This is Rohin speaking through Vegan. I lost my login details.
You should use average equity rather than equity at the beginning of the year.
We might be increasing our equity during the year and hence in order to calculate the true value of the return generated from the equity available, it would make sense to calculate the return based on the average equity available. More complicated methods would be to use Simpsons rule to approximate the average equity. Jokes... just take the simple arithmetic average.
Year 2 ROE = 134/(0.5*(273+318)) = 0.45