A company's valuation is based on discounted expected future earnings. With bitpay you have to look at how much will they be earning next year, then the next, then the next? We already know that their revenues grew 10x last year. We've also heard that BitPay is presently making buckets of profit. Bitcoin hasn't even began to hit consumer adoption yet, so if the trend continues then there should be many years worth of exponential growth with a high profit margin.
Exactly. Some numbers:
Bitpay processes about 500m a year. Their revenue is probably about 0.75% of that, or say roughly 4m.
They have 40k merchants now and they add more than 1k every week. They growth is about 10% monthly, or 3x annually.
In other words, if you imagine their growth rate continues for 5 years, their revenues are 4m, 12m, 36m, 108m, 324m.
Then add another 5 years of slower growth, and apply a discount rate to that. It's quite easy to see why a 160m valuation isn't ridiculous at all.