# Depreciation Methods

A depreciation method is the systematic manner in which the cost of a tangible asset is expensed out to income statement. Popular depreciation methods include straight-line method, declining balance method, units of production method, sum of year digits method. For tax, MACRS is the relevant depreciation method.

Amount spent on acquisition of an asset is initially recorded as an asset on balance sheet and charged to income statement over the useful life of the asset. The purpose of depreciation is to match revenues with expenses, hence the depreciation method must replicate the manner in which a particular asset is expected to generate revenues or cost savings.

Depreciation methods can be broadly classified into two types: the **time-factor methods** and the **usage-factor-methods**. The time factor methods (straight-line method and declining balance method) works out depreciation based on passage of time and usage-factor methods work out depreciation based on actual usage of the asset.

## Straight-Line Method

Under the straight-line method, equal depreciation expense is charged in each period of the asset’s useful life. Straight-line method is appropriate for assets which are expected to be equally productive in all periods of its useful life.

Depreciation expense under the straight-line method is calculated by dividing the depreciation amount by the total useful life of the asset. Depreciable amount equals historical cost minus the salvage value.

$$ D_{SLN}=\frac{C-S}{y} $$

Where DSLN is the depreciation expense in each period under the straight-line method, C is the historical cost of the asset, S is the salvage value and y is the total number of periods of useful life.

Straight-line depreciation can also be calculated using Microsoft Excel SLN function.

Depreciation rate under the straight-line method equals 1/y. If an asset is used only for a fraction of the period, the depreciation expense is worked out by multiplying the whole-period depreciation expense with the proportion of the period in which the asset was used.

Straight-line method is the most popular depreciation method due to the ease with which depreciation expense can be worked out using it. It may be the most appropriate method to depreciate to a plan whose production is constant in all years of its useful life.

### Example of Straight-Line Method

Parvaz Air, Inc. purchased an airplane for $200 million. It is expected to last 70,000 decompression cycles or 10 years. Let’s work out straight-line depreciation if the the plane’s salvage value is equal to 20% of the cost. Depreciation in each year under the straight-line method equals $16 million (($200 million - $200 million × 20%)/10). It remains the same for all years i.e. the same for Year 1 and Year 10.

## Declining Balance Method

Under the declining balance method, depreciation expense charged in the first year is the highest and it decreases as the asset gets older. Since higher depreciation expense is charged in initial years, it is called accelerated depreciation method.

There are many variants of the declining balance depreciation method: 150%-declining balance method, 200%-declining balance method (also called double-declining balance method).

The depreciation expense under the declining balance method is calculated by multiplying the beginning carrying value of the asset with the depreciation rate. The depreciation rate under the declining balance depreciation method equals 1 divided by the total useful life of the asset multiplied by a factor (which is 1.5 in case of 150%-method and 2 in case of double-declining method).

The following is a direct formula for calculating declining balance depreciation:

$$ D_{DB}={\rm CV}_B\times\frac{1}{y}\times f $$

Where CV_{B} is the beginning carrying value, y is the total useful life and f is the factor.

### Example of Declining Balance Method

Let’s continue with the example above assuming a 200%-declining balance method. The following process is used to calculate declining balance depreciation:

- Step 1: Find out the cost of the asset, its salvage and total useful life. In case of the airplane in the example, it is $200 million, $40 million and 10 years respectively.
- Step 2: work out depreciation rate which equals 1/y multiplied by the declining factor. For the airplane in question, it works out to 0.2 (=1/10× 2).
- Step 3: for the first year, calculate depreciation expense by multiplying the depreciation rate (i.e. 0.2 calculated above) with the cost of the asset i.e. $200 million (remember, it’s not depreciable amount). The first-year depreciation works out to $40 million.
- Step 4: work out the carrying value at the end of the year (i.e. cost minus depreciation expense). In this example, it is $160 million (i.e. $200 million - $40 million).
- Step 5: for each next period, calculate depreciation expense by applying the depreciation rate worked out in Step 2 to the opening carrying value; For the second year, depreciation expense is $32 million (=0.2 × $160 million).
- Step 6: continue charging depreciation unless the carrying value equals salvage value.

The following table shows the depreciation schedule for the whole life of the airplane:

Year | Opening Carrying Value | Depreciation Expense | Accumulated Depreciation | Closing Carrying Value |
---|---|---|---|---|

0 | 200,000,000 | - | - | 200,000,000 |

1 | 200,000,000 | 40,000,000 | 40,000,000 | 160,000,000 |

2 | 160,000,000 | 32,000,000 | 72,000,000 | 128,000,000 |

3 | 128,000,000 | 25,600,000 | 97,600,000 | 102,400,000 |

4 | 102,400,000 | 20,480,000 | 118,080,000 | 81,920,000 |

5 | 81,920,000 | 16,384,000 | 134,464,000 | 65,536,000 |

6 | 65,536,000 | 13,107,200 | 147,571,200 | 52,428,800 |

7 | 52,428,800 | 10,485,760 | 158,056,960 | 41,943,040 |

8 | 41,943,040 | 1,943,040 | 160,000,000 | 40,000,000 |

9 | 40,000,000 | - | 160,000,000 | 40,000,000 |

10 | 40,000,000 | - | 160,000,000 | 40,000,000 |

In Year 8, depreciation of only $1,943,040 is charged because the carrying value can’t be lower than the salvage value. The company seizes to depreciate the airplane in Year 8.

## Units of Production Method

Units of production method is a depreciation method in which depreciation expense in a period equals the depreciable amount divided by total number of units the asset is expected to produce multiplied by the total number of units produced in the period.

For example, airplanes useful life is measured in number of decompression cycle i.e. the number of time a plane takes off and is exposed to pressure. The units of production method might be very relevant to depreciation of the fuselage and cabin of the plane.

The following formula can be used to calculate units of production depreciation expense:

$$ D_{UP}=\frac{x}{y}\times(C\ -\ S) $$

Where x is the total number of units produced int eh period, y is the total number of units the asset can produce, C is the cost and S is the salvage value.

### Example of Units of Production Method

Continuing with the example above, let’s assume that instead of using the straight-line method or the double-declining balance method, the company wants to depreciate the airplane based on the flights it takes in each year. The following schedule shows the flights taken each year and the relevant depreciation expense.

Year | Flights | Depreciation Expense | Accumulated Depreciation | Closing Carrying Value |
---|---|---|---|---|

0 | 200,000,000 | |||

1 | 11,000 | 25,142,857 | 25,142,857 | 174,857,143 |

2 | 9,500 | 21,714,286 | 46,857,143 | 153,142,857 |

3 | 10,000 | 22,857,143 | 69,714,286 | 130,285,714 |

4 | 10,200 | 23,314,286 | 93,028,571 | 106,971,429 |

5 | 8,000 | 18,285,714 | 111,314,286 | 88,685,714 |

6 | 6,500 | 14,857,143 | 126,171,429 | 73,828,571 |

7 | 6,000 | 13,714,286 | 139,885,714 | 60,114,286 |

8 | 3,500 | 8,000,000 | 147,885,714 | 52,114,286 |

9 | 2,500 | 5,714,286 | 153,600,000 | 46,400,000 |

10 | 2,800 | 6,400,000 | 160,000,000 | 40,000,000 |

Total | 70,000 | 160,000,000 |

For illustration, the 4th year depreciation expense is calculated using the following formula:

$$ D_{UP}=\frac{10,200}{70,000}\times(200,000,000\ -\ 40,000,000)=$23,314,286 $$

Written by Obaidullah Jan, ACA, CFA and last modified on