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a project with an initial cost of $30,500 is expected to provide cash flows of $10,650, $11,600, $14,700, and $9,200 over the next four years, respectively. if the required return is 9 percent, what is the project's profitability index?

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The profitability index of the project is 1.34. This means that the project is expected to generate a return of 134% of the initial investment.

To calculate the profitability index (PI) of the project, you need to divide the present value of the future cash flows by the initial cost of the project. The present value of a cash flow is the current value of a future cash flow, taking into account the time value of money.

To find the present value of the cash flows, you can use the following formula:

  • Present value = Future cash flow / (1 + required return)^n

Where "required return" is the required rate of return on the investment and "n" is the number of periods (in this case, years).

Plugging in the values from the question, we can calculate the present value of each of the future cash flows as follows:

  • Year 1: $10,650 / (1 + 0.09)^1 = $9,722.73
  • Year 2: $11,600 / (1 + 0.09)^2 = $10,442.92
  • Year 3: $14,700 / (1 + 0.09)^3 = $12,634.99
  • Year 4: $9,200 / (1 + 0.09)^4 = $8,093.57

The sum of these present values is $40,894.21, which is the present value of the future cash flows.

To find the profitability index, we can then divide this present value by the initial cost of the project:

  • PI = $40,894.21 / $30,500 = 1.34

So, the profitability index of the project is 1.34. This means that the project is expected to generate a return of 134% of the initial investment.

Learn more about The profitability index here:

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