# Annuity Method of Depreciation: Definition and FormulaÂ

## What Is the Annuity Method of Depreciation?

The annuity method of depreciation is a process used to calculate depreciation on an asset by calculating its rate of return—just as if it were an investment. It is commonly used with assets that have a large purchase price, long life, and a fixed (or at least constant) rate of return.

This annuity method of depreciation requires the determination of the internal rate of return (IRR) on the cash inflows and outflows of the asset. The IRR is then multiplied by the initial book value of the asset, and the result is subtracted from the cash flow for the period to find the actual amount of depreciation that can be taken.

### Key Takeaways

• The annuity method of depreciation, also called the compound interest method of depreciation, looks at how an asset depreciates by determining its rate of return.
• To calculate using the annuity method of depreciation, you determine the internal rate of return (IRR) on the asset's cash inflows and outflows, then multiply by the initial book value of the asset, then subtracted from the cash flow for the period of time that is being assessed.
• This method of depreciation works especially well for assets that are pricey upfront and are expected to last for many years, such as property or buildings that a company might lease.
• On the upside, this method takes into account the interest lost on the money spent to buy the asset, which many depreciation methods don't do.
• On the downside, the annuity method of depreciation can be hard to understand and may necessitate frequent recalculations.

## How the Annuity Method of Depreciation Works

The annuity method of depreciation is also referred to as the compound interest method of depreciation. If the cash flow of the asset being depreciated is constant over the life of the asset, then this method is called the annuity method.

Many methods of measuring depreciation fail to take into account the interest lost on capital invested in an asset. The annuity method of depreciation makes up for this deficiency. The annuity method assumes that the sum spent on buying an asset is an investment that should be expected to have a yield. The reasoning is that, had one invested an amount equal to the cost of the asset elswhere, they would have earned some sort of return or interest on it.

As such, the interest is charged on the diminishing balance of the asset. It is then debited to an asset account and also credited to an interest account, which is then transferred to a profit and loss account. The asset is then credited with a fixed amount of depreciation for each successive year. How much depreciation is assigned is calculated by using an annuity table. The amount that is depreciated depends on the interest rate and the lifetime of the asset in question.

## Calculating the Annuity Method of Depreciation

The annuity method of depreciation focuses on figuring for a constant rate of return on any asset. It can be calculated using these steps:

1. Make an estimate of the future cash flows that are associated with an asset.
2. Determine what the internal rate of return will be on those cash flows.
3. Multiply that IRR by the asset's initial book value.
4. Subtract the above result from the cash flow for the current period.
5. The result of Step 4 will be the depreciation to charge to expense in the current period.

This process yields the amount of depreciation that can be accounted for over a set period of time.

The annuity method calculation can also be expressed in a formula:

\begin{aligned}&\text{Annuity}=\frac{i\times\text{TDA}\times(1+i)^n}{(1+i)-1^n}\\&\text{Depreciation}=\text{annuity}-(i\times\text{BVSY})\\&\textbf{where:}\\&i=\text{Interest rate percentage}/100\\&\text{TDA}=\text{Total depreciation on amount} \\&n=\text{Annuity number of years}\\&\text{BVSY}=\text{Book value start of year}\end{aligned}

The annuity method of depreciation is useful for assets that have a high initial cost and a long life span, such as property and buildings secured under leases. It takes into account the interest lost on the money spent to buy the asset, which many depreciation methods don't do.

The annuity method of depreciation is not endorsed under generally accepted accounting principles (GAAP).

Some disadvantages of using this method are that it can be difficult to understand and that it may require frequent recalculations depending on the asset. Also, it can be burdensome to profit and loss accounting over time, as the level of depreciation diminishes with every year.

Article Sources
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1. Accounting Tools. "Annuity Method of Depreciation Definition." Accessed Jun. 7, 2021.
2. Allbusiness. "Annuity Method of Depreciation." Accessed Jun. 7, 2021.
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