b$)$ Codent Ltd wishes to evaluate an investment in machinery used in manufacturing a new type of solar heating system. This Solar$-$heating would help to address the increasing demand for eco$-$friendly heating systems in housing and business sectors$.$ Codent Ltd is not sure which Machine to invest in$.$ They have the option to choose from $3$ different machines. The life of the machines and the purchase prices are as follows.

Machine A Machine B Machine C

Initial investment $()300,000360,000510,000$

Life of the machine $4$ years $5$ years $3$ years

In each case the initial investment represents the purchase of plant and equipment whose residual value will be $20\%$ of initial cost, receivable in addition to the net operating cash flow, at the end of the life of the project. Forecast sales volume, selling price and other costs are as follows;

Sales volume $($units$/$year$)$ Selling price per unit $()$ Variable cost per unit $()$ Fixed cost per annum $()$

Machine A $5001,20072080,000$

Machine B $4501,20065080,000$

Machine C $6501,200570130,000$

Machines B and C have only recently been introduced to the market and have not been fully tested in operating conditions. Because of the higher risk involved, the appropriate discount factor for machines B and C is believed to $12\%$ per year, $2\%$ higher than the discount rate for Machine A$.$

Requirement

For each of the three projects:

I. Calculate the accounting rate of return $($based on the average investment method$).$

II$.$ Calculate the payback period.

III. Calculate the net present value.