Have another coffee,
It really depends on what the airline is trying to achieve and the regulatory requirements, if that goal is to gain the highest takeoff weight, then you might have a straight out departure based upon the Type A aerodrome chart.
If you elect to ignore the straight out departure and follow the SID, then the only protection that you are offered is based on your own assessment of the aircrafts ability to meet the required climb gradient.
Old_smokey and J_T show us all how the OEI assessment should be conducted in an ideal world, however within airlines due to monetary constraints, attitudes or just a pure lack of knowledge, their ideal world doesn’t always exist.
In the FAA world, we do not assess all SIDS, we provide either a straight out departure or a specific engine failure procedure.
Mutt.