EME 460
Geo-Resources Evaluation and Investment Analysis

Business Costs that May Be Capitalized

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Depreciation and Depreciation Methods

As explained before, depreciation is a method to capitalize and recover business costs over a specified period of time or over the useful life of the investment.

The term depreciation usually refers to the process of losing value over the time for a property, like wear and tear. When a machine is purchased to produce and generate income, it won’t be as good when it becomes older. It happens because the machine gets exhausted or production becomes obsolete. Therefore the machine loses its value over time and can’t be sold for high value. Tax law allows the company to deduct the depreciated value of the asset from the generated income. There are permitted methods (will be explained later in this lesson) to calculate the depreciated value, which might be different from how the asset depreciates in reality. For example, the asset might be still functional while it is already fully depreciated in tax calculations. In this text by the term annual depreciation deduction we refer to tax allowance.

A depreciable property:

  1. Must be used (or be ready to be replaced) for producing income
  2. Must have a determinable lifetime longer than one year
  3. Must lose its value over time
  4. Must be used or be ready to be used

For example, land is an asset that is not permitted for depreciation. More information about depreciation can be found at the Internal Revenue Service (IRS) website. Depreciation is usually applied to the tangible property while amortization is for intangible property.

Depreciation Methods

This section explains four major depreciation methods including:

  1. Straight Line
  2. Declining Balance
  3. Declining Balance Switching to Straight Line
  4. Modified Accelerated Cost Recovery Systems (MACRS)

Please watch the following video (4:20): After Tax Cash Flow: Expensing Versus Capitalizing Investment Costs.

After Tax Cash Flow: Expensing Versus Capitalizing Investment Costs
Click for the transcript of Expensing Versus Capitalizing Investment Costs Video

PRESENTER: As explained in the previous video, tax law allows investors to recover some of their investments through tax deductions. In explaining that, there are two main methods for the investment costs, cost that can be expensed and cost that can be capitalized. And the difference is only time, the cost that can be expensed or the cost that can be deducted in full amount from the income and cost that can be capitalized or the cost that can be deducted gradually over time, more than one year from the revenue income.

So depreciation is one of the methods of business cost that can be capitalized. They have to be deducted from revenue or income over the years, more than one year, gradually. The depreciation means the process of losing the value over time for property, like wear and tear.

For example, when an investor buys a machine for producing and generating income, after a couple of years the machine gets older. It would require maintenance and repair more frequently. The quality of the units that it produces becomes lower. The technology becomes obsolete. And the machine loses its value over time and it cannot be sold for a very high value.

So the tax law allows the company, the investor, to deduct the depreciated value of the asset from the generated income. So tax law allows some standard methods to apply the depreciation and using the tax deduction to recover the costs of the depreciated property or machinery or building.

These are standard accounting methods. And they might be different from the actual physical depreciation of the property. So the property might still be functional and working while it is fully depreciated. And the cost of it is recovered through tax deductions. So these are different.

So depreciation method is allowed to be used for property that has these four characteristics. The property must be used or be ready to be replaced for producing income. The property must have a determinable lifetime longer than one year.

The property must lose its value over that time. For example, land, it is assumed that land doesn't lose its value over time. So we cannot use depreciation for recovering land costs. And, also, the property must be used or be ready to be used.

There are four major depreciation methods; a straight line method, declining balance, declining balance switching to straight line [AUDIO OUT], and modified accelerated cost recovery system, or MACRS, that I will explain in the following videos.

Credit: Farid Tayari

1. Straight Line Depreciation

This method is the simplest way of calculating the depreciation. In this method, depreciation is constant and equally distributed over the allowable life time of the property as:

Straight Line Depreciation per year = (Cost of the asset- Salvage value)/Allowable depreciation life time
Equation 7-3

The biggest problem in this method is straight line depreciation is very slow and capital cost is recovered slowly. The faster costs are recovered the lower tax is paid in early years and it enhances the economics of the project.

Straight line depreciation is the method that used to calculate the non-cash capital cost deduction in Example 7-3.

Example 7-4:

Following the Example 7-3, assume allowable depreciation life time is 5 years, starting from year 1. Also assume the investor buys a piece of land for $25000 at time zero that can be sold at year 10 for $35,000.

Straight Line Depreciation=(100,000)/5= $20,000 per year from year 1 to year 5

Note that investment for land is not depreciable. The land resale value of $35,000 should be added to the income of 10th year. But the initial value of land is deductible as “Write-off”. Because, just the profit ($35,000 - $25,000 = $10,000) made on selling the land is taxable.
After-Tax Cash Flow will be determined as:

Year 0 1 2 3 4 5 6 7 8 9 10

Revenue $38,000 $38,000 $38,000 $38,000 $38,000 $38,000 $38,000 $38,000 $38,000 $38,000
+Land resale $35,000
- Operating cost -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 -$12,000
- Depreciation -$20,000 -$20,000 -$20,000 -$20,000 -$20,000
- Write-off -$25,000

Taxable income $6,000 $6,000 $6,000 $6,000 $6,000 $26,000 $26,000 $26,000 $26,000 $36,000
- Income tax $1,500 $1,500 $1,500 $1,500 $1,500 $6,500 $6,500 $6,500 $6,500 $9000

Net Income $4,500 $4,500 $4,500 $4,500 $4,500 $19,500 $19,500 $19,500 $19,500 $27,000
+ Depreciation $20,000 $20,000 $20,000 $20,000 $20,000
+ Write-off $25,000
- Capital cost -$100,000
- Land -$25,000

ATCF -$125,000 $24,500 $24,500 $24,500 $24,500 $24,500 $19,500 $19,500 $19,500 $19,500 $52,000

ROR for After-Tax Cash Flow will be 14.5%.

Half-year convention

Under half-year convention properties are assumed to be placed in service in the middle of the year. Consequently, half of the first year normal depreciation has to be applied to the year that the property is placed in service. For example, if half-year convention is applied to the first year in example 7-4 to calculate the depreciation using Straight Line method, then the calculated deprecation would be:

Half-year convention straight line depreciation by year
Year Half-year convention straight line Depreciation
1 ($100,000)(1/5)(1/2)=$10,000
2 ($100,000)(1/5)=$20,000
3 ($100,000)(1/5)=$20,000
4 ($100,000)(1/5)=$20,000
5 ($100,000)(1/5)=$20,000
6 ($100,000)(1/5)(1/2)=$10,000
Total $100,000

Note that because we applied half-year convention to the strait line depreciation method we considered half of the first year normal depreciation for year 1, thus we needed to add the rest (other half) to the year 6; consequently there will be 6 years of depreciation periods.

Please watch the following video (23:32): Straight Line Depreciation Method.

Straight Line Depreciation Method
Click for the transcript of Straight Line Depreciation Method Video

PRESENTER: In previous videos, I explained investment costs that can be capitalized, and I briefly explained the depreciation methods. So as I explained, there are four major depreciation methods. First one is a straight line that I'm going to explain in this video.

Second one is declining balance. The third one is declining balance switching to the straight line. And the last one is modified accelerated cost recovery system, or MACRS, that I will explain in the next videos.

Straight line depreciation is the simplest method in calculating depreciation. In this method, we uniformly distribute depreciation over the years of allowable lifetime of the property. So the equation is the cost of the asset-- the actual cost that you pay for the asset-- minus the salvage value, if there is any salvage value, divided by the number of years that we want to depreciate that property over those years.

So this method is very simple. But the problem is, it is very slow, as we explained before. The investor would like to recover the capital cost as soon as possible. The more years, the longer it takes, to recover the money. So they get the same amount of money every single year. They get the same amount of depreciation every single year.

So and we know that the faster costs are recovered, the lower taxes paid in the early years. And it is going to enhance the economics of the project. The earlier the investor gets the tax deduction, it improves the economics of the project.

So let's assume an investor pays $100,000 for a machine, that this investment can be depreciated using the straight line depreciation over the five years, from year one to year five. The machine will start producing and generating revenue from year one to year 10, with a revenue off $38,000, and operating costs of $12,000. The salvage value is going to be zero.

And also, the investor has to buy land, for cost of $24,000, at time, zero. But because land doesn't lose its value over time, we assume the land resale value, in the end of the year 10, is going to be $35,000. So we consider the income tax of 25%, and we want to calculate after-tax cash flow.

First, we need to calculate the depreciation. The capital cost for the machinery was $100,000. And it can be depreciated over five years. And with a straight line depreciation, we have five years of uniform distribution. And the salvage value is zero.

So the depreciation for each year is going to be calculated as $100,000, divided by 5 years. And we are going to have $20,000 of depreciation for each year, from year one to year five, that can be deducted from revenue as tax deductions. Here, please note that the land is not depreciable.

So the land is purchased for $25,000, at present time, and it is going to be sold at $35,000, in the end of the year 10. So the investor is going to make $10,000, which is the difference between the purchasing cost and the resale cost, resale price. The investor has to pay tax on the $10,000 of profit that is going to be earned at year 10.

And now, the second step is, we draw this table. We start with revenue, whatever generates income. The first is, we have $38,000 of revenue created by the machine. Then, we are going to have-- we are going to sell the land at year 10. So we are going to have $35,000 of cash, after we sell the land in year 10, but we can see, we-- I'll show you later, in a bit, that just $10,000 of debt has to be taxed.

So then we start adding costs-- the operating cost of $12,000 from year one to year 10. Then we add depreciation. So the depreciation should be-- we should enter depreciation with a negative sign. And we can-- it has to be deducted from revenue as tax deduction, before calculating the tax.

So we have five years of depreciation, and it is uniformly distributed. Every year is $20,000 we deduct from revenue, from year one to year five. And I had this item called write-off, because we are going to sell the land at $35,000. We are going to have the revenue of $35,000 at the year 10. But we pay $25,000 for land, at the present time.

So this profit that we made on the land is taxable, and not the actual capital cost that we pay for the land. So we write these land write-off, of minus $25,000, to adjust these income that-- saying that, OK, just the $10,000 of the money that we made on the land is taxable.

Then, we calculate the taxable income, which is the summation over each column. And the income tax of 25%, which is 25% of taxable income. And we calculate that for every column.

And what we have is net income, which is the summation of these two rows. If we enter the tax with a negative sign, this is going to be with the summation. If we don't enter the tax with negative sign, then it will be the difference between these two. So taxable income minus income tax is going to give us net income.

And we calculate that for every single year, from year zero-- from present time-- to year 10. Here, because we don't have any income or any cost, we don't have any net income at year zero, but later on we will see that we are going to have all our capital costs and land costs here at year zero.

So then, we start adding back whatever we deducted here, for tax deductions. So we deducted the depreciation. We calculated the tax. And then, we add that back again. So negative sign here, and then you add that with the positive sign. These are exactly the same.

The next thing is land write-off. We add back the land write-off of $25,000, and then we enter the capital cost. So we had-- the investor invested $100,000 at present time, for buying the machinery, and the land, which was purchased for $25,000. Please note that for the write-off, we have a minus number here, before calculating the tax, and we add that back again. And here, we have the resale value of the land.

And we calculate the after-tax cash flow, by making a summation over each column-- net income plus depreciation plus write-off minus capital cost minus land. And this is going to be our after-tax cash flow.

So let's work on this example in a spreadsheet, and see how we can use a spreadsheet-- Microsoft Excel or any other spreadsheet-- to approach these problems. So first, I'm going to write the year. I start from year zero. There are 10 years. The lifetime of the project is going to be 10 years, so I will have 10 years of project lifetime, here.

Then, the first thing that I have to do, I start with the revenue, with the items that have the nature of making money, creating some revenue. So revenue that is generated by the machine-- machine comes to production at year one, and produces from year one to year 10, and generates $38,000. One important point, here, is you have to have all your input data in a separate section, and you have to refer to those cells that you need.

And very good feature about the spreadsheet is if you update some inputs, it is going to automatically update your output, as well. So instead of writing $38,000, from here, here, here, and to year 10, I will just refer that to the input data that I have, here. So I write equals sign and this one.

And because-- so it writes the $38,000, here, but because I want to apply this to the other 10 years, I will put a dollar sign before there, the column number. Then, when I apply this, it keeps the-- the year keeps the same cell for all the years. So there is no revenue at year zero, so I skipped that. I left that blank.

Then, I'm going to have land resale value. Excel is confusing this as an equation, so I can just delete that, because I start with a positive sign. So I can just put the sign, and it will accept it as just the text. So the land resale is going to be $35,000, at year 10.

Then, I will add the operating cost with the negative sign. Operating cost-- so I'm going to add the operating cost from year one to year 10. So negative sign-- I read the operating cost from here. I fixed the column number, and then apply that from year one to year 10.

Then I'm going to have the depreciation with the negative sign. Depreciation-- I can actually calculate the depreciation number here, and read that from-- refer to that cell. I can say year depreciation, year zero, year zero, one, two, three, four, five.

And the depreciation equals the capital cost divided by 5 years of depreciation. I fixed this one. And this is a straight line, so I'm going to have $20,000 per year from year one to year five. Sorry, I don't have depreciation at year zero. So I'm going to enter depreciation with a negative sign, here. Year one, year two, three, four, and five.

And I will add the land write-off with the negative sign. Then I will draw a line, here, because I want to calculate the taxable income.

So taxable income, I have to make a summation over each column. There is nothing, at present time. So summation of all these values, at year one, and I apply that to year 10. I calculate the tax with the negative sign. So that is going to be 25% of this amount, 25% of taxable income. And I apply this to year 10.

Again, I draw a line here, and I calculate net income, which is going to be-- I could have the tax with the positive sign, and then deduct these two, or I could have the tax with the negative sign, and just simply make a summation, here. So I will enter the tax with the negative sign, and make a summation here, and calculate the net income.

After we calculate the net income, we have to add back whatever we had, here, as the tax deductions. So we had this depreciation, and we had land write-off. So we add them back with the positive sign.

And it is exactly the same as here. So I will just multiply this number with the negative sign. This is for five years. I apply that for five years. Then the land write-off with the positive sign, which is going to be at year 10.

And we are going to have the capital cost with a negative sign. So the capital cost-- what was happening at the present time. So negative, and I read it from here. And we paid for land, at present time.

So land-- again, I draw a line here, because I want to calculate the after-tax cash flow. And after-tax cash flow is simply the summation between these two lines. So now I have the after-tax cash flow calculated in this row. OK.

There is a version of straight line depreciation method that is called half-year convention. So in this method, it's exactly the same as the straight line depreciation, but we move everything for six months forward. So the intuition behind that is, it takes a while, maybe, for the machinery to come to production.

So we start in the middle of the year, not in the beginning of the year. So we move everything for six months forward. So we take six months from the first year, and we add an extra year to the end, with only six months.

So for example, if you want to calculate the same depreciation for the same example-- investing $100,000 into machinery-- using half-year convention, we just move everything for half a year to forward. For the straight line depreciation, for each year we had one-fifth, because we had 5 years of depreciation, and the salvage value was zero. So $100,000 divided by 5. For each year, we are going to have $20,000 of depreciation from year one to year 20.

But if we use the half-year conventional straight line depreciation, for the first year, we are going to have half of the depreciation. So we are going to have half of the $20,000, which is $10,000, which means that we have just six months in the year one, and we add that to the last year. So we are going to have one extra year in the end. And we are going to have, add this six months to these-- we are going to have this extra year with only six months.

Again, the summation here is exactly $100,000, and the summation here is exactly $100,000. Please note that with half-year convention, we have one more year, here. So if you want to apply this half-year convention straight line depreciation to our spreadsheet, we come back here. We are going to have one more extra year, here.

So we divide this by 2, which we are going to have $10,000 here. And we are going to have this $100,000 divided by 5, divided by 2, here. Again, if I calculate the summation here, it should be exactly same as $100,000.

We go back here to this depreciation. We can see it is updated from here, but because we are going to have one more year, I need to apply this to one more year. And here, I'm going to apply, add that to, one more year, here. So we have six months less, here, but we have one more year, here, with extra six months.

Credit: Farid Tayari

2. Declining Balance Depreciation

This method is also called “exponential depreciation” and calculates the depreciation based on constant rate (instead of constant amount as the case for straight line depreciation). This method is not allowed in United States, but in some other countries companies can use it. In this method, a constant declining rate is multiplied by Adjusted Basis to calculate each year’s depreciation. And the Adjusted Basis equals residual book value of the asset (cost - cumulative depreciation previously taken).

Declining Balance Depreciation Per Year=(Declining Rate)*(Adjusted Basis)

While for any depreciation method,

Adjusted Basis=Cost or Other BasisCumulative Depreciation Previously Taken
Equation 7-4

For example, if the declining rate is 0.25 and the asset is purchased at $100.

First year deprecation=0.25*$100=$25Second year adjusted basis would be $100$25=$75 and deprecation=0.25*$75=$18.75Third year adjusted basis would be $75$18.75=$56.25 and deprecation=0.25*$56.25=$14.06Fourth year adjusted basis would be $56.25$14.06=$42.19 and deprecation=0.25*($42.2)=*($10.55)

Some governments announce the declining balance rate as a percentage that needs to be multiplied by 1/n (n is the depreciation life) to give the declining rate. For example, if an asset has the depreciation life of 5 years and the government announces 150% declining balance rate, then the declining curve would be 1.5/5= 0.3.

Example 7-5:

Calculate the depreciation in Example 7-3, assuming declining balance depreciation method, declining balance rate of 150%, and depreciation life of 5 years.

Since depreciation life is considered 5 years, then declining rate equals 150%/5 = 0.3 so depreciation can be calculated as:

Adjusted basis and declining balance depreciation by year
Year Adjusted Basis Declining Balance Depreciation
1 $100,000 0.3*$100,000=$30,000
2 $100,000$30,000=$70,000 0.3*$70,000=$21,000
3 $70,000$21,000=$49,000 0.3*$49,000=$14,700
4 $49,000$14,700=$34,300 0.3*$34,300=$10,290
5 $34,300$10,290=$24,010 0.3*$24,010=$7,203
Total                                                                                     83,193

As you can see, the last row shows that total of $83,193 is less than the capital spent on the property ($100,000). Thus in this method asset will not be fully depreciated.

Please watch the following video (15:34): Declining Balance Depreciation Method.

Declining Balance Depreciation Method
Click for the transcript of Declining Balance Depreciation Method Video

PRESENTER: In the previous videos, I explained that investors can recover some types of their investments using tax deductions. Tax deductions are categorized in two main groups-- investment costs that can be expensed and investment costs that can be capitalized. Time is the only difference between these two categories.

If a cost can be deducted from revenue in full amount as tax deduction in the year that it has happened, the cost is expensed. Costs such as operating costs can be in this category. If a cost has to be deducted from revenue as tax deduction in more than one year, it is called capitalized, such as money that is paid for machinery, building, and so on. Things that generally lose their value over time are allowed to be in this category.

Then in the previous video, I explained the depreciation as one method that we can capitalize on investment cost. And as I explained in the previous video, there are four major methods of depreciation. I explained the straight line and the straight line half year convention in the previous video. And in this video, I'm going to describe the second method, which is declining balance depreciation method.

Declining balance depreciation is also called exponential depreciation. This method is not used and allowed in the United States. But the modified versions of this method are widely used. So we're going to learn this method first, because the other methods are based on the declining balance depreciation. So declining balance depreciation considers a constant depreciation rate. In the straight line, the depreciation was constant.

Here, for the declining balance, the depreciation rate is constant over the years. So in this method, we multiply the constant declining rate by the adjusted base. Let's work on this example to see how the declining balance depreciation works. In this example, we assume the declining rate is 25%, and the asset is purchased at $100 with no salvage value.

So the residual book value for year one includes $100 minus a salvage value of zero. So we are going to have $100 of residual book value for year one. In order to calculate the depreciation for year one, we multiply the rate of 25% by the $100. And we're going to get $25 of depreciation for year one.

For the second year, we deducted the depreciation rate from $100. And we are going to have the adjusted base of $75 for year two. We multiply that by 25%. And we get $18.75 of depreciation for year two.

For year three, we need to calculate the adjusted base first. In order to calculate the adjusted basis, with deduct the depreciation of the previous year from the adjusted base of the previous year to calculate the adjusted base for year three.

So $75 is the adjusted base in year two. And the $18.75 is the depreciation at year two. And it is going to be equal to $56.25. We multiply that by the declining rate, which is constant over the rate over the years. And we are going to have $14.06 of depreciation for year three.

For the year four, we follow the same method-- adjusted base of previous year minus the depreciation of the previous year. And it is going to give us $42.19 of adjusted base for year four. We multiply that by the declining rate depreciation rate, and we get $10.55 for depreciation for year four.

So here we calculated the depreciation just for four years. Some countries announce the declining balance rate as a percentage that has to be divided by the number of years, by the depreciation life, n, to calculate the declining rate per year. For example, if the asset can be depreciated over the lifetime of five years, and the government announced a 150% of declining balance rate, to calculate a declining rate per year, we just need to divide the 150% by the 5.

Let's work on another example. In the previous video, I calculated the depreciation for an asset that was purchased at $100,000 with the salvage value of 0, using the straight line appreciation method. In this example, I'm going to calculate the depreciation using the declining balance method. And I'm going to consider declining balance rate of 150% and depreciation life of five years.

So the first thing that we have to do is we have to calculate the declining rate per year. So we divide the 150% by the five years of the depreciation life. And we are going to get 30% of depreciation rate per year.

So to calculate the depreciation for the first year, we multiply the adjusted base, which was $100,000, by the declining rate that we have, 30%. And we are going to get $30,000 of depreciation for year one.

For year two, we need to deduct the depreciation of the previous year from the adjusted basis of the previous year, so $100,000 of the adjusted base at year one minus $30,000-- the depreciation at year one-- equals $70,000. And this is the adjusted basis at year two. We multiply that by the declining balance of 30%. This is the constant rate. And we are going to get $25,000 of depreciation for year two.

For year tree, $49,000 of adjusted base for year three-- we multiplied that by the declining rate and $14,700 of depreciation for year three. We follow the same method for year four-- adjusted basis of the previous year minus the depreciation of the previous year. It gives us the adjusted base for year four. We multiply that by the depreciation rate per year. And we calculate the depreciation. And for year five.

So one very important thing here to notice is the cumulative depreciation here-- the summation of all the appreciations from year one to year five-- is less than the depreciable value, which was $100,000. So in this matter, the asset is not fully depreciated. And for the straight line method, for the straight line depreciation method, we fully depreciated the asset.

So we had $20,000 of depreciation at each year. And the summation was $100,000. But in this method, the money that the investor gets is less than the money spent on the asset. But this method is very fast. The investor gets the biggest portion of the money very quickly. As you can see here, almost 50% of the depreciated value is received as tax deduction in the first two years.

So let's work on this example on an Excel spreadsheet and see how we can formulate these kind of examples, these kind of problems, using a spreadsheet. So in this spreadsheet, we can see the previous example that we had half year convention straight line depreciation. So I'm just going to delete these and apply the declining balance rate. So depreciation equals--

So the declining rate per year equals the 150% divided by five years of depreciation [? lifetime. ?] And we are going to have that 30% of depreciation rate or declining rate per year. So here I'm going to use vertical formatting this time-- year adjusted base here and depreciation. One, two, three, four, five.

So adjusted base for year one equals $100,000. So the depreciation equals adjusted base, multiply the declining rate. So we are going to have $30,000 of depreciation for year one.

For year two, in order to calculate the adjusted base, I need to deduct the depreciation of the previous year from the adjusted base of the previous year. So adjusted base equals $100,000 minus depreciation of the previous year. And the appreciation for year two equals the adjusted base, multiply the declining rate.

For year three, adjusted base of the previous year minus the depreciation of the previous year. And depreciation equals adjusted base, multiply the declining rate per year. And we do this for year four and year five.

Again, here very important thing to note is the summation of all these depreciation in the declining balance rate method is less than $100,000. So I calculate this summation.

So we can see the summation is less than the $100,000 of capital cost. And now, I enter these depreciations to the cash flow. So year to the before-tax cash flow. So depreciation for year one equals minus this number. Depreciation for year two equals $21,000 that I calculated, depreciation for year three and so on to year four.

And you can see-- because I have already everything set up, the depreciation is going to be updated after I calculated the net income. They are going to be exactly the same and with a positive sign. And there is nothing here, so we'll just end.

Credit: Farid Tayari

3. Declining Balance Switching to Straight Line

In this method, depreciation is calculated using declining balance for early years and then switches to the straight line method. It is desirable to switch to straight line from declining balance in the year when you will get an equal or larger deduction by switching. This occurs when the straight line rate equals or exceeds the declining balance rate, because when you switch, the remaining basis is depreciated by straight line method over the remaining years of depreciation life.

Example 7-6:

Calculate the depreciation in Example 7-3, applying declining balance depreciation switching to straight line method for declining balance rate of 150% and depreciation life of 10 years.

Depreciation life is considered 10 year, then declining rate equals 150%/10 = 0.15.

Here, it’s more economically desirable to switch to the straight line method after the fourth year, because the annual depreciation will be higher when switching from declining balance to straight line.

Adusted basis and declining balance depreciation by method and year
Year Method Adjusted Basis Declining Balance Depreciation
1 DB $100,000 0.15*$100,000=$15,000
2 DB $100,000$15,000=$85,000 0.15*$80,000=$12,750
3 DB $85,000$12,750=$72,250 0.15*$80,000=$12,750
4 DB $72,250-$10,837.5=$61,412.5 0.15*$61,412.5=$9,211.9
5 SL $61,412.5$9211.9=$52,200.6 $52,200.6/6=$8700.1
6 SL $52,200.6 $8700.1
7 SL $52,200.6 $8700.1
8 SL $52,200.6 $8700.1
9 SL $52,200.6 $8700.1
10 SL $52,200.6 $8700.1

To find out which year is better to switch, we can draw a table that includes straight line calculations for each year and compare it with declining balance. The year that has the higher depreciation for straight line than declining balance is the best year to switch. The grey row in following table indicates this year.

Adjusted Basis an Deling Balance Depreciation with Straight Line Depreciation by Year
Year Adjusted Basis Declining Balance Depreciation Straight Line Depreciation
1 $100,000 0.15*$100,000=$15,000 $100,000/10=$10,000
2 $100,000$15,000=$85,000 0.15*$80,000=$12,750 $85,000/9=$9,444.4
3 $85,000-$12,750=$72,250 0.15*$72,250=$10,837.5 $72,250/8=$9,031.3
4 $72,250-$10,837.5=$61,412.5 0.15*$61,412.5=$9,211.9 $61,412.5/7=$8,773.2
5 $61,412.5-$9211.9=$52,200.6 0.15*$52,200.6=$7,830.1 $52,200.6/6=$8700.1
6 $52,200.6-$7,830.1=$44,370.5 0.15*$44,370.5=$6,655.6 $44,370.5/5=$8,874.1
7 $44,370.5-$6,655.6=$37714.9 0.15*$37714.9=$5,657.2 $37714.9/4=$9,428.7
8 $37714.9-$5,657.2=$32,057.7 0.15*$32,057.7=$4,808.7 $32,057.7/3=$10,685.9
9 $32,057.7-$3,355.4=$27,249.1 0.15*$27,249.1=$4,087.4 $27,249.1/2=$13,624.5
10 $27,249.1-$2,684.4=$23,161.7 0.15*$23,161.7= $3,474.3 $23,161.7/1=$23,161.7

Please watch the following video (20:50): Declining Balance Switching to Straight Line Depreciation Method.

Declining Balance Switching to Straight Line Depreciation Method
Click for the transcript of Declining Balance Switching Video

PRESENTER: In the previous videos, I explained that investors can recover some types of their investments using the tax deductions. Tax deductions are categorized into two main categories-- investment costs that can be expensed and investment costs that can be capitalized. Time is the only difference between two categories.

If a cost can be deducted from revenue in full amount as tax deduction in the year that it has happened, the cost is expensed. Costs such as operating costs are in this category. And if a cost has to be deducted from revenue in more than one year as tax deduction, it is called capitalizing the cost. Investment costs such as money paid for machinery, building, equipment, and so on are in this category.

And also in previous videos, I explained the depreciation as one method that we can capitalize some types of investment costs. There are four major methods for depreciation-- straight line, declining balance, declining balance switching to straight line, and MACRS or modified accelerated cost recovery system. I explained the first two in the previous videos, and I'm going to explain the declining balance switching to straight line and modified accelerated cost recovery in this video.

So the third method to calculate the depreciation is called declining balance switching to straight line. In this method, for early years, we use the declining balance rate, and for later years we switch to the straight line method. So in this method, we switch from declining balance to straight line depreciation method. When the straight line becomes higher, gives us the higher depreciation than the declining balance in later years.

So let's work on an example and see how we can calculate the depreciation using this method. So we are going to work on the same example, but we are going to consider the depreciation life of 10 years and the declining balance rate of 150%. So we calculate the depreciation for 10 years.

Again, the first thing that we have to calculate is calculating the declining rate per year, which we divide the 150% of declining balance rate by the 10 years of depreciation life. And we are going to get 15% of depreciation or declining rate per year. So we calculate a declining balance depreciation for each share. We learned this method in previous video.

For year 1, the adjusted base equals $100,000, because the asset is purchased at $100,000. And the salvage value was 0. So the adjusted base is $100,000, and the depreciation for year 1 equals the adjusted base at year 1, multiply the depreciation rate or declining rate. And we are going to have $15,000 of depreciation for year 1.

For year 2, we need to calculate that adjusted base first. Adjusted base for year 2 equals the adjusted base for previous year minus the depreciation for previous year. So $100,000 minus $15,000 equals $85,000. And it is the adjusted base for year 2. In order to calculate the depreciation for year 2, we multiply the declining rate or depreciation rate by the adjusted base that we just calculated. And we are going to have $12,750 year 2.

For year 3, to calculate the adjusted base, we deduct the depreciation of the previous year from the adjusted base of the previous year. And we are going to have $85,000, which was the adulated base of year 2 minus the depreciation of the year 2 And we are going to have $72,250 for adjusted base for year 3. And the depreciation, which is going to be the adjusted base, multiply the depreciation rate. And this is the depreciation for year 3.

And we follow the same method for all the years, and we calculate the depreciation to year 10. So in the third column, we calculate the depreciation using the straight line. And to calculate the straight line, we use the adjusted base on that year. So for this straight line, we know that the depreciation is constant for every year. So in this row, we calculate the depreciation for 10 years using the appreciable value of this asset, which was $100,000. And we depreciate it for 10 years. And we are going to have $10,000 of depreciation per year.

For year 2, we need to use whatever is left over. So we have $85,000 of the value of the asset to be depreciated. And we have nine more years. So using this straight line, we are going to divide the $85,000 by 9, and we are going to have $9,444 of depreciation for year 2 using the straight line.

For year 3, again, we use the adjusted balance at year 3. And there are eight years left. So we divide them, and we get the depreciation for year 3 using the straight line. For year 4, we follow the same method. The adjusted base for year 4 that we have it here-- we calculate it here-- divided by the leftover years.

We have seven more years to depreciate these assets. And we divide the adjusted base by the years that are left over. And so on, and we calculate it to the year 10. For year 10, this $23,162 is the adjusted base that we calculated at year 10. And we have just one more year of depreciation, which is the year 10. And we are going to have this amount for depreciation at year 10.

So in the next step, we have to compare these two columns and find the earliest year that the straight line depreciation gives us higher rate than declining balance depreciation. So as we can see here, until year 4, everything in this column is higher than this column. Starting from year 5, straight line depreciation gives us higher depreciation than the declining balance depreciation.

So the year 5 is the year that we switch from the declining balance depreciation to the straight line depreciation. So the depreciation is going to be $15,000, $12,750 $10,838, $9,212, and for the fifth year, we are going to have $8,700 and so on. In the first and second column, I wrote the declining balance depreciation and straight line depreciation. So as we can see here, year 5 is the earliest year that the straight line depreciation gives us higher depreciation than declining balance depreciation.

So in this year, we switch from declining balance to the straight line. So before year 5, we are going to have depreciation calculated from the declining balance. I wrote that in the last column. And at year 5, we switch from declining balance to the straight line. So we are going to have $8,700 of depreciation at year 5 based on the straight line depreciation method.

So please note that this is the depreciation that we calculated based on the declining balance for year 1 in the column 1. Year 2 is the depreciation based on declining balance for year 2, year 3, and year 4. And year 5 is the year that we switch to the straight line depreciation.

So we are going to have the constant depreciation for remaining years from year 5 to year 10. And, again, please note that this depreciation is calculated based on the adjusted base and the remaining years. Another important thing about the declining balance switching to straight line is the summation of this depreciation from year 1 to year 10 equals the depreciable value of the asset, which was $100,000.

So let's use Excel spreadsheet to formulate this problem and see how we can use a spreadsheet to calculate the depreciation using the declining balance switching to straight line method. So declining balance rate was 150%, depreciation life 10 years. Capital cost was $100,000 and 0 salvage value. The first thing we have to do is calculating depreciation rate, which is we have to divide this 150% by the 10% of depreciation life. So we are going to have 15% of depreciation rate or decline rate per year.

So we have 10 years of depreciation. So I just write this 10 years here. The adjusted base for year 1 equals the capital cost, because the salvage value is 0. Declining balance equals adjusted base, multiply the depreciation rate per year. And because this is constant for all the 10 years, I fix this number-- this cell.

Adjusted base for year 2 equals the previous year adjusted base minus the depreciation that we calculated for the previous year. And the depreciation for year 2 equals adjusted base, multiply the depreciation rate. And I fix this cell.

So because I'm following the same equation for all the years, I can apply this to the other year. So this is going to be the adjusted base minus the depreciation for the previous year. And I will do the same for this one, because I fixed the depreciation rate. So Excel is going to read the depreciation from this cell, and it is going to read the adjusted base from this cell. So I can continue this and calculate these one by one or I can just apply these to the later years and apply these to the following years.

So this is the depreciation rate for 10 years using the declining balance. Now I will have to calculate the straight line depreciation. So please note that for each year, I need to use whatever is left-- the years that are left and the depreciable value that is left.

For example, for the year 1, I have $100,000 and 10 years to be depreciated. So I will just divide $100,000, which is here-- I just read it from here-- the number of years, 10. And I'm going to have $10,000 per year of depreciation. So this cell is going to give me the depreciation for each year. Because this is a straight line, it is constant for every year.

So for the second cell, I will use the leftover, the appreciable value of the asset, which is this $85,000, because we already received this $15,000 of depreciation as tax deduction for year 1. And we are going to have nine more years. So I'm going to formulate this in a way that I can just apply that to the other years. So I will use this depreciation life. I will fix it minus the year and plus 1, because this is the year 2. But I need to consider the year 2 as well.

So this is going to give me the depreciation if I use the straight line. And again, this is constant for nine years. So from year 9, from year 2 to year 10, including year 2, the depreciation is going to be $9,444 if I use the straight line. And I can apply these to the other years, because I use the same equation. And for example, here for year 3 I use the adjusted base that I just calculated here. And this is the leftover depreciable value of the asset divided by eight years. So I have this 10 year minus 3, which is 7, plus 1, and it gives me 8. And so on to year 10.

So the next step is going to be comparing this column with this column. So the earliest year that the straight line depreciation method gives me higher depreciation than the declining balance is the year that I have to switch. So as we can see here, year 5 is the first year that straight line is higher than the declining balance. So I'll just highlight this.

So in the next step, I'm going to write the depreciation here. For the first year, the declining balance is giving me higher rates, for the second year as well, and year 3 and year 4. But for the year 5, year 5 is the first year that this straight line is going to be higher than the declining balance. So I will have $8,700 of straight line for the depreciation for year 5 and so on.

So please note that this number means if you depreciate the left over depreciable value of $52,200 of adjusted base for six more years for the leftover-- six more years-- you're going to have $8,700 per year. So this is going to be constant for six years.

So from here after, I will switch to straight line and for every year this number is going to be constant and equal to $8,700 for each year. So for the sixth year, I'm going to have the same. For the seventh year, I'm going to have the same. For the eighth year, I'm going to have the same. Or what I could do here is I could just fix the row number here and apply this to the other years.

So please note that very important thing here to know is in this method, the summation of all these depreciation per year for each year, the summation-- the cumulative depreciation-- should be exactly equal to the $100,000 of capital cost.

So to double-check your calculations, calculate the summation, and it must be equal to $100,000. So let's check and, yes, this is correct and $100,000 of total. So the asset is fully depreciated, and the investor receives the entire value of depreciable value of $100,000 over 10 years.

Credit: Farid Tayari

4. Modified Accelerated Cost Recovery Systems (MACRS)

This is a popular method in United States to recover the cost of most intangible depreciable assets. MACRS depreciation methods for personal property include 200% and 150% declining balance switching to straight line. U.S. Internal Revenue Service (IRS) publishes tables that indicate the deprecation allowance for different depreciation lifetime and different property types.

Example 7-7:

Calculate the depreciation in Example 7-3, Modified Accelerated Cost Recovery Systems (MACRS) for 5-year half-year convention, starting from year 1.

In order to calculate the depreciation for each year, depreciation rate can be read from table A-1 and then multiplied by the investment cost of $100,000:

Depreciation rates by year
Year MACRS 5-year half-year Depreciation Rate Declining Balance Depreciation
1 20% 0.2*$100,000=$20,000
2 32% 0.32*$100,000=$32,000
3 19.2% 0.192*$100,000=$19,200
4 11.52% 0.1152*$100,000=$11,520
5 11.52% 0.1152*$100,000=$11,520
6 5.76% 0.0576*$100,000=$5,760
Total = $100,000

Note that, since question and table are for half-year convention, the deprecation is distributed over 6 years.

Please watch the following video (6:37): Modified Accelerated Cost Recovery Systems (MACRS) Depreciation Method.

Modified Accelerated Cost Recovery System (MACRS)
Click for the transcript of MACRS Video

In the previous videos, I explain depreciation and I described that there are four main methods to calculate depreciation. In the three previous videos, I explained this straight line, declining balance, and declining balance switching to a straight line. And in this video, I'm going to talk about modified accelerated cost recovery system, or MACRS.

The fourth method of calculating depreciation is called modified accelerated cost recovery system, or MACRS, and it is a very popular method in the United States to recover cost of most intangible depreciable assets. So MACRS is actually a declining balance switching to straight line method that considers half year convention. But the good thing about this method is rates are calculated in the standard tables, and they are in the IRS website.

So if you search the IRS website and look for table A-1 that includes the MACRS rates, you will find this page and you will find this table. This is the address, the web address here that I will provide in the comments section. And this is the table A-1. So these columns are including the standard rates. For example, if you are considering the projects, the depreciation life three years, these are the rates that you have to apply. And because this is half-year convention, we are going to have four years. And this is if we have the depreciation life of five years, depreciation life of seven years, depreciation life of 10 years, and so on.

So again, as you can see here, because this is half-year convention so everything is shift forward for six months. So the first year has just six months of depreciation. And you can see this is the first year that we are switching from declining balance to the straight line. And again, because this is half convention, the last year is just considering six months of depreciation. So this rate is half of the year before.

So again, one thing to remember here, this column includes the MACRS for a seven year half year convention. But because this is half-year convention, we're going to have actually eight years for an eight rate for depreciation. This is 10 years. Please consider that we are going to have 11 years of depreciation. So if you are having a question that asks you to use the 10 years table, and you are going to have, let's say, eight years of depreciation, or nine years of depreciation, what you can do is you follow these rates for year 1, 2, 3, 4, 5, 6, 7, and 8. And for the rest, let's say you are going to have eight years of depreciation. For year 8, you will add up these later years, year 11, year 10, year 9, and year 8, all this four, and put that four year 8 to make sure the summation is 100%.

So year 1 is the same, 2, 3, 4, so on. For year 8, you will put the summation of year 8 to year 11. You put the summation of all these eight numbers. So if you are using the seven years-- another example. If you're using the 7 years column, 7 years of depreciation life, but you're just going to have, let's say, four years, this is a rate for year 1, year 2, year 3. For the year 4, you will add the other numbers and add that to year 4. So you will add these 12.49 plus this, plus this, plus this, and plus this, and you add that for year 4.

So let's work on this example. The example that we worked before. The asset is purchased at $100,000 with 0 salvage value. And we are going to have to use the five year half-year convention for calculating the depreciation for this asset. So we will go to the table. This is a five-year column. So we just read the rates-- 20%, 32, 19.2, and so on. And we extract these rates and we write them here. And the rest is very easy. We just multiply the depreciable value, which was $100,000, with the rates. And these are the depreciation that we get for each year. And again, this method, because it is based on the declining balance, which includes straight line, the summation should be exactly equal to 100,000 of depreciable value. For year 1, be multiply the depreciable value by the rate that we read from table. And again, we are going to have six years of depreciation.

If the question asks us to specifically have five years, we just add this sixth year to the fifth year. And we just add these two, and we make sure the summation is $100,000.

Credit: Farid Tayari

Italicized sections are from Stermole, F.J., Stermole, J.M. (2014) Economic Evaluation and Investment Decision Methods, 14 edition. Lakewood, Colorado: Investment Evaluations Co.