A bulldozer with purchase price of $N4,500,000\mathrm{.}00$ is estimated to eliminate manual operations costing $N1,100,000\mathrm{.}00$ per year. The machine will last for $5$ years with a residual value of N$600,000\mathrm{.}00$ at the end of its life. You are required to calculate:

$($a$)$ The discount cash flow $($i$.$e$.$ the internal rate of return$).$

$($b$)$ The net present value $($NPV$)$ if the cost of capital is $10\%.$