Edwards Manufacturing Company$($EMC$)$ is considering replacing one machine with another. The old machine was purchased $3$ years ago for an installed cost of $$10,000.$ The firm is depreciating the machine under$$ MACRS, using a$5-$year recovery period.$($See table LOADING... for the applicable depreciation$$ percentages.$)$ The new machine costs $$23,700$ and requires $$2,070$ in installation costs. The firm is subject to a $40\%$ tax rate. In each of the following$$ cases, calculate the initial investment for the replacement.

a$.$ EMC sells the old machine for $$11,800.$

b$.$ EMC sells the old machine for $$7,090.$

c$.$ EMC sells the old machine for $$2,900.$

d$.$ EMC sells the old machine for $$1,500.$