What is sum of the years digits depreciation?

Sum of the year's digits depreciation is a method of calculating the depreciation of an asset over the years. Sum of the year's digits falls under the category of accelerated depreciation methods, as opposed to straight-line depreciation.

Accelerated depreciation methods are considered to be more conservative calculations of depreciation and also more accurate methods of depreciation calculation. Accelerated depreciation calculation methods assume and rest on the idea that an asset will lose value more quickly at the beginning of its useful life as opposed to losing value at a steady rate throughout its depreciable life. Another method of calculating depreciation that falls under accelerated depreciation is double-declining balance depreciation, or just plain declining balance depreciation.

Here's a simple way to describe how sum of the years digits works.

1. Take the expected life of the asset (make sure that it is in years). Count from the top number back to one. Then add all of the numbers together. So if you purchase a piece of machinery that is expected to last for 12 years, you would do the following:
12 years useful life = 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 Sum of the years = 78


2. To calculate the depreciation of an asset for each year of its useful life, you take the year of its useful life and set it as a percentage of the sum of the years.
This means that in the first year of your machine's life, it would end up being depreciated 12/78 in value. This fraction comes out to 15.38%. So the asset loses 15.38% of its value in the first year. The second year, the machine will be depreciated 11/78, or 14.10% of its value. In the third year, your machine will depreciate 10/78 in value, or 12.82% of its value. And so on and so forth.


3. Let's look at an example. Let's simply use the machine from up above. Let's say that this particular machine cost you $17,000. It has a salvage value of $900. Its useful life is 12 years. We have already calculated the sum of the years for the machine, and it comes out to 78.

We have already calculated that in the first year of use, the machine is going to depreciate by 15.38%. This means that in the first year of use, you will see depreciation expenses of $2467.18 (after subtracting the salvage value from the historical cost). In the second year, the machine has depreciation expenses of 14.10%. This means that you will see depreciation expenses of $2270.10. In the third year, the value will depreciate by 12.82%. Your depreciation expenses will end up being $2064.02.

That was the simple way of describing sum of years digits depreciation. Here's the more technical and complicated way of describing its formula.

Sum of years digits can also be described as a historical depreciation method. Its accelerated is in between straight line depreciation and declining balance depreciation. Here is the formula that is used to determine sum of years digits depreciation.
N = depreciable life of an asset
B = cost basis
S = salvage value
D(t) = depreciation charge for year t
Sum = (N(N + 1))/2
Then
D(t) = (N - t + 1) x ((B - S)/Sum)

Sum of the years digits depreciation is a way of calculating depreciation that will allocate the cost of whatever asset you have over its useful life. A simpler way of describing the formula than that above is to simply say that the numerator of the fraction is the number of years left to be depreciation out of the useful life of the asset. The denominator is the sum of the years digits, determined with the formula: ( N (N + 1) ) / 2 where N is the years of the depreciable life

The sum of the years’ digits, often referred to as SYD, is a form of accelerated depreciation. (A more common form of accelerated depreciation is the declining balance method used in tax depreciation.) The sum of the years’ digits method will result in greater depreciation in the earlier years of an asset’s useful life and less in the later years. However, the total amount of depreciation over an asset’s useful life should be the same regardless of the depreciation method used. The difference is in the timing of the total depreciation.

To illustrate the sum of the years’ digits method of depreciation, let’s assume that a plant asset is purchased at a cost of $160,000. The asset is expected to have a useful life of 5 years and then be sold for $10,000. This means that the asset’s depreciable amount will be $150,000 to be expensed over its useful life of 5 years.

Next the digits in the years of the asset’s useful life are summed: 1 + 2 + 3 + 4 + 5 = 15. In the first year of the asset’s life, 5/15 of the depreciable amount (5/15 of $150,000) or $50,000 will be debited to Depreciation Expense and $50,000 will be credited to Accumulated Depreciation. In the second year of the asset’s life, $40,000 (4/15 of $150,000) will be the depreciation amount. In the third year, $30,000 (3/15 of $150,000) will be the depreciation. The fourth year will be $20,000 (2/15 of $150,000) and the fifth year will be $10,000 (1/15 of $150,000). As indicated earlier, the total depreciation during the asset’s useful life needs to sum to the depreciable cost (in this case $150,000) regardless of the depreciation method used.

Instead of adding the individual digits in the years of the asset’s useful life, the following formula can be used: n(n+1) divided by 2. In this formula, n = the useful life in years. Let’s use the formula to check our calculation above. When the useful life is 5 years, the formula will be 5(5+1)/2 = 5(6)/2 = 30/2 = 15. If the useful life is 10 years, the formula will show 10(10+1)/2 = 10(11)/2 = 110/2 = 55. In the first year of the asset having a 10 year useful life, the depreciation will be 10/55 of the asset’s depreciable cost. The second year will be 9/55 of the asset’s depreciable cost. In the tenth year, the depreciation will be 1/55 of the asset’s depreciable cost.
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Flexible Budget

budget is a plan for the future. Hence, budgets are planning tools, and they are usually prepared prior to the start of the period being budgeted. However, the comparison of the budget to actual results provides valuable information about performance. Therefore, budgets are both planning tools and performance evaluation tools.

Usually, the single most important input in the budget is some measure of anticipated output. For a factory, this measure of output is the number of units of each product produced. For a retailer, it might be the number of units of each product sold. For a hospital, it is the number of patient days (the number of patient admissions multiplied by the average length of stay).

The static budget is the budget that is based on this projected level of output, prior to the start of the period. In other words, the static budget is the “original” budget. The static budget variance is the difference between any line-item in this original budget and the corresponding line-item from the statement of actual results. Often, the line-item of most interest is the “bottom line”: total cost of production for the factory and other cost centers; net income for profit centers.

The flexible budget is a performance evaluation tool. It cannot be prepared before the end of the period. A flexible budget adjusts the static budget for the actual level of output. The flexible budget asks the question: “If I had known at the beginning of the period what my output volume (units produced or units sold) would be, what would my budget have looked like?” The motivation for the flexible budget is to compare apples to apples. If the factory actually produced 10,000 units, then management should compare actual factory costs for 10,000 units to what the factory should have spent to make 10,000 units, not to what the factory should have spent to make 9,000 units or 11,000 units or any other production level.

The flexible budget variance is the difference between any line-item in the flexible budget and the corresponding line-item from the statement of actual results.

The following steps are used to prepare a flexible budget:

1. Determine the budgeted variable cost per unit of output. Also determine the budgeted sales price per unit of output, if the entity to which the budget applies generates revenue (e.g., the retailer or the hospital).

2. Determine the budgeted level of fixed costs.

3. Determine the actual volume of output achieved (e.g., units produced for a factory, units sold for a retailer, patient days for a hospital).

4. Build the flexible budget based on the budgeted cost information from steps 1 and 2, and the actual volume of output from step 3.

Flexible budgets are prepared at the end of the period, when actual output is known. However, the same steps described above for creating the flexible budget can be used prior to the start of the period to anticipate costs and revenues for any projected level of output, where the projected level of output is incorporated at step 3. If these steps are applied to various anticipated levels of output, the analysis is called pro forma analysis. Pro forma analysis is useful for planning purposes. For example, if next year’s sales are double this year’s sales, what will be the company’s cash, materials, and labor requirements in order to meet production needs?

A flexible budget can help managers to make more valid comparisons. It is designed to show the expected revenue and the allowed expenditure for the actual number of units produced and sold. Comparing this flexible budget with the actual expenditure and revenue it is possible to distinguish genuine efficiencies. The question is: how to prepare a flexible budget? This post provide a simple overview of how a flexible budget is prepared.

Before a flexible budget can be produced, managers must identify which costs are fixed and which are variable. The allowed expenditure on variable costs can then be increased or decreased as the level of activity changes. “Fixed costs” are those costs which will not increase or decrease over a given range of activity. The allowance for these items will therefore remain constant. Let us continue with the example…

Management have identified that the following budgeted costs are fixed:

Direct labor = $8,400
Overheads = $53,000

It is now possible to identify the expected variable cost per unit produced and sold:



Now that managers are aware of the fixed costs and the variable costs per unit it is possible to ‘flex’ the original budget to produce a budget cost allowance for 1,000 units produced and sold.

The budget cost allowance for each item is calculated as follows:

Cost allowance = budgeted fixed cost + (number of units produced and sold x variable cost per unit)



For the costs which are wholly fixed or wholly variable the calculation of the budget cost allowance is fairly straightforward. The remaining costs are semi-variable, which means that they are partly fixed and partly variable.

The budget cost allowance for direct labor is calculated as follows:

Cost allowance for direct labor = $8,400 + (1,000 units x $4) = $12,400
The budgeted sales price per unit is $120,000 / 1,200 = $100 per unit.


If it is assumed that sales revenues follow a linear variable pattern (because the sales price remains constant) the full flexible budget can now be produced.

To make sure that you followed it, let’s do further example.

Following the example of the calculation of the budget cost allowance for direct labor, calculate a revised budget cost allowance for all costs for an activity of 1,000 units and produce a revised variance statement for April.

Firstly, we need to compute the cost allowance for the overhead. Here we go:

Cost allowance for overhead = $53,000 + (1,000 units x $7) = $60,000

Next, we can make “flexible budget comparison” for April as below:



This revised analysis shows that in fact the profit was $7,610 higher than would have been expected from a sales volume of 1,000 units.
The largest variance is a $10,000 favorable variance on sales revenue. This has arisen because a higher price was charged than budgeted.


Could the higher sales price have been the cause of the shortfall in sales volume?

Although the answer to this question is not available from this information, without a flexed budget comparison it was not possible to tell that a different selling price had been charged. This is an example of variances which may be interrelated – a favorable variance on sales price may have caused an adverse variance on sales volume.
The cost variances in the flexible budget comparison are mainly adverse. These overspendings were not revealed when a fixed budget was used and managers may have been under the false impression that costs were being adequately controlled. You may be wondering what has happened to the remainder of the $6,990 adverse profit variance shown in our original budget comparison at the beginning of this example. This could be analyzed as follows:

Difference in budgeted profit -

causedby volume shortfall ($26,200 - $11,600) = ($14,600)
Profit variance from flexible budget comparison = $7,610
Total profit shortfall, per original budget comparison = ($6,990)

This shows clearly that the adverse variance was caused by the volume shortfall, and not by differences in the expected cost and revenues from the sales that were made.



Using Flexible Budgets for Planning

Although flexible budgets can be useful for control purposes they are not particularly useful for planning. The original budget must contain a single target level of activity so that managers can plan such factors as the resource requirements and the product pricing policy. This would not be possible if they were faced with a range of possible activity levels.