A firm is considering a project that requires an initial outlay of £65,000. It will have a life of 6 years. It will generate free cash flows of £10,000 in years 1 – 4 and £20,000 in years 5 and 6. The firm has a cost of capital of 8%.Using Internal Rate of Return (IRR), should it accept or reject this project?

To determine whether the firm should accept or reject the project using the Internal Rate of Return (IRR), we first need to calculate the IRR. The IRR is the discount rate that makes the Net Present Value (NPV) of a project zero.

Here are the steps to calculate the IRR:

1. Identify the cash flows: The initial outlay is £65,000 (which is an outflow so we consider it as negative) and the inflows are £10,000 for years 1-4 and £20,000 for years 5 and 6.

2. Set up the equation for NPV and set it equal to zero. The general formula for NPV is:

   NPV = ∑ [Cash inflow / (1 + r)^n] - Initial outlay

   Where: r = discount rate (which is the IRR in this case) n = year

   So, the equation becomes:

   0 = -£65,000 + £10,000/(1+IRR) + £10,000/(1+IRR)^2 + £10,000/(1+IRR)^3 + £10,000/(1+IRR)^4 + £20,000/(1+IRR)^5 + £20,000/(1+IRR)^6

3. Solve the equation for IRR. This is typically done using a financial calculator or software as it involves solving a polynomial equation.

If the IRR is greater than the cost of capital (8% in this case), the project should be accepted. If it's less, the project should be rejected.

Please note that this is a simplified explanation and actual business decisions should take into account other factors as well.