Question

XYZ is evaluating a project that would require an initial investment of $74,600.00 today. The project is expected to produce annual cash flows of $9,000.00 each year forever with the first annual cash flow expected in 1 year. The NPV of the project is $7,500.00. What is the IRR of the project?

A.10.96% (plus or minus 0.02 percentage points)
B.12.06% (plus or minus 0.02 percentage points)
C.10.05% (plus or minus 0.02 percentage points)
D.13.41% (plus or minus 0.02 percentage points)
E.None of the above is within 0.02 percentage points of the correct answer

Answer 1

The IRR of the project with an initial investment of $74,600 and perpetual annual cash flows of $9,000, with an NPV of $7,500, is approximately 10.96%, matching option A: 10.96% (plus or minus 0.02 percentage points).

Step-by-step explanation:

The internal rate of return (IRR) of a project is the interest rate at which the net present value (NPV) of all the cash flows (both positive and negative) from a project or investment equal zero. In this case, we are given an investment with perpetual annual cash flows, which means this project is essentially an example of a perpetuity. The formula for the present value of a perpetuity is given by Present Value (PV) = Annual Cash Flow / IRR. Using this formula, since the NPV is $7,500 and the initial investment is $74,600, we can express the NPV equation as follows: NPV = Present Value of perpetual cash flows - initial investment, or $7,500 = ($9,000 / IRR) - $74,600.

Solving for the IRR, we get IRR = $9,000 / ($74,600 + $7,500), which equals to $9,000 / $82,100. This results in an IRR of approximately 10.96%, which corresponds to option A: 10.96% (plus or minus 0.02 percentage points).