Question

Milson Services purchased an equipment with $1.8 million. The equipment has 6 years of economic life. How much are the annual depreciation costs (using straight - line method and using MACRS mehtod)? MACRS annual tax allowance percentage are: 20%,32%,19%,12%,11%,6%. If the tax rate is 40%, how much are annual tax savings using each method? What is present value of the tax saving under each approach?

(HINT: use 10% Interest Rate)

(For finding the Present Value Please explain how you found those values using a financial calculator)

Answer 1

Straight line method
Annual Depreciation cost under Straight line Method
= (Asset cost - Salvage Value)/ Asset Life
= (1,800,000 - 0) / 6
= $ 300,000 per annum
Annual Tax savings of depreciation under Straight line Method each year upto 6 years
= Depreciation per year x tax rate
= 300,000 X 0.4
= $120,000 per annum
Present value of Tax savings under Straight line Method for 6 years
= Annual Tax savings of depreciation under Straight line Method x Present value of annuity factor for a period of 6 years @ 10 years
= 120,000 x 4.35526069943
= 522631.283931 $

MACRS
Annual Depreciation cost Depreciation under MACRS
= Cost of Asset x MACRS Depreciation Rate
Depreciation under MACRS Year 1 = 1800000 x 20% = 360000
Depreciation under MACRS Year2 = 1800000 x 32% = 576000
Depreciation under MACRS Year3 = 1800000 x 19% = 342000
Depreciation under MACRS Year4 = 1800000 x 12% = 216000
Depreciation under MACRS Year5 = 1800000 x 11% = 198000
Depreciation under MACRS Year6 = 1800000 x 6% = 108000

Annual Tax savings of Depreciation under MACRS
= Cost of Asset x MACRS Depreciation Rate x tax rate
Tax savings of Depreciation under MACRS Year 1 = 1800000 x 20% x 40% = 144000
Tax savings of Depreciation under MACRS Year2 = 1800000 x 32% x 40%= 230400
Tax savings of Depreciation under MACRS Year3 = 1800000 x 19% x 40% = 136800
Tax savings of Depreciation under MACRS Year4 = 1800000 x 12% x 40% = 86400
Tax savings of Depreciation under MACRS Year5 = 1800000 x 11% x 40% = 79200
Tax savings of Depreciation under MACRS Year6 = 1800000 x 6% x 40% = 43200

Present value of Tax savings under Under MACRS Depreciation upto 6 years
Year Tax savings(a) Present value factor @ 10% (b) Present value of tax savings (axb)
1 144000 0.90909090909 130909.090908
2 230400 0.82644628099 190413.22314
3 136800 0.7513148009 102779.864763
4 86400 0.68301345536 59012.3625431
5 79200 0.62092132305 49176.9687855
6 43200 0.56447393004 24385.2737777
Present value of Tax savings under Under MACRS Depreciation upto 6 years = 556676.783916 $

Note :
For finding the Present Value using a financial calculator
Present value factor for n years @ y% = 1 divided by ( 1 + y%)ⁿ
Present value factor for 1 st year @ 10% = 1 divided by (1 + 10%)¹ = 1 / 1.1 = 0.90909090909
Present value factor for 2nd year @ 10% = 1 divided by (1 + 10%)² = 1 / (1.1 x 1.1) = 0.82644628099
Present value factor for 3rd year @ 10% = 1 divided by (1 + 10%)³ = 1 / (1.1 x 1.1 x 1.1) = 0.7513148009
Present value factor for 4th year @ 10% = 1 divided by (1 + 10%)⁴ = 1 / (1.1 x 1.1 x 1.1 x 1.1) = 0.68301345536
Present value factor for 5th year @ 10% = 1 divided by (1 + 10%)⁵ = 1 / (1.1 x 1.1 x 1.1 x 1.1 x 1.1) = 0.62092132305
Present value factor for 6th year @ 10% = 1 divided by (1 + 10%)⁶ = 1 / (1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1) = 0.56447393004
Present value of annuity factor for a period of 6 years @ 10 years
= Present value factor for 1 st year @ 10% + Present value factor for 2 year @ 10% + Present value factor for 3 year @ 10% + Present value factor for 4 year @ 10% + Present value factor for 5 year @ 10% + Present value factor for 6 year @ 10%
= 0.90909090909 + 0.82644628099 + 0.7513148009 + 0.68301345536 + 0.62092132305 + 0.56447393004
= 4.35526069943