Calculate time to commute from home to office, add fuel, add car payments; add insurance; taking the pay-cut makes sense.
I don't think that's accurate. You're losing money, but reducing your expenditures. End result is you may be taking a
smaller pay cut than intended. However, that's still a pay cut.
I'd propose an alternative. Let me work from home, and don't give me a raise for one year. Let work from home, and the savings from that, be my raise.
Totally worth it, and in certain circumstances, doing that could be a bigger raise than what I would've been expecting anyways.