All Witches is a Halloween decorations manufacturer planning to purchase a new packing machine for $$123,000$ with a useful life of $8$ years and a terminal value of $$10,250$Savings due to the machine are expected to be $$25,500$ per year, however, parts of the machine must be replaced every year, so a working capital investment of $$4,250$ must be maintained. This amount will be recoverable upon disposal. Required rate of return is $8\%.$ All cash flows occur at year$-$end except for the initial investment. Ignore income taxes in your analysis.

Required:

$1.$ Calculate NPV$.$

$2.$ Describe two methods to determine the IRR.

$3.$ Without using the methods in requirement $2,$ state whether the IRR will be lower or higher than $8\%.$ How do you know?

$4.$ Calculate AARR based on net initial investment.