Depreciation

#What can be depreciation?

• Assets must be used in business or held for production of income.
• Assets must have a definite useful life and a life > one year.
• Assets that must be sth that wears out, gets used up, become obsolete or lose value.

🔖Depreciable property includes buildings, machinery, equipment, vehicles and some intangible properties(such as copyrights, designs, etc).

#Cost basis

The total cost that is claimed as an expense over an asset's life, which includes the actual cost of the asset and all incidental expenses such as freight, insurance, and site preparation.

#Salvage value

The salvage value of an asset is an asset’s estimated value at the end of its life. It is the amount eventually recovered through sale, trade-in, or salvage.

#Method of depreciation

#Straight-Line Method(直线折旧法)

$$D _ { n } = ( I - S ) / N$$

constant for all n: I = cost basis, S = salvage value, N = depreciable life.

#Modified Accelerated Cost Recovery System(MACRS,修正的加速折旧法)

• Only a half-year of depreciation is allowed for the first year.
• A full year’s depreciation is allowed in each of the remaining years.
• The remaining half-year’s depreciation is incurred in the year following the end of the recovery period.
• A half-year of depreciation is also allowed for the year in which the property is disposed of, or is otherwise retired from service, anytime before the end of the recovery period.
• Switching from the DB method to the SL method.

🔖关键在于：项目的第一年只允许计提半年的折旧。如果项目生命周期大于折旧年限（比如 5 年），那么需要在第六年计提第一年剩下的半年的折旧。如果项目生命周期小于折旧年限，那么在项目的最后一年计提半年的折旧。

🌰5-YEAR MACRS

#Declining Balance Method(余额递减法)

加速折旧法的一种。

$$\alpha = ( 1 / N ) \times (multiplier) \quad D _ { n } = \alpha B _ { n - 1 }$$

$\alpha B _ { n - 1 }$为上一年的 Book value，$B_n=B_{n-1}-D_n$

🔖If $\alpha$ is chosen to be the upper bound, $\alpha = 2(1/N)$, we call it a 200% DB or double declining balance method.(双倍余额递减法)

🔖因为余额递减折旧法是按比例折旧，所以在不考虑有残值的情况 ($S=0$) 下，使用余额递减折旧法永远也不能将固定资产 (cost basis) 计提干净。

🔖因为余额递减折旧法不考虑残值，所以要注意在有残值的情况下，不允许固定资产的账面折余值小于预计残值收入。国内对折旧期年限到期以前的两年折旧额的处理采用直线法，即倒数第二年的期初账面余额减去残值，然后除以 2，得到最后两年的平均年折旧额。

#Switching policy(DB Switching to SL)

🌰Assum S=0, cost basis=10000, depreciation life=5, double declining balance:

Without switching table

With switching to SL table

📌使用转换策略时，SL 计算中的 N 是还剩下的折旧年数。

#Units-of-Production Method(单位产品工作量法)

$$D _ { n } = \frac { \text { Service units consumed for year } n } { \text { total service units } } ( I - S )$$