Calculate the net present value for the machine

Annacott Pty Ltd is considering purchasing a new machine to alleviate a bottleneck in its production facilities. At present, it uses an old machine that can process 8,000 units of Product X per week. The company could replace it with machine YZ, which is product-specific and is able to produce 20,000 units per week. Machine YZ costs $500,000. Removing the old machine and preparing the area for machine YZ would cost $20,000.

The company expects demand for Product X to be 12,000 units per week for another three years. After this, in the fourth year, the new machine would be sold for $50,000. This sale is not expected to take place until later in the fourth year. The existing machine would have no scrap value. Each Product X sells for $7.00 and has a contribution to sales ratio of 0.2. The company works for 48 weeks in the year. Normally, the company expects a payback within two years and its after-tax cost of capital is 10% per annum.

Moreover, the company pays corporation tax at 30% and receives writing-down allowances of 25%, reducing balance on the investment and any costs incurred in removing the old machine and installing the new machine. Corporation tax is payable one year in arrears.

Question:

1. Calculate the net present value for the machine.

2. Recommend, with reasons, whether the machine should be purchased.