Your firm is considering a project that would require purchasing

$$$$7\mathrm{.}57\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

$20\%20\%$

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

$5\%5\%$

for all maturities.

a$.$ Straight$-$line over a

$1010-$year

$$period$,$ with the first deduction starting in one year.

b$.$ Straight$-$line over a

$55-$year

$$period$,$ with the first deduction starting in one year.

c$.$ Using MACRS depreciation with a

$55-$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$).$