The percentages in MACRS GDS for personal property were calculated based on the

Question

The percentages in MACRS GDS for personal property were calculated based on the following principles:
• The 3-, 5-, 7- and 10-year classes use 200% and the 15- and 20-year classes use 150% declining balance depreciation.
• All classes convert to straight-line depreciation in the optimal year, shown with the asterisk (*).
• A half-year of depreciation is allowed in the first and last recovery years.
• Salvage value are assumed to be zero for all assets.
If the 15- and 20-year classes also use 200% declining balance depreciation, what would be the depreciation schedule for the 15- and 20-year classes?

Explanation / Answer

The year classes define the life period of class.

i.e, a 3 year class has life period of 3 years.

Depreciation = Annual depreciating rate * book value at beginning of year.

When you are using 200 % Declining depreciation,

Annual Declining Depreciation = 200 * Depreciation rate from straight line method/100

In straight line method, it is assumed that depreciation is constant in each year.

depreciation rate in straight line method = 1/life period *100

For 15 year Class

Life period = 15

Straight line depreciation rate = 1/15 * 100 =

Declining method depreciation rate = 200 * 1/15 * 100/100 = 13.33%

since we are using half year method,

half the first year depreciation is used for tax exemption in first year.

i.e,

If face value is'x'

Then first year depreciation = x * 13.33 /2 /100

Depreciation expressed as % of inital value = x*13.33/2/100 *100/x = 6.65 %

In depreciation schedule we depict depreciation in years based on initial value.

So

for first year depreciation = 6.65 %

book value at the end of year 1 = 1 - depreciation/100 = 1 - 6.65/100 = 0.9335

for the 2nd year

depreciation = 0.1333 * book value at the end of year 1 = 0.1333 * 0.9335 * 100 = 12.44 %

Book value at end of year 2 = book value at end of year 1 - depreciation = 0.9335 - 12.44/100 = 0.8091

for 3rd year

depreciation = 0.1333 * book value at the end of 2nd year = 0.1333 * 0.8091 * 100 = 10.78 %

In this way we calculate upto year 15

In year 16

depreciation = 0.1333 * book value at end of year 15 / 2

since we consider only half year in year 16.

(b) Repeat the above pressure but with life period of 20 year

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