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:

Pay $$1,000,000$ in cash immediately.

Pay $$420,000$ immediately and the remainder in $10$ annual installments of $$80,000,$ with the first installment due in one year.

Make $10$ annual installments of $$135,000$ with the first payment due immediately.

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.