Question

Your firm is considering a project that would require purchasing $7.5 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 8% 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).

Answer 1

PV of depreciation tax shield = sum of PVs of depreciation tax shields of each year

Depreciation tax shield = depreciation amount * tax rate

PV of each year's depreciation tax shield = depreciation tax shield / (1 + cost of capital)n

where n = number of years after which the depreciation tax shield occurs

a]

Depreciation in each year = cost of equipment / depreciable life in years

$1,197,813

b]

Depreciation in each year = cost of equipment / depreciable life in years

$1,006,512

c]

Depreciation in each year = cost of equipment * depreciate rate for the year

The depreciate rate for each year is taken from the MACRS tables for 5-year life

$1,314,348

d]

The entire cost is depreciated immediately in year 0

$1,500,000

The calculations are below

The calculations are below

The calculations are above

The calculations are above