AB plc is considering a new product with a three$-$year life. The product can be made with existing machinery, which has spare capacity, or by a labour saving specialised new machine which would have zero disposal value at the end of three years.

The following estimates have been made at current prices.

Sales volume $1$ million units per annum

Selling price $$15$ per unit

Labour costs $($without new machine$)$ $$6$ per unit

Material cost $$2$ per unit

Variable overheads $$2$ per unit

Additional fixed overheads for the new product are estimated to be $$3$ million per year.

The new machine would cost $$5$ million now and would halve the labour cost per unit.

Because of competition, selling price increases will be limited to $2\%$ per annum, although labour cost is expected to rise at $12\%$ per annum and all other costs at $8\%$ per annum.

The company's money cost of capital is $15\%$ and, apart from the cost of the new machine, all other cashflows can be assumed to arise at year ends.

$($a$)$ Calculate the NPV of the new product assuming that manufacture uses existing machinery.

$($b$)$ Calculate the NPV assuming that the new machine is purchased.

$($c$)$ Recommend what action should be taken, and comment on your recommendations