$4.(5$ points$)$

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 $\backslash (\backslash$$ $1,000,000\backslash )$ in cash immediately.

$2.$ Pay $\backslash (\backslash$$ $420,000\backslash )$ immediately and the remainder in $10$ annual installments of $\backslash (\backslash$$ $82,000\backslash ),$ with the first installment due in one year.

$3.$ Make $10$ annual installments of $\backslash (\backslash$$ $138,000\backslash )$ with the first payment due immediately.

$4.$ Make one lump$-$sum payment of $\backslash (\backslash$$ $1,520,000\backslash )$ five years from date of purchase.

Required:

Determine the best alternative for Hard Hat, assuming that Hard Hat can borrow funds at an $7\mathrm{.}25\backslash \%$ interest rate. Show inputs you used on your financial calculator for possible partial credit if you answer is wrong.