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:$1.$ Pay $$1,000,000$ in cash immediately$\mathrm{.}2.$ Pay $$420,000$ immediately and the remainder in $10$ annual installments of $$82,000,$ with the first installment due in one year$\mathrm{.}3.$ Make $10$ annual installments of $$138,000$ with the first payment due immediately$\mathrm{.}4.$ Make one lump$-$sum payment of $$1,520,000$ five years from date of purchase.Required:Determine the best alternative for Hard Hat, assuming that Hard Hat can borrow funds at an $7\mathrm{.}75\%$ interest rate. Show inputs you used on your financial calculator for possible partial credit if you answer is wrong.