会计学原理-笔记-Chapter 6

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参考技术A Accounting For Sales (Selling products or services)

A. Sales

Recognition of Revenue:

1. Revenue recognition principle

Revenue should be recognized when earned and realized

Earned : The work (providing goods or services) has been substantially completed.

Realized :Cash, or a valid promise of future payment, has been received.

2. 5 steps for revenue recognition

    Identify contract with customer

    Identify its separate performance obligations

    Determine the transaction price

     Allocate transaction price to the separate performance obligations

    Recognize revenue when entity satisfies a performance obligation

3. Revenue Recognition Method

a. Percentage of completion method

Recognizing revenue on long-term contracts as production occurs

    Does not require waiting until the final product is delivered

    Associated expenses must be recognized by the company

 Used when:

    There is surety of receiving payment 

    Progress measures are dependable 

    Contract obligations are explicit

b. Completed contract method

Recognizing revenue on long-term contracts that delays recognition of both revenue and related expenses until completion of the contract

Used when:

    there is uncertainty about customers paying at end of contract (U.S. GAAP)

    the outcome of a contract cannot be estimated reliably (IRFS)

4. Typical Line of business about sale

Negotiation -> Contract -> Collect Cash -> Deliver Product -> Continuing Service

        OR

Deliver Product -> Collect Cash (Cash Discount?) -> Customer Return -> Bad Debt -> Continuing Service

Measurement of Sales

1. Gross Sales and Net Sales

Gross Sales : initial revenues or asset inflows based on the initial sales price

Net sales : Total amount of sales after deducting returns, allowances, and discounts

2. Sales Return and Allowances

A  sales return  occurs when a customer returns previously purchased merchandise

A  sales allowance  is a reduction of the original selling price

A contra account (Sales Returns and Allowances) combines both returns and allowances in a single account

Contra revenue account

• Used instead of reducing the revenue account directly

• Combines both returns and allowances

• Helps monitor changes in the level of returns and allowances

• Helps in forecasting demand and managing inventory

3. Sales Discount

Sale discounts  are rewards for prompt payment

Credit Terms: 

p=discount percentage

n= # of days in discount period

x=otherwise, the full amount is due

m=maximum days in credit period

Discount  is a reduction in the full price due to either a sale, promotion or prompt payment

Trade discounts  offer one or more reductions to the gross selling price for a particular class of customers

The  Gross sales  is the price received after deducting the trade discount

There is no contra account for trade discount

4. Credit Card Discount

Credit Card Fees: typically 1%  4% of gross sales

• An alternative to sales discount

• Deduct from gross sales directly

• Or Record as credit card discount

5. Reporting for Net Sales Revenue

B. Bad Debts

Record:

1. Classification of Receivables

Accounts Receivable, Notes Receivable, Interest Receivable, Dividends receivable, Other Receivables

2. Uncollectible Accounts of A/Rs

Occur when customers do not pay for items or services purchased on credit

When an account receivable becomes uncollectible, a firm incurs a bad-debt expense

3. The Direct Write-off Method

journal entries:

when credit sales are made:

when an A/R becomes uncollectible:

when cash received on the previously bad account:

Method is  objective  because bad debt expense is written off at the time it proves to be uncollectible.

This method is  not consistent with the matching principle(All costs and expenses in generating revenues must be identified with those revenues period by period) .

4. The Allowance Method

The firm estimates the amount of sales that will ultimately be uncollectible in the same period in which those credit sales are made.

A contra asset account( allowance for bad debts , or, Allowance for doubtful accounts坏帐准备 ) is set up and deducted from the A/R account on the BS.

journal entries:

when credit sales are made:

Bad debts are estimated and recognized in the same period as credit sales are made:

when actually write off a bad account:

when credit customers eventually pay:

The Allowance Method: Reversing Written-off Receivables

Estimate:

1. As a Percentage of Credit Sales  (matching+IS focus )

Amount of uncollectibles=a straight percentage of the current year’s credit sales.

Based on experience of prior years, modified for changes expected in current year.

Any existing balance in Allowance for Bad Debts is not considered

2. As a Percentage of Total Receivables  (realizable+BS focus)

Amount of uncollectibles = a percentage of total receivables balance at period’s end.

Focus is on estimating total bad debts existing at the end of the period.

The ending balance in Allowance for Bad Debts is the amount of total receivables estimated to be uncollectible.

3. Aging Accounts Receivable  (realizable+BS focus)

A more refined version of % of total receivable method.

Based on how long receivables have been outstanding to estimate the ending balance in the Allowance for Bad Debts.

Each receivable is categorized according to age , such as

Current

1-30 days past due

31-60 days past due, etc.

The total amount in each classification is multiplied by an appropriate uncollectible percentage

C. Analyze and management of Accounts Receivable

Assessing Management of Receivables

1. Accounts Receivable Turnover     应收帐款周转率

为什么这是一个有效的衡量指标？

Determines the number of times during a year a company is “turning over” or collecting its receivables.

Measure of how many times old receivables are collected and replaced by new receivables.

2. The Days to Collect A/Rs (Average collection period,  应收账款平均收账期)

Converts A/Rs turnover into the number of days it takes to collect receivables.

For each dollar revenue, how long it takes the firm to collect the cash.

Balancing the desire to extend credit in order to increase sales with the need to collect cash quickly to pay the company’s bills.

3. Earning Manipulation through Bad Debt Expense

Overestimate:

    Years incurring huge loss

    CEO turnover - big bath

    Merger & Acquisition 

    Outside Negative forces

Underestimate:

    Loss Aversion

    Earnings growth

D. Cash Management & Internal Control

1. What is Internal Control?

a. Internal Control is an organizational plan and the designed to accomplish the following:

Safeguard assets

Encourage employees to follow company policies

Promote operational efficiency related measures 

Ensure accurate, reliable accounting records

b. Checklist of internal control:

Reliable personnel with clear responsibilities

Separation of duties makes it harder to collude 

Adequate documentation (source documents) 

Proper authorization for normal/abnormal transactions

Well-documented policies and procedures

Physical safeguards over items of value

Vacations and rotation of duties

Independent review of all systems

Cost-benefit considerations should apply

2. Internal Control of Cash

Bank Reconciliations    Daily Deposits    Purchase Approval    Payment Approval 

Check Signatures    Pre-numbered Checks

Internal Control of Cash Receipts:

A mail room employee opens all mail and records the checks on a remittance advice.

The Treasurer is responsible for depositing the checks, documented with a deposit receipt.

The remittance advice goes the Accounting Department where is it recorded.

The Controller’s office matches the remittance advice and the deposit receipt.

Controls Over Cash Payments:

Bills are only approved for payment by the accounting department when all the documents related to the transaction are matched together.

A payment voucher authorizes a check to be sent to the vendor.

Bank Reconciliation:

A mathematical explanation of the difference between two numbers.

With a bank reconciliation, there is often a difference between the bank statement balance and the general ledger cash balance.

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六、微观几何

每个可见的表面点都包含了很多为表面的法线，每个法线都会将光反射到不同方向。因为这些方向都是随机的，所以可以使用统计学分布来表示。这个分布是连续的，并且在宏观表面法线处有明显峰值。分布越“紧凑”，表面越光滑；分布越“平坦”，表面越粗糙。

因微观尺度的粗糙度上升而引起的视觉效果是，使反射的环境细节更加模糊。统计形态的不同，使得聚合高光的形状也不同。

对于大部分表面，微观表面法线分布是各向同性的，也就是说是旋转对称的，无内在的方向性。而各向异性的表面在不同方向上，微观表面法线分布不同，这导致模糊和高光在不同方向上不同。

一些表面有高度结构化的微几何，这使得微法线分布和表面外观呈现出很大的不同，如纤维就是最常见的情况。

除了不同的表面法线外，微几何也会产生其他的影响，如阴影（shadowing）和遮挡（masking），如图所示：

阴影和遮挡会很大程度上改变法线分布。对于所有的表面类型，当入射角 θ i \\theta_i θi​增大时，宏观层面上的不规则度会降低。结合菲涅尔效应，使得在观察角度和光线角度都接近 9 0 ο ⁡ 90^\\operatorname\\omicron 90ο时，表面会变得高度反光，产生类似镜面的效果。

被微表面遮挡的光线不会消失，而是可能经过多次弹射后进入眼睛。

如果微表面的尺寸大于次表面散射的距离，那么阴影和遮挡会导致逆反射（retroreflection）效应，即光线会被反射回入射方向。

七、微表面理论

微表面理论（Microfacet）是对微几何的反射率的数学分析。微表面理论的基础是，将微几何体建模为微表面的集合。

每个微表面都是平坦的，有单独的法线 m \\mathbf m m；并且根据微BRDF f μ ( l , v , m ) f_\\mu(\\mathbf l,\\mathbf v,\\mathbf m) fμ​(l,v,m)单独反射光线，最后将所有的反射率相加，得到总的表面BRDF。

微表面法线分布定义为表面的法线分布函数（normal distribution function，NDF）， D ( m ) D(\\mathbf m) D(m)。

对 D ( m ) D(\\mathbf m) D(m)微表面法线的整个球面进行积分，可以得到微表面的面积。更常用的是，对 D ( m ) ( n ⋅ m ) D(\\mathbf m)(\\mathbf n\\cdot\\mathbf m) D(m)(n⋅m)（即 D ( m ) D(\\mathbf m) D(m)在宏观表面上投影）进行积分，可以得到宏观表面的面积，等于 1 1 1。公式如下：
∫ m ∈ Θ D ( m ) ( n ⋅ m ) d m = 1 \\int_\\mathbf m\\in\\ThetaD(\\mathbf m)(\\mathbf n\\cdot\\mathbf m)d\\mathbf m=1 ∫m∈Θ​D(m)(n⋅m)dm=1
要注意的是，这里的积分域是整个球面。

更普遍的情况，会将微表面和宏观表面投影到垂直于视线方向 v \\mathbf v v的平面：
∫ m ∈ Θ D ( m ) ( v ⋅ m ) d m = v ⋅ n \\int_\\mathbf m\\in\\ThetaD(\\mathbf m)(\\mathbf v\\cdot\\mathbf m)d\\mathbf m=\\mathbf v\\cdot\\mathbf n ∫m∈Θ​D(m)(v⋅m)dm=v⋅n

可见微表面的投影之和等于宏观表面的投影面积。在数学表达上，可以定义一个遮挡函数（masking function） G 1 ( m , v ) G_1(\\mathbf m,\\mathbf v) G1​(m,v)，定义了在 v \\mathbf v v方向上可见的部分的法线 m \\mathbf m m；可得如下定义：
∫ ∈ Θ G 1 ( m , v ) D ( m ) ( v ⋅ m ) + d m = v ⋅ n \\int_\\in\\ThetaG_1(\\mathbf m,\\mathbf v)D(\\mathbf m)(\\mathbf v\\cdot\\mathbf m)^+d\\mathbf m=\\mathbf v\\cdot\\mathbf n ∫∈Θ​G1​(m,v)D(m)(v⋅m)+dm=v⋅n

其中 G 1 ( m , v ) D ( m ) G_1(\\mathbf m,\\mathbf v)D(\\mathbf m) G1​(m,v)D(m)称为可见法线分布（distribution of visible normals）。

满足条件的 G 1 ( m , v ) G_1(\\mathbf m,\\mathbf v) G1​(m,v)函数并不唯一，因为 D ( m ) D(\\mathbf m) D(m)并不能完全定义微表面； D ( m ) D(\\mathbf m) D(m)只定义了法线指向特定方向的微表面数量，却没有定义如何排布。

只有Smith函数是唯一一个既符合上述公式，且是法线遮挡独立的（normal-masking independence）。在 m ⋅ v ≥ 0 \\mathbf m\\cdot\\mathbf v\\ge 0 m⋅v≥0时，Smith函数不依赖于 m \\mathbf m m，其定义如下：
G 1 ( m , v ) = χ + ( m ⋅ v ) 1 + Λ ( v ) G_1(\\mathbf m,\\mathbf v)=\\cfrac\\chi^+(\\mathbf m\\cdot\\mathbf v)1+\\Lambda(\\mathbf v) G1​(m,v)=1+Λ(v)χ+(m⋅v)​
其中， χ + ( x ) \\chi^+(x) χ+(x)是正特征函数；而 Λ \\Lambda Λ函数则对不同NDF有不同函数。

Smith函数的缺点：对于不同的实际表面结构，有不同的满足条件，甚至有些在物理上是无法实现的。

给定微BRDF f μ ( l , v , m ) f_\\mu(\\mathbf l,\\mathbf v,\\mathbf m) fμ​(l,v,m)，法线分布函数 D ( m ) D(\\mathbf m) D(m)，遮挡函数 G 1 ( m , v ) G_1(\\mathbf m,\\mathbf v) G1​(m,v)，则宏观表面的BRDF可以表示为：
f ( l , v ) = ∫ m ∈ Ω f μ ( l , v , m ) G 2 ( l , v , m ) D ( m ) ( m ⋅ l ) + ∣ n ⋅ l ∣ ( m ⋅ v ) + ∣ n ⋅ v ∣ d m f(\\mathbf l,\\mathbf v)=\\int_\\mathbf m\\in\\Omegaf_\\mu(\\mathbf l,\\mathbf v,\\mathbf m)G_2(\\mathbf l,\\mathbf v,\\mathbf m)D(\\mathbf m)\\cfrac(\\mathbf m\\cdot\\mathbf l)^+|\\mathbf n\\cdot\\mathbf l|\\cfrac(\\mathbf m\\cdot\\mathbf v)^+|\\mathbf n\\cdot\\mathbf v|d\\mathbf m f(l,v)=∫m∈Ω​fμ​(l,v,m)G2​(l,v,m)D(m)∣n⋅l∣(m⋅l)+​∣n⋅v∣(m⋅v)+​dm
这个积分是的积分域是 Ω \\Omega Ω，即 n \\mathbf n n侧的半球面； G 2 ( l , v , m ) G_2(\\mathbf l,\\mathbf v,\\mathbf m) G2​(l,v,m)是联合遮挡阴影函数（joint masking-shadowing function），从 G 1 ( m , v ) G_1(\\mathbf m,\\mathbf v) G1​(m,v)推导而来。这使得BRDF引入了遮挡和阴影；缺点是没有微表面之间的内部反射，这使得渲染结果会显得更暗。

G 2 G_2 G2​函数的几个版本：