CFA® Level 1: Projects with Multiple Internal Rates of Return

Projects with Multiple Internal Rates of Return

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Question

Which of the following projects would likely result in multiple Internal Rates of Return?

Project A -

Initial investment outlay: ($450,000)

t1: $400,000

t2: ($40,000)

t3: $190,000

Project B -

Initial investment outlay: ($50,000)

t1: $0.00

t2: $0.00

t3: $75,000

Project C -

Initial investment outlay: ($300,000)

t1: $15,000

t2: ($34,000)

t3: $0.00

t4: $400,000

Project D -

Initial investment outlay: ($100,000)

t1: $150,000

t2: $380,000

t3: $45,000

t4: $45,000

Project E -

Initial investment outlay: ($1,000,000)

t1: $1,500,000

t2: $1,300

t3: $0.00

t4: $60,000

Answers

Explanations

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A. B. C. D. E. F.

E

In evaluating projects with "non-normal cash flows" the Internal Rate of Return method will often produce multiple IRRs which leads to an incorrect accept/reject decision. Non-normal cash flows are defined as cash flows in which the sign changes more than once. Projects A, and C involve cash outflows superimposed within their cash inflows, resulting in a sign change from positive to negative and negative to positive. In examining projects such as these, it is advisable to use either the NPV or MIRR methods, which are not subject to the problem of multiple IRRs. From observation alone, we can determine that project A and C are non- normal projects, and are thus likely to result in multiple IRR calculations. While project B, D, and E have periods of zero cash flow, they have only one change of sign in the overall cash flow process, and therefore should be characterized as "normal." While the cost of capital has been provided, it is not necessary for the determination of the correct answer in this case. What you should look for are projects with non-normal cash flows, and this should not involve any computational analysis. Besides, the cost of capital is not incorporated into the Internal Rate of Return calculation, rather is a component of the NPV and MIRR.