Hi @smallcapvaluefind, below are my observations on your approach.
First things first, I am no banking expert, so take what I say with a pinch of salt 
I see that your approach hinges on two basic assumptions:
- NPA and PE/PB are inversely proportional
- These are the most important metrics to gauge the fair value of the bank
Thoughts on assumption 1: While that may be true, they are not linearly proportional. For example, Bank A with a PE of 10 and an NPA of 2% is much better off as far as I am concerned than Bank B with a PE of 5 and an NPA of 4%. The element if increased risk outwights the lower valuation. And so I don’t take Karnataka Bank into consideration at all as there is a high risk of permanent loss of capital.
Thoughts on assumption 2: While PE/PB are important metrics, the market values banks primarily on their future earnings growth. And to grow earnings in the future, the banks need to do to things - increase advances and reduce costs.
In the last four years (FY 17 to FY 20), Federal Bank has increased advances at 26%, 25%, 20% and 12% YoY. DCB Bank has increased advances at 22%, 28.5%, 16% and 7.5%. So Federal Bank seems to be the more aggressive bank in terms of increasing the top line.
Now on the cost front, the CASA ratio plays a big role in reducing the cost of borrowing. which is usually the biggest cost for banks. The CASA ratio for Federal Bank for FY 20 was 30.7% while CASA for DCB Bank was 21.5%. This is reflected in the cost of liabilities as well which is lower for Federal Bank than for DCB Bank. So on these parameters Federal is a clear winner.
However, inspite of having higher advances and lower cost of liabilities, Federal has lower NIMs and yields than DCB Bank. And this is primarily because Federal has higher NPAs. And this strain on profitability because of NPAs becomes even more important in these times of uncertainty.
This is why DCB Bank is definitely a better bet than Federal Bank at the moment in my view.