1．Which of the following projects would have multiple internal rates of return (IRRs)? The cost of capital for all projects is 9.75 percent.

Cash Flows	Blackjack	Roulette	Keno
T0	-10,000	-12,000	-8,000
T1	10,000	7,000	4,000
T2	15,000	2,000	0
T3	-10,000	2,000	6,000

A)   Projects Roulette and Keno.

B)   Projects Blackjack and Keno.

C)   Project Keno only.

D)   Project Blackjack only.

2．If a project has net annual cash outflows during its life or at the end of its life:

A)   there will be multiple net present values.

B)   there will be a negative internal rate of return.

C)   one will not be able to calculate the net present value.

D)   there will be more than one internal rate of return.

3．Which of the following statements about the internal rate of return (IRR) for a project with the following cash flow pattern is TRUE?

 Year 0: -$ 2,000

 Year 1: $ 10,000

 Year 2: -$ 10,000

A)   It has a single IRR of approximately 38 percent.

B)   It has a single IRR of approximately 260 percent.

C)   It has two IRRs of approximately 38 and 260 percent.

D)   No IRRs can be calculated.

4．Which of the following statements about NPV and IRR is FALSE?

A)   The NPV will be positive if the IRR is less than the cost of capital.

B)   The IRR can be positive even if the NPV is negative.

C)   The NPV method is not affected by the multiple IRR problem.

D)   When the IRR is equal to the cost of capital, the NPV equals zero.

5．Which of the following statements regarding the internal rate of return (IRR) is most accurate? The IRR:

A)   assumes that the reinvestment rate of the cash flows is the cost of capital.

B)   ignores the time value of money.

C)   and the net present value (NPV) method lead to the same accept/reject decision for independent projects.

D)   can lead to multiple IRR rates if the cash flows extend past the payback period.

答案和详解如下：

1．Which of the following projects would have multiple internal rates of return (IRRs)? The cost of capital for all projects is 9.75 percent.

Cash Flows	Blackjack	Roulette	Keno
T0	-10,000	-12,000	-8,000
T1	10,000	7,000	4,000
T2	15,000	2,000	0
T3	-10,000	2,000	6,000

A)   Projects Roulette and Keno.

B)   Projects Blackjack and Keno.

C)   Project Keno only.

D)   Project Blackjack only.

The correct answer was D)

The multiple IRR problem occurs if a project has non-normal cash flows, that is, the sign of the net cash flows changes from negative to positive to negative, or vice versa. For the exam, a shortcut to look for is the project cash flows changing signs more than once. Only Project Blackjack has this cash flow pattern. The 0 net cash flow in T₂ for Project Keno and likely negative net present value (NPV) for Project Roulette would not necessarily result in multiple IRRs.

2．If a project has net annual cash outflows during its life or at the end of its life:

A)   there will be multiple net present values.

B)   there will be a negative internal rate of return.

C)   one will not be able to calculate the net present value.

D)   there will be more than one internal rate of return.

The correct answer was D)

Projects with non-normal cash-flow patterns (where the sign of the net cash flow goes from minus to plus to back to minus) will have multiple internal rates of return. However, one will still be able to calculate a single net present value for the cash flow pattern.

3．Which of the following statements about the internal rate of return (IRR) for a project with the following cash flow pattern is TRUE?

 Year 0: -$ 2,000

 Year 1: $ 10,000

 Year 2: -$ 10,000

A)   It has a single IRR of approximately 38 percent.

B)   It has a single IRR of approximately 260 percent.

C)   It has two IRRs of approximately 38 and 260 percent.

D)   No IRRs can be calculated.

The correct answer was C)

The number of IRRs equals the number of changes in the sign of the cash flow. In this case, from negative to positive and then back to negative. Although 38 percent seems appropriate, one should not automatically discount the value of 260 percent.

Check answers by calculation:

10,000/1.38 - 10,000/1.38² = 1995.38

And

10,000/3.6 - 10,000/3.6² = 2006.17

Both discount rates give NPVs of approximately zero and thus, are IRRs.

4．Which of the following statements about NPV and IRR is FALSE?

A)   The NPV will be positive if the IRR is less than the cost of capital.

B)   The IRR can be positive even if the NPV is negative.

C)   The NPV method is not affected by the multiple IRR problem.

D)   When the IRR is equal to the cost of capital, the NPV equals zero.

The correct answer was A)

This statement should read, "The NPV will be positive if the IRR is greater than the cost of capital. The other statements are true. The IRR can be positive (>0), but less than the cost of capital, thus resulting in a negative NPV. The IRR method is affected by the multiple IRR problem. One definition of the IRR is the rate of return for which the NPV of a project is zero.

5．Which of the following statements regarding the internal rate of return (IRR) is most accurate? The IRR:

A)   assumes that the reinvestment rate of the cash flows is the cost of capital.

B)   ignores the time value of money.

C)   and the net present value (NPV) method lead to the same accept/reject decision for independent projects.

D)   can lead to multiple IRR rates if the cash flows extend past the payback period.

The correct answer was C)

NPV and IRR lead to the same decision for independent projects, not necessarily for mutually exclusive projects. IRR assumes that cash flows are reinvested at the IRR rate. IRR does not ignore time value of money (the payback period does), and the investor may find multiple IRRs if there are sign changes after time zero (i.e., negative cash flows after time zero).