Davis Pizza is analyzing the prospect of purchasing an additional fire$-$brick oven. The oven costs $$200,000$ and would be depreciated straight$-$line to a salvage value of $$120,000$ in ten years. The extra oven would increase annual revenue by $$120,000$ and annual operating expenses by $$90,000.$ Davis$$ marginal tax rate is $40\%.$ Show your calculations.

A$.$What would be the annual free$-$cash flow generated by the new oven?

$(120,00090,000)*(0\mathrm{.}6)(200,000/10)$

$30,000*0\mathrm{.}620,000$

$18,00020,000=-$$$2000$

B$.$What is the payback period for the additional oven?

$200,000/18,000=$ payback period of $11\mathrm{.}11$ years

C$.$Suppose the required rate of return is $12\%,$ what is the net present value of the additional oven?

NPV $=$ cash flow $/(1+$r$)^$ t $-$ Initial investment

$=$ $$22,419\mathrm{.}24-$ $$200,000$

NPV $=-$$$177,580\mathrm{.}76$

D$.$What is the profitability index for the additional oven?

$(-$$$177,580\mathrm{.}76+200,000)/200,000$

$22,419\mathrm{.}24/200,000$

$=$ profitability index of $0\mathrm{.}1121$

E$.$What is the internal rate of return of the additional oven? ONLY NEED THIS PART ANSWERED PLEASE SHOW WORK WITHOUT EXCEL