We must decide between purchasing an automatic machine that costs \(\$ 100,000\) and will last 10 years and have a zero salvage value, or purchasing a manual machine that costs \(\$ 40,000\) and will last 5 years and have a zero salvage value. If we purchase the manual machine initially, after 5 years we must decide between a manual machine having the same characteristics as the first machine and a semiautomatic machine costing \(\$ 80,000\) that would have a \(\$ 40,000\) salvage value after 5 years of life. The annual operating costs for each of the machines are automatic, \(\$ 20,000 /\) year; manual \(\$ 28,000 /\) year; semiautomatic, \(\$ 22,000 /\) year.

a. Draw a decision tree to represent this situation.

b. Using a PW method with a MARR of 10 percent, determine what decisions should be made.