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.