IRR Calculation for Net Cash Flows

D

Time line:

0123 Periods

1,520-1,000-1,500500

Financial calculator solution: Using cash flows,

Inputs: CF(0) = 1,520; CF(1) = -1,000; CF(2) = -1,500; CF(3) = 500.

Output: IRR% = 23.98%.

To determine the Internal Rate of Return (IRR) of the project, we need to find the discount rate that equates the present value of the net cash flows to zero. The IRR is the rate at which the project's net present value (NPV) is zero.

Here are the given net cash flows for the project:

Time 0: -$1,520 Time 1: -$1,000 Time 2: -$1,500 Time 3: -$500

To calculate the IRR, we will set up the following equation and solve for the discount rate (IRR):

0 = -1,520 / (1 + IRR)^0 - 1,000 / (1 + IRR)^1 - 1,500 / (1 + IRR)^2 - 500 / (1 + IRR)^3

To solve this equation, we can use the trial and error method, or we can use financial calculators or spreadsheet software that have built-in IRR functions. Let's use trial and error for this example.

Using the trial and error method, we will try different discount rates until we find the rate that makes the equation equal to zero.

Let's start with answer choice A: 36%. We substitute 0.36 for IRR in the equation:

0 = -1,520 / (1 + 0.36)^0 - 1,000 / (1 + 0.36)^1 - 1,500 / (1 + 0.36)^2 - 500 / (1 + 0.36)^3

Simplifying the equation gives us:

0 = -1,520 - 1,000 / 1.36 - 1,500 / 1.36^2 - 500 / 1.36^3

Calculating further:

0 = -1,520 - 735.29 - 825.03 - 278.71