Payback comparisons Nova Products has a $6-$year maximum acceptable payback period. The firm is considering the purchase of a new machine and must choose between two alternatives. Th first machine requires an initial investment of $$51,000$ and generates annual cash inflows of $$9,000$ for each of the next $9$ years. The second machine requires an initial investment of $$29,000$ and provides an annual cash inflow of $$5,000$ for $30$ years.

a$.$ Determine the payback period for each machine.

b$.$ Comment on the acceptability of the machines, assuming that they are independent projects.

c$.$ Which machine should the firm buy? Why?

d$.$ Does this problem illustrate any of the payback method's weaknesses?

a$.$ The payback period for the first machine is years. $($Round to two decimal places.$)$