Firstly, Average accounting return (AAR) is calculated by dividing the average net income by the average book value. A project is accepted if the AAR is greater than a preset rate. However, the discount rate value of money is ignored. Also, it uses accounting earnings which include net income and book value of an investment. In capital budgeting, we use cash flow instead of accounting earning because it is more accurate in calculating budget. Also, the accounting numbers are arbitrary, for example, net income includes depreciation expense which is not an actual payment for every year.
Payback period has a disadvantage that it does not discount the amount in future back to present time. Even Discounted Payback Period uses the discount rate, these two methods only calculate the time period required for to recover the initial investment. After calculating the required time period, the cash flow after that period will be totally ignored. Therefore, it would be a disadvantage for Payback period and Discounted Payback Period because the amounts after payback period do matter in some aspects.
Only Internal Rate of Return (IRR), Profitability Index (PI) and Net Present Value (NPV) use all cash flow and discount value.