$7-22.$ A company is considering the purchase of a capital asset for $$100,000.$ Installation charges needed to make the asset serviceable will total $$30,000.$ The asset will be depreciated over six years using the straight$-$line method and an estimated salvage value $($SV$6)$ of $$10,000.$ The asset will be kept in service for six years, after which it will be sold for $$20,000.$ During its useful life, it is estimated that the asset will produce annual revenues of $$30,000.$ Operating and maintenance $($O&M$)$ costs are estimated to be $$6,000$ in the first year. These O&M costs are projected to increase by $$1,000$ per year each year thereafter. The after tax MARR is $12\%$ and the effective tax rate is $40\%.$

$(7\mathrm{.}9)$

a$.$ Use the tabular format given in Figure $7-5$ to compute the after$-$tax cash flows.

b$.$ Compute the after$-$tax present worth of the project, and use a uniform gradient in your formulation.

c$.$ The before$-$tax present worth of this asset is $$$$50,070.$ By how much would the annual revenues have to increase to make the purchase of this asset justifiable on a before$-$tax basis?