A proposed steel mill may include a co-generation electrical plant. This plant will add $2.6 Million in first cost with a present worth of net annual savings equal to $270,000. The plant will have a $400,000 salvage value after 25 years. the firm uses an interest rate of 12% and present worth index (PWI) in its decision making.

The public utility offers a subsidy for co-generation facilities because it will not have to invest as much in new capacity. This subsidy is calculated as 20% of the co-generation facilities's first cost, but it is paid annually.

a) Is the plant economically justifiable to the firm without the subsidy? what is the PWI?

b) Is the plant economically justifiable to the firm with the subsidy? now, what is the PWI?

Please show a step by step solution.