A company is considering an investment in new machinery. The annual incremental profits$/($losses$)$ relating to the investment are estimated to be:

Year $1$ TZS $(11,000)$

Year $2$ TZS $3,000$

Year $3$ TZS $34,000$

Year $4$ TZS $47,000$

Year $5$ TZS $8,000$

Investment at the start of the project would be TZS $175,000.$ The investment sum, assuming nil disposal value after five years, would be written off using the straight$-$line method. The depreciation has been included in the profit estimates above, which should be assumed to arise at each year end.

Required:

a$)$ Calculate the net present value $($NPV$)$ of the investment at a discount rate of $10\%$ per annum $($the company$$s required rate of return$).$

Discount factors at $10\%$ are:

Year $10\mathrm{.}909$

Year $20\mathrm{.}826$

Year $30\mathrm{.}751$

Year $40\mathrm{.}683$

Year $50\mathrm{.}621$

b$)$ State, on the basis of your calculations, whether the investment is worthwhile. Justify your statement.