XYZ Company Limited has decided to sell a new line of product. The company will sell the new product for $$330/$unit with a variable cost of $$280/$unit$.$ The projected demand for Year #$1$ is expected to be $5,000$ and this is expected to increase by $1,000$ units every year for the next $6$ years. However due to the new product, the existing product is expected to decline in sales by $1,500$ units each year for the next $6$ years. The sale price $/$unit for the existing unit is $$160$ with variable cost of $$100/$unit$.$

The initial project investment cost is expected to be $$600,000$ for purchase of new machine and installation cost of $$100,000.$ The new machine is expected to be depreciated using straight line method over the $6$ year period with a salvage value of $$100,000.$ Applicable tax rate is $20\%$ with company$$s cost of capital of $12\mathrm{.}5\%.$

Note:

The sale price for new product is expected to increase by $$10$ every year while variable cost will increase by $$5.$

$($ii$)$ Due to competitive pressure, there will be no change for existing product.

Required

$($a$)$ Calculate the discounted payback for the above project.

$($b$)$ Evaluate the new project using NPV criteria.

$($c$)$ Determine the benefit cost ratio $($BCR$).$

$($d$)$ Identify the ROI and IRR

$($e$)$ Using above criteria, summarize the result and advice the management accordingly.