Your firm is considering a project that would require purchasing $ $7\mathrm{.}5$ million worth of new equipment. Determine the present value of the depreciation tax shield associated with this equipment if the$$ firm's tax rate is $20\%$ using the alternative depreciation methods below. Note that because the depreciation tax shield is essentially a riskless cash flow$($assuming the$$ firm's tax rate remains$$ constant$),$ the appropriate cost of capital to evaluate the benefit from accelerated depreciation is the$$ risk$-$free rate; assume this rate is $5\%$ for all maturities.

a$.$ Straight$-$line over a$10-$year period, with the first deduction starting in one year.

b$.$ Straight$-$line over a$$ five$-$year period, with the first deduction starting in one year.

c$.$ Using MACRS depreciation with a$$ five$-$year recovery period and starting immediately.

d$.100\%$ bonus depreciation$($all the depreciation expense occurs when the asset is put into$$ use, in this case$$ immediately$).$

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