In case, the projects are divided under capital rationing an appropriate project appraisal method is

Net present value method
Profitability index method
Internal rate of return method
Payback period method

The correct answer is: A. Net present value method.

The net present value (NPV) method is a capital budgeting method that calculates the present value of all future cash flows (both positive and negative) of a project and compares it to the initial investment. A project is considered to be financially feasible if the NPV is positive.

The NPV method is a more accurate method of project appraisal than the payback period method or the internal rate of return method because it takes into account the time value of money. The time value of money is the concept that a dollar today is worth more than a dollar tomorrow because you can invest the dollar today and earn interest on it.

The payback period method is a capital budgeting method that calculates the number of years it takes for a project to recover its initial investment. A project is considered to be financially feasible if the payback period is less than the company’s required payback period.

The payback period method is a simple and easy-to-understand method of project appraisal, but it is not as accurate as the NPV method because it does not take into account the time value of money.

The internal rate of return (IRR) method is a capital budgeting method that calculates the rate of return that a project will generate. A project is considered to be financially feasible if the IRR is greater than the company’s required rate of return.

The IRR method is a more accurate method of project appraisal than the payback period method, but it is more complex to calculate.

In case, the projects are divided under capital rationing, an appropriate project appraisal method is the NPV method. This is because the NPV method takes into account the time value of money and allows for the comparison of projects with different cash flow patterns.