# How to use the SYD function

**What is the SYD function?**

The SYD function calculates the yearly asset depreciation of a given year.

#### Table of Contents

## 1. Introduction

**What is SYD function an abbreviation of?**

SYD stands for the "Sum-of-the-Years-Digits" depreciation method, which is a way of calculating depreciation such that the charges decrease each year over an asset's lifespan.

**What is the "Sum-of-the-Years-Digits" depreciation method?**

The sum-of-the-years-digits (SYD) method is a way to calculate depreciation such that the charges decrease each year over an asset's lifespan.

For example, say an asset has a 5 year life. The SYD fractions for each year would be:

Year 1: 5/15

Year 2: 4/15

Year 3: 3/15

Year 4: 2/15

Year 5: 1/15

(Sum 1+2+3+4+5 = 15)

Depreciation in year 1 is (Cost-salvage) * 5/15, in year 2 it's (Cost-salvage) * 4/15, becoming smaller each year.

**What is depreciation of an asset?**

Depreciation is an accounting method that allows businesses to allocate the cost of a tangible asset over its useful life. It represents how much of an asset’s value has been used up over time.

Depreciation helps businesses to match their expenses with their revenues, and to reduce their taxable income by deducting the depreciation expense.

**What is a depreciable asset?**

A depreciable asset is a long-term tangible or physical asset like machinery or equipment that loses value over time due to wear and tear from usage. Depreciation allows a business to recover the cost of the asset as an expense over its useful lifespan.

**What is the difference between DB function and the SYD function?**

The DB function calculates the fixed-declining balance depreciation each period using a fixed rate, while SYD calculates the sum-of-the-years-digits depreciation based on a declining charge-off fraction each period.

**What is the difference between DDB function and the SYD function?**

DDB uses fixed declining percentages of the book value to calculate depreciation each period, while SYD calculates the sum-of-the-years-digits depreciation based on a declining charge-off fraction each period.

**Depreciation functions in Excel**

Function | Description |
---|---|

SYD(cost, salvage, life, period) | Sum-of-the-years digits depreciation |

DB(cost, salvage, life, period, [month]) | Fixed-declining balance depreciation |

DDB(cost, salvage, life, period, [factor]) | Double-declining balance depreciation |

AMORLINC(cost, date_purchased, first_period, salvage, period, rate, [basis]) | Depreciation for period using linear method |

AMORDEGRC(cost, date_purchased, first_period, salvage, period, rate, [basis]) | Depreciation from date of purchase to end of period |

VDB(cost, salvage, life, start_period, end_period, [factor], [no_switch]) | Variable declining balance depreciation |

**What is the math formula behind this function?**

The math formula for the SYD function is:

((cost - salvage) * (life - per + 1) * 2) / (life * (life + 1))

- cost: The initial cost of the asset.
- salvage: The estimated salvage value (value at the end of the asset's useful life) of the asset.
- life: The number of periods over which the asset is being depreciated (useful life).
- per: The period for which you want to calculate the depreciation. Per must use the same units as life.

The formula calculates the depreciation for a given period by first determining the total depreciable cost (cost - salvage). It then applies a fraction based on the remaining useful life of the asset (life - per + 1) and a scaling factor (2 / (life * (life + 1))) to distribute the depreciable cost over the asset's useful life using the Sum-of-Years' Digits method.

## 2. Syntax

SYD(*cost*, *salvage*, *life*, *per*)

cost |
Required. The cost of an asset. |

salvage |
Required. The final value after depreciation (salvage value). |

life |
Required. The number of periods the asset is depreciated. |

per |
Required. The period you want to know the depreciation for. |

**What is salvage value?**

Salvage value is the estimated value of an asset at the end of its useful life. It is also known as scrap value or residual value. It is used to calculate the depreciation expense of an asset over its useful life.

## 3. Example 1

**A company purchased a machinery for $50,000 with an estimated salvage value of $5,000 and a useful life of 10 years. Calculate the depreciation for the 3rd year using the Sum-of-Years' Digits method?**

This image above shows this example of calculating the depreciation of an asset using the Sum-of-Years' Digits method.

The arguments provided are:

- Cost: $50,000.00
- Salvage: $5,000.00
- Life: 10 years
- Per: 3 (indicating the depreciation calculation for the 3rd year)

Formula in cell C22:

The formula in cell C22 returns $6,545.45 which represents the depreciation value for period 3 (year 3).

The chart displays the depreciation and asset value over the asset's useful life. The blue line represents the depreciation value which starts high and decreases each year. The orange line represents the asset value which starts at the initial cost and decreases as depreciation is applied.

The table below the formula shows the depreciation values and remaining asset values for each period (year) in the asset's useful life.

The math formula for the SYD function is:

((cost - salvage) * (life - per + 1) * 2) / (life * (life + 1))

Lets plug the argument values in this math formula and see what we get.

= ((50,000 - 5,000) * (10 - 3 + 1) * 2) / (10 * (10 + 1))

= (45,000 * 8 * 2) / (10 * 11)

= 720,000 / 110

= 6,545.45

This matches the value displayed in cell C22 and the depreciation value for period 3 (year 3) in the table.

## 4. Example 2

*A vehicle costing $25,000 with an estimated salvage value of* 10%, is expected to have a useful life of 5 years. Find the depreciation for the 4th year using the Sum-of-Years' Digits method?

This image above shows this example of calculating the depreciation of an asset using the Sum-of-Years' Digits method.

The arguments provided are:

- Cost: $25,000.00
- Salvage: $2,500.00 (10% salvage value)
- Life: 5 years
- Per: 4 (indicating the depreciation calculation for the 4th year)

Formula in cell C22:

The formula in cell C22 returns $3,000.00 which represents the depreciation value for period 4 (year 4).

The chart displays the depreciation and asset value over the asset's useful life. The blue line represents the depreciation value which starts high and decreases each year. The orange line represents the asset value which starts at the initial cost and decreases as depreciation is applied.

The table below the formula shows the depreciation values and remaining asset values for each period (year) in the asset's useful life, from period 0 (zero) to 5.

The math formula for the SYD function is:

((cost - salvage) * (life - per + 1) * 2) / (life * (life + 1))

Lets plug the argument values in this math formula and see what we get.

= ((25,000 - 2,500) * (5 - 4 + 1) * 2) / (5 * (5 + 1))

= (22,500 * 2 * 2) / (5 * 6)

= 3000

### Functions in 'Financial' category

The SYD function function is one of 27 functions in the 'Financial' category.

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