Question

Your firm is considering a project that would require purchasing $7.8 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 10% 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

Solution:

Depreciation tax shield=Depreciation*tax rate

a)Annual depreciation=Cost/life

=$7800,000/10 years

=$780,000

Depreciation tax shield for each year=$780,000*20%=$156000

Present value of Tax shield=Depreciation tax shield for each year*Present value annuity factor for 10 years @10%

=$156000*6.145

=$958,620

b)Annual depreciation=$7800,000/5 years

=$1560,000

Depreciation tax shield for each year=$1560,000*20%=$312,000

Present value of tax shield=$312,000*Present value annuity factor for 5 years @10%

=$312,000*3.791

  =$1182,792

c)Statement showing present value of the depreciation tax shield

Since the depreciation is starting immediately,thus year1 depreciation is depreciation at year 0 and so on.   

Year	Depreciation(a)	Tax shield(a*tax rate)	Present value factor@10%	Present value of tax shield
1	$7800,000*20%=$1560,000	$312,000	1	$312,000
2	$7800,000*32%=$2496,000	$499,200	0.909	$453772.80
3	$7800,000*19.20%=$1497,600	$299,520	0.826	$247,403.52
4	$7800,000*11.52%=$898,560	$179,712	0.751	$134,963.71
5	$7800,000*11.52%=$898,560	$179,712	0.683	$122,743.30
6	$7800,000*5.76%=$449,280	$89,856	0.621	$55800.58
Present value of tax shield	$1326,684.00

d)Depreciation=100% of cost in first year

=$7800,000

Tax shield=$7800,000*20%=$1560,000

Present value of tax shield=$1560,000/(1+0.10)

=$1418,181.82