Premium Pie Company needs to purchase a new baking oven to replace an older oven that requires too much energy to run. The industrial size oven will cost $$1,200,000.$ The oven will be depreciated on a straight$-$line basis over its six$-$year useful life. The old oven cost the company $$800,000$ just four years ago. The old oven is being depreciated on a straight$-$line basis over its expected ten$-$year useful life. $($That is$,$ the old oven is expected to last six more years if it is not replaced now.$)$ Due to changes in fuel costs, the old oven may only be sold today for $$100,000.$ The new oven will allow the company to expand, increasing sales by $$300,000$ per year. Expenses will also decrease by $$50,000$ per year due to the more energy efficient design of the new oven. Premium Pie Company is in the $40\%$ marginal tax bracket and has a required rate of return of $10\%.$

a$.$ Calculate the net present value and internal rate of return of replacing the existing machine

b$.$ Explain the impact on NPV of the following:

i$.$ Required rate of return increases

ii$.$ Operating costs of new machine are increased

iii. Existing machine sold for less