1.What are the pros and cons of the decision rules for the NPV, the IRR, the MIRR, and the payback methods? Which is the most accurate method and why?

The Net Present Value (NPV) is maybe the most commonly used technique for evaluating a potential investment opportunity. Using this technique all cash flows in a business case at the opportunity cost of capital. The pros- accounts for the fat that the value of a dollar today is more than the value of a dollar received a year from now- that is the time of money concept. Another pro is that is that it recognizes the risk associated with future cash flow, its less certain. Cons- is that it does not give visibility into how long a project will take to generate a positive (NPV) due to the calculations simplicity. One other drawback is that the model assumes that capital is abundant- that there is no capital rationing.

The Internal Rate of Return (IRR) or discounted cash flow rate of return gives analysts a way to quantify the rate of return provided by the investment. The internal rate of return is defined as the discount rate where the (NPV) 0f cash flows are equal to zero. The pros- is mainly accepted in the finances as a quantified measure of return and it’s also based on discounted cash flows- so accounts for the time value of money. When it is used correctly it can provide excellent guidance on a project’s value and associated risk. Cons- There are three, one is multiple or no rates of return, two changes in discount rates and three IRRs do not add up.
The Modified Internal Rate of Return (MIRR) assumes that positive cash flows are reinvested at the firm’s cost of capital, and the initial outlays are financed at the firm’s financing cost. Therefore, MIRR more accurately reflects the cost and profitability of a project. Cons-the MIRR overcomes the reinvestment assumption of IRR and serves as a much better metric for ranking projects. The cons of MIRR are that it requires two inputs not required by IRR: the reinvestment rate and the finance rate. But the result is far more meaningful. It allows comparisons among projects with widely different patterns of cash flows.
The Payback Method will allow a company to see how rapidly a project returns the initial investment back to the company. In general companies establish rules around payback when evaluating a project. Pros- it will allow for an easy understanding by management and stakeholders of when the initial investment will be recovered. Cons- It does not take into account the time value of money. Discounted cash flow should be the preferred way to evaluate payback since it does recognize the time value of money.
Conclusion
Even though the (NPV) and (IRR) methods yield better decision making data based on them being leading edge capital budgeting techniques, the payback method is not without reason. The payback method is a quick and easy way to filter a project to see if the time should be spent to further analyze whether the project should move forward. The (NPV) and (IRR) methods both give good accept reject results. Nevertheless, (IRR) is the preferred method by most since its results are portrayed in rates of return, which most financial managers see as illustrative across the board.

Sunk costs are costs that have already been incurred without prospect. Because they are in the past they cannot be changed by the decision to accept or reject the project. Sunk costs are not incremental cash outflows.
Pertinent cash flows are inflows and outflows of cash whose inclusion or exclusion from investment appraisal can affect the overall investment decision. Which means that finance or funds have already been committed will not be considered while performing your capital budgeting. Once the company incurred the expense, the cost became irrelevant for any future decision.

References
Brigham, E. F., & Houston, D. J. F. (2014). Fundamentals of Financial Management, Concise Edition (with Thomson ONE – Business School Edition 6-Month Printed Access Card), 8th Edition. [VitalSource Bookshelf version]. Retrieved from http://digitalbookshelf.southuniversity.edu/books/9781305217218/outline/12
Benefits Realization and Business Cases. Retrieved from http://benefitsrealization.blogspot.com