Does a dividend of $1 in year 1 or a dividend of $2 in year 3 increase IRR more, assuming entry equity of $20 and exit equity of $60 over 5 years?

An exit equity of $60 vs. an entry equity of $20 is a 3x multiple of capital ($60 / $20). Over 5 years, a 3x multiple of capital is a 25% IRR.

Dividends are assumed to be reinvested at the IRR. Reinvesting $1 in year 1 at 25% IRR for 2 years would get us $1 x 1.25^2, which is below $2. Therefore, receiving a $2 dividend in year 3 would increase IRR more than a $1 dividend in year 1.