Answer:
If both firms have a lot of depreciable fixed assets, using the MACRS depreciation schedule or some other type of accelerated depreciation method will increase their expenses during the first years resulting in lower operating income. This situation reverses in the later years when the depreciation expense becomes much lower, resulting in higher operating income. On the other hand, using straight line depreciation makes your depreciation expense more stable and sometimes even more realistic.
Companies use MACRS depreciation to lower their tax liabilities by lowering their income. Remember that $1 saved today is worth more than $1 saved tomorrow.
In this case, Rogers Corporation might yield a lower income during the first years that it depreciates its assets, but then it will show much higher income (during the last years). Peyton Corporation should show more stable income.