Factory worker al Ghazi Sulaiman was using an emery cloth on a rotating lathe to reduce the size of metal rods when disaster struck at Sankey Laminations in Anchor Lane, Bilston.
The 18-year-old had not been properly trained for the job, Wolverhampton Crown Court heard.
There had been a 'serious and systemic failure' to assess health and safety risk, said Mr Harpreet Sandhu, prosecuting on behalf of the Health and Safety Executive.
He continued: "This had been allowed to persist for several years and it was through luck that no incidents of this magnitude had occurred earlier."
The firm had failed to carry out a risk assessment of the work for three and a half years and did not realise official guidance identifying the dangers of using emery cloth in these circumstances had been issued ten years before Mr Sulaiman was injured on October 15 2014.
The engineering information sheet highlighted the risk of entanglement and warned this method should only be used as a 'last resort'.
"The guidelines were ignored through lack of knowledge, exposing a number of workers to significant risk," said Mr Sandhu.
The firm had a grinder which could have completed the same task with less risk, the court heard.
Mr Sulaiman had been 'encouraged' to use unsuitable gloves which stuck to the emery cloth and four of his fingers had to be amputated after his right hand became trapped.
He now faced the 'humiliation' of requiring help from his family despite having a prosthetic hand. He was unable to drive and had difficulty finding suitable employment, the judge was told.
Sankey Laminations started to use a grinder for the job after the accident.
The tool room had since been closed while the workforce was cut from 130 to 77, the court heard.
Mr Mark Balysz, defending, said: "Their failure fell through the net of an otherwise good health and safety system. It was not highly likely that this incident would occur."
The 67-year-old company, with a 'good but not exemplary' safety record, admitted two charges of failing to obey health and safety regulations