payment with the same present value. So, using a financial calculator: n = 5; i = 10%; PV = −$85,815.74; FV = 0; CPT PMT = $22,637.98

Question 8

What happens to the equivalent annual cost of a project as the opportunity cost of capital decreases?
A) It increases.
B) It decreases.
C) It is not affected.
D) It depends on whether or not the projects are mutually exclusive.

Accepted Answer

The equivalent annual cost (EAC) is calculated as the sum of annual cash flows discounted at the opportunity cost of capital. As the opportunity cost of capital decreases, the discount rate used to calculate the EAC decreases, which in turn decreases the numerator of the equation. Therefore, the EAC decreases as the opportunity cost of capital decreases.

Question 9

A project's payback period is determined to be 4 years.If it is later discovered that additional cash flows will be generated in years 5 and 6,then the project's payback period will:
A) be reduced.
B) be increased.
C) be unchanged.
D) change but the discount rate must be known to determine the nature of the change.

Accepted Answer

The payback period only considers the time it takes to recover the initial investment, so additional cash flows after the payback period do not affect it.

Question 10

If two projects offer the same positive NPV,then they:
A) also have the same IRR.
B) have the same payback period.
C) are mutually exclusive projects.
D) add the same amount of value to the firm.

Accepted Answer

If two projects have the same positive NPV, it means that both projects will add the same amount of value to the firm. The IRR and payback period may be different for each project, but those metrics are not indicative of the total value added to the firm. Mutually exclusive projects are those where the acceptance of one project precludes the acceptance of the other project, which is not necessarily the case here. Therefore, the correct answer is D.

Question 11

If a project has a payback period of 5 years and a cost of capital of 10%,then the discounted payback will:
A) exceed 5 years.
B) be less than 5 years.
C) decrease if the cost of capital increases.
D) decrease if the payback period increases due to revised cash flows.

Accepted Answer

The discounted payback period is the time it takes to recover the initial investment in today's dollars, taking into account the time value of money. Since the cost of capital is 10%, the discounted payback period will be longer than the regular payback period of 5 years. Therefore, the best choice is A, which states that the discounted payback period will exceed 5 years.

Question 12

Selecting the project(s)with the highest NPV(s)is not the correct decision rule when:
A) there is capital rationing.
B) there are mutually exclusive projects.
C) projects are long-lived.
D) projects are independent.

Accepted Answer

When there is capital rationing, the available funds are insufficient to fund all the projects with positive NPV. In such a situation, it is essential to prioritize the projects based on other criteria such as the profitability index or internal rate of return. Selecting projects based solely on NPV might lead to the omission of projects with better financial viability but a lower NPV. Therefore, considering other decision rules is more appropriate in the presence of capital rationing.

Question 13

You can continue to use your less efficient machine at a cost of $8,000 annually.Alternatively,you can purchase a more efficient machine for $12,000 plus $5,000 annual maintenance.If the new machine lasts 5 years and the cost of capital is 15%,you should:
A) buy the new machine and save $600 in equivalent annual costs.
B) buy the new machine and save $388 in equivalent annual costs.
C) keep the old machine and save $388 in equivalent annual costs.
D) keep the old machine and save $580 in equivalent annual costs.

Accepted Answer

NPV = −$12,000 − $5,000[(1 / 0.15) − 1 / 0.15(1.15)⁵] = −$28,760.78Using a financial calculator:N = 5; I = 15%; PV = −$28,760.78; FV = 0; CPT PMT = $8,579.79Change in annual cost = $8,579.79 − 8,000 = $579.79

Question 14

A firm plans to use the profitability index to select between two mutually exclusive investments.If no capital rationing has been imposed,which project should be selected?
A) Select the project with the higher profitability index
B) Select the project with the lower profitability index
C) Without capital rationing, both projects can be selected
D) Without capital rationing, the NPV method must be used instead

Accepted Answer

Without capital rationing, the NPV method should be used to select between mutually exclusive projects, as it directly measures the value added by the project.

Question 15

To justify postponing a project for one year,the NPV needs to increase over that year by a rate that is equal to or greater than:
A) the project's IRR.
B) the risk-free rate.
C) the cost of capital.
D) zero.

Accepted Answer

The NPV needs to increase by at least the cost of capital to justify postponing a project, as this represents the minimum return required by investors.

Question 16

Because of its age,your car costs $4,000 annually in maintenance expense.You could replace it with a newer vehicle costing $8,000.Both vehicles would be expected to last 4 more years,at which point they will be valueless.If your opportunity cost is 8%,by how much must maintenance expense decrease on the newer vehicle to justify its purchase?
A) $1,625.40
B) $1,584.63
C) $1,469.08
D) $1,409.54

Accepted Answer

$8,000 = PMT [(1 / 0.08) − 1 / 0.08(1.08)⁴]; PMT = $2,415.37Maintenance expense decrease required = $4,000 − 2,415.37 = $1,584.63

Question 17

A company owns a tract of timber that will keep growing for a number of years.It calculates that the timber's value less the cost of harvesting is currently $50,000 and that this figure will grow by 10% in the next year and by 5% in the following year.If the cost of capital is 8%,when should the company harvest the timber?
A) today.
B) year 1.
C) year 2.
D) harvest a third of the timber each year.

Accepted Answer

If harvested in year 1, the timber will have an NPV in year 1 of $50,000 × 1.10 = $55,000, and an NPV today of $55,000 / 1.08 = $50,926If harvested in year 2, it will have an NPV is year 2 of $55,000 × 1.05 = $57,750 and an NPV today of $57,750 / 1.08² = $49,511

Question 18

If a project's IRR is 13% and the project provides annual cash flows of $15,000 for 4 years,how much did the project cost?
A) $44,617.07
B) $52,208.18
C) $41,909.29
D) $49,082.11

Accepted Answer

PV = $15,000 (1 / 0.13) − [1 / 0.13(1.13)⁴] = $44,617.07

Question 19

What is the minimum cash flow that could be received at the end of year 3 to make the following project "acceptable"? Initial cost = $100,000; cash flows at end of years 1 and 2 = $35,000; opportunity cost of capital = 10%.
A) $29,494
B) $30,000
C) $39,256
D) $52,250

Accepted Answer

NPV = 0 − $100,000 + ($35,000 / 1.1) + $35,000 / 1.1² + $x / 1.1³; x = $52,250A cash flow of $52,250 received in year 3, and discounted at 10%, would increase the NPV to zero.

Quiz 8: Net Present Value and Other Investment Criteria

A currently used machine costs $10,000 annually to run.What is the maximum that should be paid to replace the machine with one that will last 3 years and cost only $4,000 annually to run? The opportunity cost of capital is 12%.

According to the NPV rule,all projects should be accepted if NPV is positive when discounted at the:

What is the decision rule in the case of sign changes that produce multiple IRRs for a project?

The investment timing problem arises when:

A firm is considering a project with the following cash flows: Time 0 = +$20,000,Years 1-5 = −$4,500.Should the project be accepted if the cost of capital is 10%?

What is the equivalent annual cost for a project that requires a $40,000 investment at time zero,and a $10,000 annual expense during each of the next 4 years,if the opportunity cost of capital is 10%?

A polisher costs $10,000 and will cost $20,000 a year to operate and maintain.If the discount rate is 10% and the polisher will last for 5 years,what is the equivalent annual cost of the tool?

What happens to the equivalent annual cost of a project as the opportunity cost of capital decreases?

A project's payback period is determined to be 4 years.If it is later discovered that additional cash flows will be generated in years 5 and 6,then the project's payback period will:

If two projects offer the same positive NPV,then they:

If a project has a payback period of 5 years and a cost of capital of 10%,then the discounted payback will:

Selecting the project(s) with the highest NPV(s) is not the correct decision rule when:

You can continue to use your less efficient machine at a cost of $8,000 annually.Alternatively,you can purchase a more efficient machine for $12,000 plus $5,000 annual maintenance.If the new machine lasts 5 years and the cost of capital is 15%,you should:

A firm plans to use the profitability index to select between two mutually exclusive investments.If no capital rationing has been imposed,which project should be selected?

To justify postponing a project for one year,the NPV needs to increase over that year by a rate that is equal to or greater than:

If a project's IRR is 13% and the project provides annual cash flows of $15,000 for 4 years,how much did the project cost?

What is the minimum cash flow that could be received at the end of year 3 to make the following project "acceptable"? Initial cost = $100,000; cash flows at end of years 1 and 2 = $35,000; opportunity cost of capital = 10%.