Hard Hat Company is in the process of purchasing several large pieces of equipment from Machine Corporation. Several financing alternatives have been offered by Machine:$3\mathrm{.}88804$:$01$:$151.$ Pay $$1,000,000$ in cash immediately$\mathrm{.}2.$ Pay $$420,000$ immediately and the remainder in $10$ annual installments of $$80,000,$ with the first installment due in one year$\mathrm{.}3.$ Make $10$ annual installments of $$135,000$ with the first payment due immediately$\mathrm{.}4.$ Make one lump$-$sum payment of $$1,500,000$ five years from date of purchase.Required:Determine the best alternative for Hard Hat, assuming that Hard Hat can borrow funds at an $8\%$ interest rate.Note: Round your final answers to nearest whole dollar amount. Use tables, Excel, or a financial calculator. $($FV of $$1,$ PV of $$1,$ FVA of $$1,$ PVA of $$1,$ FVAD of $$1$ and PVAD of $$1)$PV