To calculate the Internal Rate of Return (IRR) for both Project A and Project B, we need to solve for the rate at which the Net Present Value (NPV) of the cash flows equals zero. The IRR is the rate $r$ such that:

$NPV = \sum \frac{CF_t}{(1 + r)^t} = 0$

Where $CF_t$ represents the cash flows at each time period $t$. For both projects, the initial outlay (at time 0) is negative, representing the investment, and subsequent cash flows represent returns in the following periods.

Project A's cash flows:

• Initial investment ($CF_0$): -1,300
• Year 1 cash flow ($CF_1$): 640
• Year 2 cash flow ($CF_2$): 310
• Year 3 cash flow ($CF_3$): 280
• Year 4 cash flow ($CF_4$): 400

We will calculate the IRR by finding the rate $r$ that satisfies the following equation:

$0 = -1,300 + \frac{640}{(1 + r)} + \frac{310}{(1 + r)^2} + \frac{280}{(1 + r)^3} + \frac{400}{(1 + r)^4}$

Project B's cash flows:

• Initial investment ($CF_0$): -1,300
• Year 1 cash flow ($CF_1$): 240
• Year 2 cash flow ($CF_2$): 245
• Year 3 cash flow ($CF_3$): 430
• Year 4 cash flow ($CF_4$): 850

Similarly, for Project B, we solve for the IRR from the equation:

$0 = -1,300 + \frac{240}{(1 + r)} + \frac{245}{(1 + r)^2} + \frac{430}{(1 + r)^3} + \frac{850}{(1 + r)^4}$

Now, I will calculate both IRRs.It seems I encountered an issue with calculating the IRR using my current environment. Let me try an alternative method to calculate both Project A and Project B's IRRs using the iterative approach based on their cash flows.It seems there are some issues with the tools available for calculating IRR. However, I can guide you through the steps to calculate IRR manually, or if you have access to Excel, you can easily use the IRR function there.

Step-by-Step IRR Calculation Using Excel:

1. Open Excel and in any empty column, input the cash flows:

   • For Project A: -1300, 640, 310, 280, 400
   • For Project B: -1300, 240, 245, 430, 850

2. Use the IRR function:

   • In the cell below the last cash flow, type =IRR(A1:A5) where A1:A5 are the cells containing the cash flows. This will give the IRR for Project A.
   • Similarly, calculate the IRR for Project B by typing =IRR(B1:B5) where B1:B5 contain the respective cash flows.

This will give you the IRRs for both projects.

Would you like to discuss any specific part of the IRR process, or would you like further clarification on any of the concepts? Let me know if you'd prefer an explanation of the IRR formula.