PS Ltd is a company incorporated in Singapore and prepares its financial accounts based on the Singapore Financial Reporting Standards. On its balance sheet sits a factory plant carried at $$3$ billion as at $31$ December $20$X$1.$ In January $20$X$2,$ due to the falling demand for the products of the plant, the net cash inflows in the next five years is $$300$ million a year. At the end of the fifth year, the plant should have a value of $$2$ billion. A similar plant was disposed of last month with net proceeds of $$2$ billion. The pre$-$tax discount rate of the firm is $5\%.$ Determine the impairment loss, if any, that should be recognised by PS Ltd on the plant.