You can mine on worse machines if you have lower power costs or are valuing the BTC higher than the electricity costs (ie you're long/bullish on BTC or you're doing it somewhat altruistically or alternatively not doing the math on how much it's costing.)
> I'm not sure how that would assuage the risk [averse] accountant
If the accountant's salary depends on being assuaged, this should hardly be a problem: the accountant will then just tell you that he does not believe this to be a good idea, and give reasons for his judgement.