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Multiple Choice
Given the following set of cash flows: Year 0: \(-\$1,000\), Year 1: \$2,000\), Year 2: \(-\$1,500\), how many possible internal rates of return (IRRs) could exist for this investment?
A
1
B
2
C
3
D
0
Verified step by step guidance
1
Understand the concept of IRR: The Internal Rate of Return (IRR) is the discount rate at which the net present value (NPV) of cash flows equals zero. It is used to evaluate the profitability of an investment.
Recognize the relationship between cash flow sign changes and IRRs: The number of possible IRRs is determined by the number of sign changes in the cash flow sequence. Each sign change represents a potential IRR.
Analyze the cash flow sequence: Year 0 has a cash flow of \\(-\\$1,000\\), which is negative. Year 1 has a cash flow of \\$2,000\\), which is positive. Year 2 has a cash flow of \\(-\\$1,500\\), which is negative. This sequence has two sign changes: from negative to positive (Year 0 to Year 1) and from positive to negative (Year 1 to Year 2).
Apply Descartes' Rule of Signs: According to this rule, the number of possible IRRs is equal to the number of sign changes in the cash flow sequence. Therefore, there are two possible IRRs for this investment.
Conclude the analysis: While there are two possible IRRs, further calculation or graphing would be required to determine their exact values. This step focuses on identifying the number of possible IRRs based on the cash flow pattern.