AITC Ltd is considering an investment of $220,000$ on a high$-$tech machine for use in their state of the art polishing department. It is estimated that this machine can be sold on at the end of the period for $40,000.$ AITC Ltd uses a post$-$tax cost of capital of $13\%$ for all investment appraisal purposes.

The below information has been prepared by the management accountant for your consideration:

Year $1$ Year $2$ Year $3$ Year $4$

Savings per annum $000$s $180210230190$

Fixed costs per annum $000$s $32363841$

Variable costs per annum have been calculated as $30\%$ per annum of annual savings, based upon statistical analysis completed by the management accountant.

You have been given the below information also:

$$ Tax allowable depreciation is to be spread evenly over the four years of the project with no allowance for scrap value.

$$ The applicable tax charge is $25\%$ for any relevant taxable cash$-$flows and is charged in the year of the cash$-$flow.

$$ Working capital requirement of $15\%$ of investment is needed in place at the start of the project with no release required.

Required:

a$)$ Calculate the Net Present Value $($NPV$)$ for proposed investment and advise AITC Ltd if they should proceed with this investment.

b$)$ Calculate the Internal Rate of Return $($IRR$)$ for this investment project.