Finding the Approximate External Rate of Return for a Project

What is the project's approximate external rate of return if the initial cost is $50,000, net annual cash inflows are $20,000, salvage value after five years is $2,000, and the Minimum Acceptable Rate of Return (MARR) is 10 percent?

The project's approximate external rate of return is calculated using the equation: \[ -50,000(F/P, i, 5) + 20,000(P/A, i*, 5) + 2,000 = 0 \] The correct answer is Option D: To find the project's approximate external rate of return (i*), we need to set the equation equal to zero and solve for i*. The equation represents the present worth of the cash flows associated with the project. In this case, the initial cost of the project is -$50,000 (negative because it's an outflow), the net annual cash inflows are $20,000, and the salvage value after five years is $2,000. We use the present worth factor (P/F) and the future worth factor (F/P) to discount and compound the cash flows over time. By substituting the values into the equation and solving for i*, we can determine the approximate external rate of return that makes the equation hold true. The given MARR (Minimum Acceptable Rate of Return) of 10% is not directly used in the equation. The solution to the equation will provide the value of i*, which represents the approximate external rate of return for the project. This rate indicates the percentage at which the project's cash inflows are discounted to balance the equation and achieve a present worth of zero. It's worth noting that the solution to this equation will be an approximation since it assumes a constant rate of return over the project's duration.

Understanding the Calculations

Initial Cost: The project has an initial cost of $50,000, which is considered a negative value as it represents an outflow of cash at the beginning of the project. Net Annual Cash Inflows: The project generates net annual cash inflows of $20,000, representing the positive cash flow received each year. Salvage Value: After five years, the project has a salvage value of $2,000, which is the estimated residual value of the project at the end of its useful life.

Application of Present Worth and Future Worth Factors

By utilizing the present worth factor (P/F) and future worth factor (F/P), we can discount and compound the cash flows to determine the project's external rate of return. Present Worth Factor (P/F): This factor is used to discount future cash flows to their present value at a specified interest rate over a given time period. Future Worth Factor (F/P): It is utilized to compound present cash flows to their future value at a specific interest rate over a certain duration.

Significance of MARR

The Minimum Acceptable Rate of Return (MARR) of 10% provides a benchmark for evaluating the profitability of the project. However, it is not directly incorporated into the external rate of return calculation but serves as a reference point for determining the project's viability.
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