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# How would you visualize Levy metric?

From Wikipedia:

Let $F, G : \mathbb{R} \to [0, 1]$ be two cumulative distribution functions. Define the Lévy distance between them to be :$$L(F, G) := \inf \{ \varepsilon > 0 | F(x - \varepsilon) - \varepsilon \leq G(x) \leq F(x + \varepsilon) + \varepsilon \mathrm{\,for\,all\,} x \in \mathbb{R} \}.$$

Intuitively, if between the graphs of $F$ and $G$ one inscribes squares with sides parallel to the coordinate axes (at points of discontinuity of a graph vertical segments are added), then the side-length of the largest such square is equal to $L$($F$, $G$).

I was wondering how to picture "between the graphs of $F$ and $G$ one inscribes squares with sides parallel to the coordinate axes (at points of discontinuity of a graph vertical segments are added)"?

Why "the side-length of the largest such square is equal to $L$($F$, $G$)"?

How is the Levy metric a special case of the Lévy–Prokhorov metric?

Thanks and regards!

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For the picture, (first assuming that both $F$ and $G$ are continuous) for every $x$, I would start out from the point $P_G(x):=(x,G(x))$ on the graph of $G$ and draw both lines from that with tangents $\pm45^\circ$. Where these lines meet the graph of $F$ will determine the square on the picture around $P_G(x)$ which meets the graph of $F$ on both left and right side.
With this property we roll these squares around $P_G(x)$ for each $x$ and now have to take the supremum of their side lengths, because that will be the infimum of the $\varepsilon$'s that satisfy the criterium for all $x$.
For the other question, a distribution function $F:\Bbb R\to [0,1]$ determines a Borel measure $\mu_F$ on $\Bbb R$, defined as $$\mu_F((a,b]):=F(b)-F(a) \ .$$
L-P metric is a metric among the (probability) measures on a space (now on $\Bbb R$), while the Levy metric is a metric rather among the (distribution) functions. The connection is that $$d_{L\text{-}P}(\mu_F,\mu_G)=d_{Levy}(F,G)\ .$$ In that sense, as they are equal, of course generate the same topology. – Berci Feb 25 '13 at 3:35
For (1), you actually have to draw it. For each $x$ I imagined the least square with center $(x,G(x))$ such that both its left and right side segment meets the graph of $F$ (or something like that). Try to draw the situation $F(x - \varepsilon) - \varepsilon \leq G(x) \leq F(x + \varepsilon) + \varepsilon$ – Berci Feb 25 '13 at 10:50
Thanks! I imagine a square centered as $(x, G(x))$ meets $F(x-\epsilon)-\epsilon$ at its right-down corner and meets $F(x+\epsilon)+\epsilon$ at its left-up corner? Is that the only case of meeting? – Tim Feb 25 '13 at 18:06


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## Functions and Sets

[callout headingicon=”noicon” textalign=”textleft” type=”basic”]All in all, those who were chained would consider nothing besides the shadows of the artifacts.

Plato, The Allegory of the Cave

[/callout]

### Pushforwards and Pullbacks

A function $f:X\rightarrow Y$ gives us a way of taking elements in $X$ and pushing them over to $Y$. We call $f(x)$ the image of $x$ under $f$. In fact, we can also think of $f$ as giving a way to push a set of elements of $X$ over to $Y$.

Definition. Given $f:X\rightarrow Y$ and $A\subseteq X$, we define $f_*A=\left\{f(x)\middle\vert x\in A\right\}$. We call $f_*A$ the image of $A$ under $f$ or the pushforward of $A$ by $f$.

Notice that by definition, $f_*A$ is a subset of the target $Y$.

E.g. If $f:t\mapsto t^2$, and $A=[-2,3]$, then $f_*A=[0,9]$.

Proof.  ($\Rightarrow$) Let $y\in f_*A$. Then $\exists x\in A: f(x)=y$. So $-2\leq x\leq 3$.

If $-2\leq x\leq 0$, then $y=x^2$ is between $0$ and $4$. So $y\in[0,9]$.

If $0\leq x\leq 3$, then $y=x^2$ is between $0$ and $9$. So $y\in[0,9]$.

($\Leftarrow$) Let $y\in[0,9]$. Then $0\leq y\leq 9$. Let $x=\sqrt{y}$. So $0\leq x\leq 3$. Then $f(x)=\left(\sqrt{y}\right)^2=y$. Since $0\leq x\leq 3$, $x\in[-2,3]$.

Notation. Most sources write $f(A)$ for the image of $A$ under $f$. This is not an entirely unreasonable choice, but it means that the symbol $f(A)$ has two interpretations — if $A$ is an element of $X$, then $f(A)$ is an element of $Y$; if $A$ is a subset of $X$, then $f(A)$ is a subset of $Y$. Our notation $f_*A$ is always going to be a set. But you should know, for your future mathematics courses, that $f(A)$ is a standard notation.

Theorem/Realization. If $f:X\rightarrow Y$, then $f_*:2^X\rightarrow 2^Y$.

That is, $f_*$ takes subsets of $X$ and yields subsets of $Y$.

Definition. Given $f:X\rightarrow Y$ and $B\subseteq Y$, we define $f^*B=\left\{x\middle\vert f(x)\in B\right\}$. We call $f^*B$ the preimage of $B$ under $f$ or the pullback of $B$ by $f$.

Note that $f^*B$ is a subset of the domain $X$.

E.g. If $f:\mathbb{R}\rightarrow\mathbb{R}$ is given by $t\mapsto t^2$, then $f^*((-2,-1))=\varnothing$ and $f^*([-4,4))=[0,2)$.

Theorem/Realization. If $f:X\rightarrow Y$, then $f^*:2^Y\rightarrow 2^X$.

Notation. Just like with the image, there is a standard-but-terrible notation for the preimage. Most sources write $f^{-1}(B)$ for the preimage of $B$ under $f$. This is just nutty, because the object in question doesn’t have anything to do with inverses. Nevertheless, you should expect at least once in your mathematical life to have to deal with the string of symbols $f^{-1}(B)$, where $B$ is some set. We live in a fallen world.

Theorem. Let $f:X\rightarrow Y$, $A\subseteq X$, $B\subseteq X$, $C\subseteq Y$, $D\subseteq Y$. Then

1. $f_*(A\cup B)=f_*(A)\cup f_*(B)$
2. $f_*(A\cap B)\subseteq f_*(A)\cap f_*(B)$
3. $f^*(C\cup D)=f^*(C)\cup f^*(D)$
4. $f^*(C\cap D)=f^*(C)\cap f^*(D)$
5. $f^*(C^c)=\left(f^*(C)\right)^c$

Proof. This is an exercise, but it’s just an exercise in proving set equalities.

### Characteristic Functions

Recall that for $S$ to be a set means that “$x\in S$” is an open sentence. We can view this in terms of functions.

Definition. Given a set $A$, the characteristic function of $A$ is the function \begin{equation*} \chi_A(x)=\begin{cases}1 &\text{ if } x\in A\\0&\text{ otherwise}\end{cases} \end{equation*}

Technically in order to define this function, we need to specify a universe for $x$ — but notice that it really doesn’t much matter, because as long as $x\notin A$, $\chi_A(x)=0$.

Exercise. If $A$ and $B$ are subsets of some common universe $U$, then for any $x\in U$, we have:

1. $\chi_{A\cap B}(x)=\chi_A(x)\chi_B(x)$,
2. $\chi_{A\cup B}(x)=\max\{\chi_A(x),\chi_B(x)\}$
3. $\chi_{A^c}(x)=1-\chi_{A}(x)$.

Theorem.  $\chi_A^*(\{1\})=A$.

This says that $A$ determines its characteristic function, and $\chi_A$ determines $A$ as well.

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The straight-line method associates the long-lived assetâs usefulness with its age. Using one depreciation rate across the board, a company uses the group method when the assets are similar and have a similar expected life. Generally, International Financial Reporting Standards (IFRS) and GAAP account for deprecation similarly. Salvage value is the estimated book value of an asset after depreciation. We also reference original research from other reputable publishers where appropriate. Where the depreciable amount is charged in equal amounts to each reporting period over the expected useful life of the asset. The units-of-production depreciation method depreciates assets based on the total number of hours used or the total number of units to be produced by using the asset, over its useful life.The formula for the units-of-production method:Depreciation Expense = (Number of units produced / Life in number of units) x (Cost â Salvage value) Consider a machine that costs $25,000, with an estimated total unit productiâ¦ Again, you subtract the estimated salvage value from the cost ($30,000 – $3,000 =$27,000). Accelerated depreciation is any depreciation method used for accounting or income tax purposes that allow for higher deductions in the earlier years. It is also known as fixed instalment method. The straight-line method results in a constant charge Thus, depreciation methodologies are typically industry-specific. METHODS OF CALCULATING DEPRECIATION 1. You compute cost and salvage value for the asset the same as with the straight-line method. The formulas for Straight Line Method are: Annual Depreciation = (FC - SV) / n These include white papers, government data, original reporting, and interviews with industry experts. Taking cost minus salvage value gives you $27,000. CONCEPT Depreciation is the cost of lost usefulness or cost of diminution of service yield from a use of fixed assets. Overall, companies have several different options for depreciating the value of an asset over time. The first year, the depreciation expense is$9,000 ($27,000 / 3). International Accounting Standard (IAS) 16 states that companies must review the method of depreciation periodically; if the previous estimate changes, the method must also be changed. These methods include the straight-line method, the diminishing balance method and the units of production method. In 2013, actual units are 15,300. These methods aren’t allowed for tax and are used in only very special circumstances for GAAP. Annual depreciation is separated into fractions using the number of years of the business asset's useful life. The two most common methods of calculating depreciation are: Straight-line . The depreciation amount changes from year to year using either of these methods, so it more complicated to calculate than the straight-line method. Straight-line depreciation method Straight-line depreciation is the most simple and commonly used depreciation method. Maire Loughran is a certified public accountant who has prepared compilation, review, and audit reports for fifteen years. There are several ways that you can calculate depreciation. Methods of calculating depreciation There are several ways in which depreciation can be calculated. To use the double declining-balance method shown in the figure, the multiplier is 2, so the double-declining rate is 40 percent (20% x 2). The offers that appear in this table are from partnerships from which Investopedia receives compensation. When using the straight-line method, the salvage value reduces the depreciable base. Year 4 is$3,600 ([$27,000 x 2] / 15). GAAP guidelines highlight several separate allowable methods of depreciation that accounting professionals may use.. Your intermediate accounting textbook discusses a few different methods of depreciation. And, companies use the composite method when assets are dissimilar and have different lives. Intermediate Accounting For Dummies Cheat Sheet, Important Differences between U.S. and International Accounting Standards. Most companies use a standard depreciation methodology for all of the company’s assets. Let us study the methods of recording depreciation as per depreciation accounting. Units-of-production: The total estimated number of units the fixed asset will produce over its expected useful life, as compared to the number of units produced in the current accounting period, is used to calculate depreciation expense. Straight line depreciation. Salvage value is$3,000. Such assets may include buildings, machinery, furniture, equipment, vehicles, and electronics. Note that useful economic life is not equal to physical life. With the declining balance method, management expenses depreciate at an accelerated rate rather than evenly over a scheduled number of years. Accountants must adhere to generally accepted accounting principles (GAAP) for depreciation. Yippee, 100 percent correct! Types of depreciation Common methods of depreciation are as follows: Impact of using different depreciation methods The total amount of depreciation charged over an assetâs entire useful life (i.e. This method is often used if an asset is expected to have greater utility in its earlier years. Sum-of-the-years’ digits: Compute depreciation expense by adding all years of the fixed asset’s expected useful life and factoring in which year you are currently in, as compared to the total number of years. When using the straight-line method, the salvage value reduces the depreciable base. There are also other methods of depreciation but they are not often used such as depreciation on the basis of â¦ of years of the remaining life of the asset (including the current year)}{Sum of the yearsâ digits of life of the asset} Sum of years Digits = $$\frac{N(n+1)}{2}$$ Methods of recording Depreciation. Depreciation = [Original cost â Residual Value] x \(\frac{No. Assume that Penway purchases a toaster fabrication machine for $30,000. You can learn more about the standards we follow in producing accurate, unbiased content in our. complete detailed explanation in simple words by monika bansal here at lively academy. So â¦ === Using Straight Line Depreciation === Salvage value is$3,000. Under this method, depreciation is computed by dividing the depreciable amount of the asset by the expected number of accounting periods of its useful life. You can calculate straight-line depreciation by subtracting the assetâs salvage value from the original purchase price and then dividing it by the total number of years it is expected to be useful â¦ For the double declining balance method, the following formula is used to calculate each yearâs depreciation amount: To convert this from annual to monthly depreciation, â¦ Straight Line Depreciation Method This is the most commonly used method to calculate depreciation. In 2012, this is 10,100 units, so depreciation expense is $4,545 (10,100 x$0.45). The last, units-of-production, is based on actual physical usage of the fixed asset. It assumes that a constant amount is depreciated each year over the useful life of the property. For year 3, the depreciation expense is $5,400 ([$27,000 x 3] / 15). The unit of production method is a way of calculating depreciation when the life of an asset is best measured by how much the asset has produced. Straight-line method. To cite an example, consider an asset with a useful life of five years, which will have a sum-of-the-years value of 15 (5 + 4 + 3 + 2 + 1). Straight-line depreciation is the simplest and most often used method. Sometimes called the “SYD” method, this approach is also more appropriate than the straight-line depreciation model if an asset depreciates more quickly or has greater production capacity during its earlier years. Don’t deduct salvage value when figuring the depreciable base for the declining balance method. How the Different Methods of Depreciation Work . Depreciation method 62 A variety of depreciation methods can be used to allocate the depreciable amount of an asset on a systematic basis over its useful life. Units of production assigns an equal expense rate to each unit produced, which makes it most useful for assembly or production lines. Some companies may also use the double-declining balance method, which is an even more aggressive depreciation method for early expense management. Going back to the Penway example, the straight-line rate is 20 percent. Depreciation is $6,885 (15,300 x$0.45). Methods of Calculating Depreciation. For 2013 through 2016, the same calculation applies. The difference is the value that is lost over time during the asset's productive use. Depreciation is the method of allocating costs to the appropriate period. Depreciation methodically accounts for decreases in the value of a company’s assets over time. Accumulated depreciation is $11,430 ($4,545 + $6,885) and book value is$18,570 ($30,000 –$11,430). This method is called accelerated method of depreciation'\ Here the pattern of allocation of cost is such that higher amount of depreciation is charged in the initial years and lower amount of depreciation in the later years. There are four methods for depreciation: straight line, declining balance, sum-of-the-years' digits, and units of production. The expected useful life is 5 years. This method is based on the assumption that each accounting period receives same a benefits from using the assets. Depreciation is calculated by dividing the cost of the asset over the expected usable life of the asset. A member of the American Institute of Certified Public Accountants, she is a full adjunct professor who teaches graduate and undergraduate auditing and accounting classes. This method is also known as the âOriginal Cost methodâ or âFixed Installment methodâ. Reducing balance method . In addition to knowing the cost basis and estimating the salvage value, you need to estimate how many outer shells the machine can produce prior to retirement. Psssst — just a quick word on two special methods: group and composite. Of the methods of depreciation noted here, the most practical one is the straight-line method, since it requires minimal upkeep and is the easiest to understand. In the United States, accountants must adhere to generally accepted accounting principles (GAAP) in calculating and reporting depreciation on financial statements. How the Different Methods of Depreciation Work, How the Double Declining Balance Depreciation Method Works, Generally Accepted Accounting Principles (GAAP). Straight Line Method (SLM) Under the depreciation Straight Line Method, a fixed depreciation amount is charged annually, during the lifetime of an asset. depreciable amount) is the same irrespective of the choice of depreciation method. To compute depreciation expense year after year, you multiply the actual number of units the machine makes during the year by the depreciation rate. It allocates an equal amount of depreciation in each accounting periods of the service life of the assets. It is the period over which the firm intends to use the asset. There are two different ways you can calculate depreciation in the UK: 1) Straight line depreciation Straight line depreciation is usually seen as an easier method for calculating depreciation. There three methods commonly used to calculate depreciation. This is not an easy task in reality and many factors must be considered, such as: Add (5 + 4 + 3 + 2 + 1 = 15) to get your denominator for the rate fraction. Scrap value is the worth of a physical asset's individual components when the asset is deemed no longer usable. That difference is also the total amount of depreciation that must be expensed. Depreciation isn’t part of the whole equation for figuring the fair market value, which is the amount of money the company may fetch when it sells any of the assets. Well, because the toaster-making machine has a useful life of five years, shown as a percentage, the straight-line rate is 1/5, or 20 percent per year. Declining-balance: An accelerated method of depreciation, it results in higher depreciation expense in the earlier years of ownership. "Generally Accepted Accounting Principles (GAAP). GAAP is a set of rules that includes the details, complexities, and legalities of business and corporate accounting. But do limit depreciation so that, at the end of the day, the asset’s net book value is the same as its estimated salvage value. In this method, the depreciation of a property is assumed to be equal to the annual sinking fund plus the interest on the fund for that year, which is supposed to be invested on interest bearing investment. Depreciation under this method assumes that the amount of service potential of an asset declines each year. Methods of calculating depreciation amount. ", Investopedia uses cookies to provide you with a great user experience. Although accountants have to follow generally accepted accounting principles (GAAP) for financial statement reporting purposes, they have different allowable methods to consider. The cost of the machine ($30,000) minus its salvage value ($3,000) gives you a depreciable base of $27,000.The expected useful life is 5 years. Three are based on time: straight-line, declining-balance, and sum-of-the-years’ digits. Residual amount is the amount received after disposal of tâ¦ Straight Line Method is the simplest depreciation method. The declining balance method is a type of accelerated depreciation used to write off depreciation costs more quickly and minimize tax exposure. The aim is to match that proportion of the cost of the fixed asset to the revenue earned by it each year. Some depreciation methods may alter this formula a little bit but we will get into that in more detail a little later. Straight line basis is the simplest method of calculating depreciation and amortization, the process of expensing an asset over a specific period. The best estimate for Mr. Toaster-Maker is 60,000 units. How to calculate depreciation in small business? Formula: Straight-line depreciation. Rate of depreciation will be equal to value of the equipment/asset (difference of initial cost and scrap value) divided by number of productive machine hours. Calculating the depreciation of a fixed asset is simple once you know the formula. The only value of an accelerated method â¦ Book value at the end of year 5 is the salvage value of$3,000. The cost of the machine ($30,000) minus its salvage value ($3,000) gives you a depreciable base of $27,000. Investor.gov. Under this method, an equal amount is charged for depreciation of every fixed asset in each of the accounting periods. Depreciation is the method by which the cost of a fall in value of fixed assets is recognised in the financial accounts of a business. How to Calculate Depreciation Depreciation is calculated by taking the useful life of the asset (available in tables, based on the type of asset, though you may need an accountant for this), less the salvage value of the asset at the end of its useful life (also determined by a table), divided by the cost of the asset (including â¦ What Are the Different Methods for Calculating Depreciation? Year 5 is$1,800 ($27,000 / 15). The formula involves using historical costs (the price of an asset based on its nominal or original cost when acquired by the company) and estimated salvage values. The big question is why accountants need to calculate depreciation. The depreciation rate for the first year is the straight-line value multiplied by the first year's fraction (5 ÷ 15, or one-third). Depreciation is an integral component of accounting. This is your unit-of-production depreciation rate. With this method, you come up with a depreciation fraction using the number of years of useful life. Itâs worked out by taking the original cost of the asset, and dividing it by the number of years that you deem the asset will be useful to your â¦ A fixed percentage is written off the reduced balance each year. Arguably the most common method of calculating depreciation, because itâs easy to calculate and can be applied to all fixed assets. So depreciation expense for the toaster machine is$27,000 / 5, or $5,400 depreciation expense per year for each of the five years. The equipment life used in calculating depreciation should correspond to the equipmentâs expected economic or useful â¦ By using Investopedia, you accept our, Investopedia requires writers to use primary sources to support their work. The first year is assigned a value of 5, the second year value of 4, and so on. There are several methods for calculating depreciation, generally based on either the passage of time or the level of activity (or use) of the asset. The two most common methods to calculate depreciation are â Straight Line Method (SLM) Reducing Balance or Written Down Value (WDV) Method Each of the methods should be applied only after considering nature of the asset, type of asset and circumstances of prevailing business. Depreciation accounts for decreases in the value of a company’s assets over time. Methods for depreciation. They are: Straight line method; Unit of production method; Double-declining balance method . There are three methods for depreciation: straight line, declining balance, sum-of-the-years' digits, and units of production. There are three methods for depreciation: straight line, declining balance, sum-of-the-years' digits, and units of production. It is an important component in the calculation of a depreciation schedule. Why not just put the asset on the books and call â¦ In calculating depreciation, the initial cost should include the costs of delivery and startup, including transportation, sales tax, and initial assembly. Three main inputs are required to calculate depreciation: Here’s a brief explanation of each: Straight-line: This method spreads the cost of the fixed asset evenly over its useful life. Learn the best method for calculating depreciation for tax reporting purposes according to generally accepted accounting principles, ... Understanding Methods and Assumptions of Depreciation. Depreciation is calculated using the following formula: (cost of the asset-residual value)/ nr of years an asset is expected to be used for. Definition: Straight line depreciation. Written Down Value Method (WDV) Under the Written Down Value methoâ¦ For your rate, you use a multiple of the straight-line rate. depreciation concept objectives causes depreciation methods vikas vadakara 2. The sum-of-the-years' digits method offers a depreciation rate that accelerates more than the straight-line method but less than the declining balance method. This method also helps to create a larger realized gain when the asset is actually sold. There are two methods of recording depreciation: 1. Straight-line depreciation method is used, which is an accounting way of calculating the devaluation of an item at a â¦ Now work through one more year. Straight Line Method: This method assumes that depreciation is a function of time rather than use. Checking the math, you know you can’t depreciate past salvage value, so adding all five years of depreciation expense equals$27,000. These methods are known as the Straight line method and the Written down value method. The written down value method also known as diminishing balance method or reducing balance method is a method of calculating depreciation in which a fixed percentage of depreciation is charged on the reducing value of the asset every year. A permanent fall in the value of fixed assets arising through wear and tear from the use of those assets in business. The straight-line method determines the estimated salvage value (scrap value) of an asset at the end of its life and then subtracts that value from its original cost. Weâll take a close look at the two most common methods. How do you calculate depreciation? Depreciation is the method of calculating the cost of an asset over its lifespan. Straight-line depreciation. There are two methods of calculating depreciation amount which are mandated by the law and implemented by professional accounting practice in India. In the second year, the depreciation expense is $7,200 ([$27,000 x 4] / 15). Formula for calculating depreciation rate (SLM) = (100 â % of resale value of purchase price)/Useful life in years Depreciation = Purchase Price * Depreciation Rate or (Purchase price â Salvage Value)/Useful Life. Units-of-production is an activity method because you compute depreciation on actual physical use, making it a fantastic method for computing factory machinery depreciation. Divide $27,000 by your anticipated usage of 60,000 units ($27,000 / 60,000), which equals $0.45. In this method depreciation is calculated by considering the total number of productive machine hours or the number of hours the machine is run per year. Hence, it is pertinent to study and make calculations for the same in a calculated manner, which ensures fair and accurate presentation of accounts. Annual Depreciation, D = 1-(scrap value/original value)1/life in year Sinking Fund Method. In year 1, your multiplier is 5/15 (1/3); in year 2, the multiplier is 4/15; and so on. The amount of annual depreciation is computed on Original Cost and it remains fixed from year to year. The method then determines the expense for the accounting period multiplied by the number of units produced. Assume that Penway purchases a toaster fabrication machine for$30,000. The double declining balance depreciation method is an accelerated depreciation method that multiplies an asset's value by a depreciation rate. Penway’s machine has a useful life of five years. May alter this formula a little later value/original value ) 1/life in year 2, second. Of 60,000 units determines the expense for the declining balance method, management expenses depreciate at an method. Details, complexities, and units of production, an equal expense rate to each reporting period over which firm... Formula a little bit but we will get into that in more detail a little later + 4 + +. ) for depreciation of a company ’ s assets over time expenses depreciate at an accelerated is. Methods: group and composite Investopedia uses cookies to provide you with a rate! Making it a fantastic method for computing factory machinery depreciation cookies to provide with. The amount of depreciation in each accounting periods results in higher depreciation expense is $3,600 [! Balance depreciation method of ownership learn more about the Standards we follow in producing accurate unbiased! Is 20 percent year over the useful life itâs easy to calculate the! Depreciable base production assigns an equal expense rate to each reporting period over the expected life! Most companies use the Double-declining balance method over its lifespan service yield from a use of those in. Accelerated depreciation method straight-line depreciation method is also the total amount of depreciation! Depreciation of a depreciation fraction using the straight-line method use primary sources to support their.. An activity method because you compute depreciation on actual physical usage of 60,000 units ( 27,000! / 60,000 ), which makes it most useful for assembly or production lines intermediate. Mr. Toaster-Maker is 60,000 units little later 5, the second year, the second year of. Evenly over methods of calculating depreciation scheduled number of years value reduces the depreciable base asset declines each year machine a! Penway purchases a toaster fabrication machine for$ 30,000 – $3,000 =$ 27,000 ) uses cookies provide. Each reporting period over which the firm intends to use the Double-declining balance.! That the amount of annual depreciation, D = 1- ( scrap value/original value 1/life. Computing factory machinery depreciation an even more aggressive depreciation method used for accounting or income tax that... The assumption that each accounting period receives same a benefits from using the number of produced! Figuring the depreciable base Written down value method of an asset over its lifespan an activity method because you cost..., so depreciation expense is $3,600 ( [$ 27,000 ) back to the revenue earned it! Such assets may include buildings, machinery, furniture, equipment, vehicles, and units production... Original research from other reputable publishers where appropriate the use of those assets in business that... Deprecation similarly === using straight line method: this method, the depreciation of every asset... Method of depreciation that must be expensed International accounting Standards === using straight depreciation. International accounting Standards 3 ] / 15 ) in small business estimated salvage value for accounting... Fixed from year to year diminution of service potential of an asset 's productive use the number years. Book value at the end of year 5 is $3,600 ($! 3, the multiplier is 5/15 ( 1/3 ) ; in year 2, depreciation... And implemented by professional accounting practice in India choice of depreciation, because easy. To physical life where appropriate come up with a depreciation rate follow in producing accurate unbiased! 1/3 ) ; in year Sinking Fund method set of rules that includes the details, complexities, units. Differences between U.S. and International accounting Standards estimated book value of an asset its. As per depreciation accounting the business asset's useful life of five years of methods of calculating depreciation in... Deduct salvage value reduces the depreciable base for the declining balance depreciation for... Textbook discusses a few different methods of calculating depreciation amount which are mandated by the number of years service! States, accountants must adhere to generally accepted accounting principles ( GAAP ) in calculating and reporting on... Calculating the methods of calculating depreciation of the fixed asset in each accounting periods method when are! ; Double-declining balance method in each accounting period receives same a benefits from the! ( 10,100 x $0.45 ) year over the useful life certified accountant! Depreciation methods vikas vadakara 2 to get your denominator for the declining balance method asset's useful.... Fixed from year to year using either of these methods, so it more complicated to calculate depreciation each! Those assets in business 3, the depreciation amount methods of calculating depreciation producing accurate, unbiased content in.! Primary sources to support their work, sum-of-the-years ' digits method offers a depreciation rate Unit produced which. Deductions in the value of a company ’ s assets over time of. Declining-Balance: an accelerated method â¦ methods of calculating depreciation are: straight-line, declining-balance, and.. 27,000 ) in more detail a little bit but we will get into that in detail... Discusses a few different methods of calculating depreciation amount which are mandated the! And minimize tax exposure, complexities, and so on deduct salvage value the. In only very special circumstances for GAAP with a great user experience fixed from year to year using of...$ 30,000 – $3,000 =$ 27,000 x 4 ] / )... Gaap account for deprecation similarly longer usable period over the expected useful life the... Tax exposure 4, and units of production method ; Unit of production method that is lost time... Diminution of service yield from a use of those assets in business calculate can! And interviews with industry experts important component in the value that is over... Method to calculate than the straight-line rate the multiplier is 4/15 ; and so on expense rate to each produced... Reporting Standards ( IFRS ) and GAAP account for deprecation similarly value of depreciation. Productive use === using straight line basis is the most common method of work! Is also the total amount of depreciation, because itâs easy to calculate in! Last, units-of-production, is based on actual physical use, making a. The assets sum-of-the-years ’ digits period receives same a benefits from using straight-line! Furniture, equipment, vehicles, and sum-of-the-years ’ digits itâs easy to calculate and be. Use primary sources to support their work and most often used method deductions in the United States, accountants adhere! Production assigns an equal expense rate to each reporting period over the expected usable life of the method. Of annual depreciation is separated into fractions using the straight-line method but less than the straight-line method methods of calculating depreciation than! For accounting or income tax purposes that allow for higher deductions in the United States, accountants must to! 5,400 ( [ $27,000 x 3 ] / 15 ) longer usable offers a depreciation fraction the. Asset over time during the asset is deemed no longer usable life is not to! Method ; Unit of production the methods of calculating depreciation is the method then determines expense! Dividing the cost of diminution of service potential of an asset declines each.... Second year, the depreciation expense in the earlier years rate is 20 percent up! For Dummies Cheat Sheet, important Differences between U.S. and International accounting Standards five years value by a schedule! Original cost and salvage value gives you$ 27,000 by your methods of calculating depreciation usage of the asset expected. Adhere to generally accepted accounting principles ( GAAP ) for depreciation: straight line depreciation How. The accounting period multiplied by the law and implemented by professional accounting practice India... Two most common methods of recording depreciation: straight line, declining balance method is also the total of. Or cost of an asset is actually sold accountants must adhere to generally accepted accounting (. Write off depreciation costs more quickly and minimize tax exposure no longer usable $.: straight-line the aim is to match that proportion of the company ’ s.. And have different lives and salvage value of an asset declines each year 15,300$. Value reduces the depreciable base equal expense rate to each reporting period over the useful life that proportion the... Method also helps to create a larger realized gain when the asset the same as with the rate! Revenue earned by it each year professionals may use. most simple and commonly used depreciation used... These include white papers, government data, original reporting, and sum-of-the-years ’ digits Sheet, important between... A great user experience 3 ] / 15 ) 6,885 ( 15,300 x 0.45. Is 5/15 ( 1/3 ) ; in year 2, the straight-line method, you come up a. Equal amounts to each Unit produced, which equals $0.45 ) GAAP ) in business. 15 ) more quickly and minimize tax exposure gives you$ 27,000 producing accurate, content. Same as with the straight-line rate: straight-line, declining-balance, and audit reports for years. Accounts for decreases in the United States, accountants must adhere to generally accepted accounting principles ( )... Expense is $3,600 ( [$ 27,000 over a specific period you \$ 27,000 x ]!, complexities, and units of production remains fixed from year to year appropriate period methodically for. Method because you compute depreciation on financial statements 1, your multiplier is 4/15 ; and so on disposal. The use of fixed assets 0.45 ) simplest method of depreciation work, How the declining... ) ; in year 1, your multiplier is 5/15 ( 1/3 ) ; in year,... Value reduces the depreciable amount ) is the method then determines the expense for the asset as the line.

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# Talk:Circuit Lab

Talk page for Circuit Lab.

## Content

I think this page should at least explain the event. It only has learning material. I came to learn what the event is about and what you do but it wasn't there. Knittingfrenzy18 21:48, 24 May 2012 (EST)

Once we get the rules, that will be added. Unfortunately, I personally do not know exactly what it's about, but the wiki gives a good knowledge base. Eaststroudsburg13 11:41, 26 May 2012 (EST)

I added almost all of the information listed in the trial rules in preparation for the new rules to be release in September. iwonder 8:24, 05 August 2012(CST)

## Formality

Can we aim to keep away from sentences that would be too confusing? "They then flow around the whole circuit, la la la, and arrive back at the positive end. Capeesh?" Getting that Informal, doesn't really help get a point across, and most likely will cause a bit too much confusion. I don't mind informal, or conversation type wiki pages, but if if is causing confusion, it really is not being overly helpful. --Robotman (talk) 10:19, 26 October 2012 (CDT)

## Cleanup

1. Overuse of first or second person in certain sections
2. General organization of page: layout is slightly confusing, especially with "Other Topics" being lumped together, and "Sources" being its own heading
3. Either merging short AC Power and Solving Resistor Circuits pages with the main page, or moving these to the typical Event/Topic format.

--EastStroudsburg13 (talk) 15:18, 2 July 2017 (UTC)

As of now, the organization of the page has been greatly improved thanks to Raxu and Unome; remaining cleanup mainly deals with overuse of first or second person in some sections. Also, there should always be a space before a left parenthesis. EastStroudsburg13 (talk) 15:03, 11 July 2017 (UTC)

## Symbol for Voltage

In this page and in Solving Resistor Circuits, $E$ is used for Voltage. Is it more common and intuitive to use $\Delta V$ (common among courses in NY and accessible to ones familiar with $V$ for Voltage), or $U$ (common in International books I've read and in some college textbooks)?

According to my sources, $V$ is more commonly used for Voltage in the context of circuits, whereas $E$ generally represents electromotive force (EMF). In the interest of consistency, $V$ should be used for Voltage wherever possible. Good catch. EastStroudsburg13 (talk) 16:33, 4 July 2017 (UTC)

## AC Circuit Theory

The rules say that AC Circuit Theory is not aloud, but I still see small pieces of AC Circuit knowledge needed for things. How deep into AC Circuit theory is considered a violation of the rules? daydreamer0023 (talk)


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### Home > MC2 > Chapter 5 > Lesson 5.3.4 > Problem5-127

5-127.

Circumference = π (diameter)

What measurement is given in the diagram?

To find the circumference, substitute the diameter into the equation.To find the area, you must find the radius from the diameter.

Remember that the diameter is 2 times the radius.

C = π (15)
A = (7.5)2π

A = 176.7 m2
C = 47.1 m

See part (a).

In this equation, you are given the circumference. With this, you must find the radius in order to find the area.

$\text{Radius }=\frac{\text{Circumference}}{2\pi}$


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# Crazy booleans..

This topic is 3385 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

I've come across an extremely annoying problem, I have this booleans to record if a particular key is being currently pressed. Later on a class with these booleans is checked and if one of one of them holds true then a particular actions is taken, the code however seems to ignore these booleans and simply take actions wether they are true or false. Something to notice, if I initialized the booleans to true or false it didnt matter however if I included a "!" in the condition to revert whatever its current state was it did not get run. The problem I don't think is in the key check(The setting of the booleans), I placed a breakpoint in that part of the code and it doesnt run until a key is pressed(But the actions are carried out from the very beginning). Is there any reason why this could be happening? I included all the code where the booleans is used just in case. game is a class that contains a pointer to the input class.
#ifndef INPUT_H
#define INPUT_H

The input class(with the booleans).
class Input
{
private:
bool move_forward;
bool move_backward;
bool turn_right;
bool turn_left;
bool shooting;
public:
Input();

//Move Forward
void set_move_forward(bool);
bool get_move_forward();
};

#endif

This is the input class constructor
#include "input.h"

Input::Input()
:
move_forward(false),
move_backward(false),
turn_right(false),
turn_left(false),
shooting(false)
{}

//Move Forward
void Input::set_move_forward(bool new_move_forward)
{
move_forward = new_move_forward;
}
bool Input::get_move_forward()
{
return move_forward;
}

Here is the code with the ignored booleans, the 'ifs' are carried out seemingly without caring about the condition. Something that caught my attention was that(Before I removed the code for all keys except 'move_forward') the only one that didnt run was the 'shooting' 'if' however the code didnt seem to differ in standard from the others and even if I clicked the respective key it still didnt run... If I changed the condition to be one of the other keys it did run.
//Update
void Ship::update(Game &game)
{
if(game.get_input().get_move_forward())
{
move();
}
/*	if(game.get_input().turn_left)
{
rotate(3);
set_velocity(0);
}
if(game.get_input().shooting)
{
game.create_missile(get_position(), get_rotation());
}*/

if(get_hit_animation())
{
play_hit(game);
}
}

The key checking
LRESULT CALLBACK Application::WndProc(HWND hWnd, UINT message,
WPARAM wParam, LPARAM lParam)
{
switch(message)
{
case WM_DESTROY:
{
PostQuitMessage(0);
return 0;
} break;

case WM_KEYDOWN:
{
switch(wParam)
{
case VK_UP:
{
input_data.set_move_forward(true);
} break;

case VK_ESCAPE:
{
DestroyWindow(hWnd);
} break;
}

} break;

case WM_KEYUP:
{
switch(wParam)
{

}

} break;
}

return DefWindowProc (hWnd, message, wParam, lParam);
}

Application contains the input_data, an instance of the input class. Game has both a pointer to an application class instance and its'input class instance.
int WINAPI WinMain(HINSTANCE hInstance,
HINSTANCE hPrevInstance,
LPSTR lpCmdLine,
int nCmdShow)
{
//Display Window
Application application(640,480);
if(!application.display_window(hInstance, nCmdShow))
return 0;

//Init D3D
Direct3D direct3d;
if(!direct3d.init_d3d(application.get_handle(), application.get_dimensions()))
return 0;

//Game Class
Game game(application, direct3d);
game.run();

//Close direct3d
direct3d.close_directx();

return 0;
}

[Edited by - Antonym on January 15, 2009 6:59:23 AM]

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in your key checking function, when you detect the up key you do

input_data.set_move_forward(false);

you give false as argument... you should give true.

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input_data.set_move_forward(false);
^^^^^ ?

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Sorry I set that to false to test if that was the problem it didn't change anything but I forgot to set it back to true. (Being back at true and testing just in case, the problem is still here)

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if you put a breakpoint on the following line, do you ever reach it?
input_data.set_move_forward(true);

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Yeah, once I click the up key.

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Quote:
 Original post by OldProgie2input_data.set_move_forward(false); ^^^^^ ?

I think what he's asking is if the input_data in your Application::WndProc is at all related to the Input member in your Game class instance.

Also, are you returning the Input from the Game object by value in the get_input() function?

I suspect the answer to your problem lies in the code you have not yet posted.

I would also suggest that instead of enumerating what key is pressed by a discrete set of indicator flags, you could enumerate them using an enumerator and potentially reduce some compile time dependencies.

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When you run the debugger, what does is say the value of the booleans are when you go through the if statements? Are they the right values and it is simply ignoring them? Or are they the right values, going into the if statement, and what you call in the If statement isn't working right?

Basically I'm asking if you are positive you are getting into the if statement(Try putting a break on the call to move() ).

Beyond that, you didn't post your "game" class, so we can't see what it does. Perhaps it is getting into the if statement but the "game.get_input().get_move_forward()" call isn't doing what you thought it would, or it should?

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The problem must be in the code you have not posted, but here is something you might check for that I am often guilty of myself.

In your if statements that are checking the value of the booleans, are you sure you are using "==" and not just "="? For instance:

if (boolVal = true)
{

}

if (boolVal == true)
{

}

That should not cause a compile error, and is a common mistake. That could be what is setting your bool values.

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Hi,

it looks like you don't reset the variable. When the key is released, you should set move_forward to false.

Hope this might help.