Frequently Used Formulas, Ratios, and Journal Entries

27.2 Frequently Used Formulas, Ratios, and Journal Entries

This section serves as a “go-to” quick reference guide for candidates preparing for the CPA Financial Accounting and Reporting (FAR) exam. While the preceding chapters offer in-depth conceptual explanations, what follows distills some of the most frequently used formulas, ratios, and journal entries that appear in practical accounting settings and on the exam. Organized for convenient review, these summaries help you swiftly recall essential material and reduce mistakes under exam pressure.

Overview and Purpose

• Reinforce core concepts: From core EPS calculations to bond discount amortization, easily navigate the numeric side of financial reporting and analysis.
• Enhance test readiness: Familiarize yourself with the typical style and flow of calculations required in problem-solving scenarios.
• Practice standard entries: Quickly review foundational journal entries that you’ll see repeatedly, such as revenue recognition or depreciation.

These references are designed to be supplemented by more detailed discussions found in relevant chapters of this book, such as:
• Chapter 6 for EPS (basic and diluted)
• Chapter 12 for depreciation formulas
• Chapter 16 for bond amortization entries
• Chapter 8 for in-depth ratio analysis

Essential Formulas for the FAR Exam

Below are some of the most common formulas tested on the FAR exam, organized by topic. While each formula is simple on its own, practicing complete examples is crucial to fully internalize the context in which these formulas apply.

Earnings per Share (EPS)

1. Basic EPS

   Basic EPS measures net income allocated to each share of common stock outstanding.

   Using KaTeX for clarity:

   $$ \text{Basic EPS} = \frac{\text{Net Income} - \text{Preferred Dividends}}{\text{Weighted Average Number of Common Shares Outstanding}} $$

   Key Points:

   • Subtract any preferred dividends for cumulative preferred stock, whether or not declared.
   • The weighted average number of shares accounts for stock splits, stock dividends, and issuance or repurchase of shares during the year.

2. Diluted EPS

   Diluted EPS adjusts the denominator (and sometimes the numerator) for potential common shares (e.g., stock options, convertible bonds).

   $$ \text{Diluted EPS} = \frac{\text{Net Income} - \text{Preferred Dividends} + \text{After-Tax Interest Savings on Convertible Debt}}{\text{Weighted Average Number of Common Shares + Dilutive Potential Shares}} $$

   Key Points:

   • Potential shares are included only if they reduce EPS (i.e., they are dilutive).
   • The “if-converted” method is used for convertible instruments.
   • The treasury stock method is used for stock options, warrants, and similar instruments.

Depreciation, Amortization, and Depletion

Depreciation is one of the most common accounting calculations. FAR relentlessly tests knowledge of different depreciation methods, each with unique formulas.

1. Straight-Line Method (SL)

   $$ \text{Annual Depreciation Expense} = \frac{\text{Cost of Asset} - \text{Salvage Value}}{\text{Useful Life}} $$

   Straight-line is uniform over the asset’s life.

2. Declining-Balance Method (e.g., Double Declining Balance)

   $$ \text{Annual Depreciation Expense in Year } i = \left( \frac{2}{\text{Useful Life}} \right) \times \text{Book Value at Beginning of Year } i $$

   Key Points:

   • Salvage value is usually ignored in calculating the depreciation base, but book value should not fall below salvage value.
   • Most common variant: Double Declining Balance (DDB), using 2 ÷ Useful Life as the accelerated rate.

3. Sum-of-the-Years’-Digits (SYD)

   $$ \text{Annual Depreciation Expense} = \left( \frac{\text{Remaining Life in Years}}{\frac{\text{Useful Life} \times (\text{Useful Life} + 1)}{2}} \right) \times (\text{Cost} - \text{Salvage Value}) $$

   The denominator is the sum of the digits from 1 to n (the “sum of years”). This method is front-loaded.

4. Units-of-Production (Activity) Method

   $$ \text{Depreciation Expense (Per Unit)} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Total Units or Hours of Production Over Life}} $$

   The expense for a period = Depreciation Expense (Per Unit) × Actual Units (or hours) produced in that period.

Bond Amortization

Accounting for bonds is a staple in FAR. Two core methods exist: (1) the Effective Interest Method (preferred under GAAP) and (2) the Straight-Line Method (an acceptable alternative only if not significantly different from the effective method, although widely used in practice for simplicity).

1. Effective Interest Method

   • The interest expense each period = carrying value × effective (market) interest rate.
   • The difference between cash interest paid and interest expense is the amortization of the bond’s discount or premium.

   Example Formula:

   $$ \text{Interest Expense} = \text{Carrying Amount of the Bond} \times \text{Yield Rate per Period} $$
   $$ \text{Amortization of Discount/Premium} = \text{Interest Expense} - \text{Cash Interest Paid} $$

2. Straight-Line Method

   • The total discount or premium is evenly amortized over the bond’s life.
   • The periodic amortization amount = (Total Discount or Premium) ÷ (Total Number of Interest Periods).
   • Then, Interest Expense = Cash Interest Paid ± Amortization of Discount (or Premium).

Key Financial Ratios

Analyzing financial statements requires familiarity with standardized metrics. Ratios help measure profitability, liquidity, solvency, and more. While each ratio has variants, these summary formulas are commonly tested.

Liquidity Ratios

• Current Ratio:

Measures short-term debt-paying ability; >1 is typically desired.

• Quick (Acid-Test) Ratio:

Excludes inventory and prepaid expenses to isolate highly liquid assets.

• Cash Ratio:

Even stricter measure of short-term liquidity.

Activity (Efficiency) Ratios

• Inventory Turnover:

High turnover indicates more frequent inventory turnover, but too high may indicate stockouts.

• Accounts Receivable Turnover:

Reflects how quickly a company collects cash from customers.

• Accounts Payable Turnover:

Measures how quickly a firm pays its suppliers.

Profitability Ratios

• Gross Margin:

• Return on Equity (ROE):

• Return on Assets (ROA):

• Net Profit Margin:

Solvency Ratios

• Debt-to-Equity:

Gauges the proportion of financing from creditors versus equity holders.

• Times Interest Earned (Interest Coverage):

Measures ability to service debt.

Standard Journal Entries: A Quick Reference

Journal entries provide the backbone of financial accounting. Mastering standard entries and variations is essential for FAR success. Below is a curated list of high-frequency entries. For thorough explanations of these and more, see Chapters 9 (Cash and Cash Equivalents), 10 (Trade Receivables), 11 (Inventory), 12 (PP&E), 16 (Debt), 17 (Equity), 20 (Revenue), and so on.

Cash and Receivables

• Recording a Cash Sale:

Debit: Cash
Credit: Sales Revenue

• Collecting Accounts Receivable:

Debit: Cash
Credit: Accounts Receivable

• Recognizing Uncollectible Accounts (Allowance Method):

1. Estimate/uncollectible:

   Debit: Bad Debt Expense
   Credit: Allowance for Doubtful Accounts

2. Write-off specific account:

   Debit: Allowance for Doubtful Accounts
   Credit: Accounts Receivable

Inventory

• Purchases (Periodic System):

Debit: Purchases
Credit: Accounts Payable

• Purchases (Perpetual System):

Debit: Inventory
Credit: Accounts Payable

• Sale of Inventory (Perpetual System):

Debit: Accounts Receivable (or Cash)
Credit: Sales Revenue
Debit: Cost of Goods Sold
Credit: Inventory

Property, Plant & Equipment (PP&E)

• Acquisition of Fixed Assets:

Debit: PP&E (e.g., Machinery)
Credit: Cash (or Accounts Payable)

• Recording Depreciation:

Debit: Depreciation Expense
Credit: Accumulated Depreciation

• Disposal of Fixed Assets (Gain):

Debit: Cash (proceeds)
Debit: Accumulated Depreciation
Credit: Equipment (historical cost)
Credit: Gain on Disposal of Equipment

Bond Issuance and Amortization

• Issuing Bonds at Discount:

Debit: Cash (issue price)
Debit: Discount on Bonds Payable
Credit: Bonds Payable (face value)

• Amortizing Discount (Effective Interest Method Example):

Debit: Interest Expense
Credit: Discount on Bonds Payable
Credit: Cash (interest payment)

• Issuing Bonds at Premium:

Debit: Cash (issue price)
Credit: Premium on Bonds Payable
Credit: Bonds Payable (face value)

• Amortizing Premium (Effective Interest Method Example):

Debit: Interest Expense
Debit: Premium on Bonds Payable
Credit: Cash (interest payment)

Equity Transactions

• Issuing Common Stock at Par:

Debit: Cash
Credit: Common Stock (at par value)
Credit: Additional Paid-In Capital (APIC) (excess)

• Repurchasing Stock (Treasury Stock, Cost Method):

Debit: Treasury Stock
Credit: Cash

• Reissuing Treasury Stock Above Cost:

Debit: Cash
Credit: Treasury Stock
Credit: APIC – Treasury Stock

Revenue Recognition

Under the new 5-step revenue recognition model (ASC 606):

• Recording Revenue (when performance obligations are satisfied):

Debit: Accounts Receivable (or Cash)
Credit: Sales/Service Revenue

If contract liabilities or unearned revenue exist:

Debit: Unearned Revenue
Credit: Revenue

Expenses and Accruals

• Accruing an Expense:

Debit: Expense
Credit: Accrued Liability (e.g., Wages Payable, Interest Payable)

• Paying an Accrued Expense:

Debit: Accrued Liability
Credit: Cash

Lease Accounting (Lessee)

• Operating Lease (ASC 842):

Initial Recognition of Right-of-Use Asset and Lease Liability:

Debit: Right-of-Use Asset (Operating)
Credit: Lease Liability

Periodic Lease Payment:

Debit: Lease Expense
Credit: Cash

(Right-of-use asset and lease liability are amortized in the background with slightly different presentation.)

• Finance Lease (Lessee):

Debit: Right-of-Use Asset (Finance)
Credit: Lease Liability

Periodic Lease Payment:

Debit: Interest Expense
Debit: Lease Liability
Credit: Cash

Record amortization of ROU asset each period:

Debit: Amortization Expense
Credit: Accumulated Amortization – ROU Asset

Contingencies

• Recognizing a Probable and Reasonably Estimable Loss:

Debit: Loss (Lawsuit, Warranties, etc.)
Credit: Liability (Lawsuit Payable, Warranty Liability, etc.)

Example Flow of a Typical Transaction

Below is a simplified diagram that illustrates the general flow of a transaction from the point of journal entry through final financial statement presentation:

    flowchart LR
	    A[Transaction Occurs] --> B[Journal Entry]
	    B --> C[General Ledger Posting]
	    C --> D[Trial Balance]
	    D --> E[Financial Statements]

1. A Transaction Occurs: It can be an invoice to the customer, accrual of an expense, or bond issuance.
2. Journal Entry: The initial accounting record, capturing debits and credits.
3. General Ledger Posting: Each journal entry is posted to the specific GL accounts.
4. Trial Balance: Summarizes all GL accounts, used to check error-free debits and credits.
5. Financial Statements: Ultimately, the numbers flow into the main statements for external reporting.

Best Practices and Common Pitfalls

1. Always match interest expense with the correct carrying value for the effective interest method.
2. Check that you have accounted for partial-year conventions when calculating depreciation if the asset is placed in service mid-year.
3. Ensure that if convertible securities are antidilutive, they are excluded from diluted EPS.
4. Watch for modifications in lease or revenue contracts that might trigger remeasurement of liabilities or updated recognition of revenue.
5. Confirm your beginning and ending balances in inventory calculations (e.g., LIFO, FIFO) align with the method used (periodic vs. perpetual).
6. Keep a mental or written “cheat sheet” of standard accounts used during typical transactions (e.g., always open or close the “Allowance for Doubtful Accounts” with the same offset accounts).

Practical Example: Recording an Interest Expense Using the Effective Interest Method

Let’s illustrate bond amortization for a single period using the Effective Interest Method. Suppose a $100,000 bond is 5 years until maturity, with a 10% stated interest rate (paid annually), sold at a discount to yield an effective rate of 12%. The discounted price was $96,535.80, which becomes the bond’s initial carrying value.

• Beginning Carrying Value: $96,535.80
• Interest Payment = $100,000 × 10% = $10,000
• Effective Interest Expense = $96,535.80 × 12% = $11,584.30
• Amortization of Discount = $11,584.30 − $10,000 = $1,584.30

Journal Entry:

Debit: Interest Expense …………….. $11,584.30
Credit: Discount on Bonds Payable …… $1,584.30
Credit: Cash (Interest Paid) ……….. $10,000

Resulting new carrying value of the bond = $96,535.80 + $1,584.30 = $98,120.10.

Real-World Scenarios and References

• Be mindful of actual business processes. For instance, when performing a partial disposal of equipment, the recognized gain or loss and the reversal of any associated accumulated depreciation can become complex.
• In practice, many large companies utilize enterprise resource planning (ERP) software that automates calculations for depreciation, amortization, and bond discount/premium tracking.
• For additional official guidance, consult FASB Accounting Standards Codification (ASC) topics:
– ASC 230 for Statement of Cash Flows
– ASC 606 for Revenue Recognition
– ASC 505 for Equity
– ASC 470 for Debt
– ASC 840 (superseded by ASC 842) for Leases

Quiz: Frequently Used Formulas, Ratios, and Journal Entries

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