WealthWiseGuys Practical Mathematics

Chapter 16

Understanding Financial Statements

Read profit, financial position, and the movement of cash

A busy business can report a profit and still struggle to pay a bill. Learn how income statements, balance sheets, and cash flow statements answer different questions about the same operation. All businesses and amounts are hypothetical; round money to cents and label each statement's date or period.

16.1

Income Statements: From Revenue to Profit

Learning objectives

After this section you will be able to:

  1. Calculate gross profit and net income.
  2. Distinguish revenue, expenses, and cash receipts.
  3. Interpret a net profit margin.

Real-life situation

A neighborhood food cart closes the month

A hypothetical Philadelphia food cart summarizes one month's earned revenue and expenses. The figures use simplified accrual accounting, so profit is not automatically the amount of cash collected.

ItemAmount
Revenue$5,000
Cost of goods sold$1,800
Gross profit$3,200
Operating expenses$2,200
Operating income$1,000
Other expense$200
Net income$800
Figure 16.1 Hypothetical monthly income statement

The concept

An income statement reports financial performance over a period, such as a month or year. Revenue records amounts earned from ordinary sales or services under the accounting method used. It is not the same as owner contributions, borrowed money, or necessarily cash collected.

For a seller of goods, cost of goods sold is the assigned cost of inventory actually sold during the period. Subtract it from revenue to find gross profit. Inventory purchased but not yet sold generally remains an asset rather than becoming this period's cost of goods sold.

Operating expenses are the costs of running the operation beyond cost of goods sold. Subtract them from gross profit to find operating income, then include other stated revenues or expenses to find net income. Figure 16.1 omits taxes solely to simplify the example, not because a real business necessarily owes none.

Net profit margin expresses net income as a percentage of revenue. It helps compare different sales levels, but a margin alone does not explain risk, cash shortages, or owner compensation. Use consistent periods and expense categories before comparing businesses.

Income Statements: From Revenue to Profit: solution map

  1. 1

    Identify the question

    Calculate the food cart's gross profit, operating income, and net income.

  2. 2

    Calculation 1

    Gross profit: $5,000 − $1,800 = $3,200.

  3. 3

    Calculation 2

    Operating income: $3,200 − $2,200 = $1,000.

  4. 4

    Calculation 3

    Net income: $1,000 − $200 = $800.

  5. 5

    Interpret and check

    Gross profit is $3,200, operating income is $1,000, and net income is $800.

Figure 16.1.V Income Statements: From Revenue to Profit: solution map. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • balance sheet

    A snapshot listing what a business owns (assets) and owes (liabilities) on one date.

  • income statement

    A report showing revenue, expenses, and profit over a period of time.

  • cash flow

    The movement of money into and out of a business or account.

Key terms

Revenue
Amounts earned from sales or services during the stated period.
Cost of goods sold
The assigned inventory cost of goods sold during the period.
Gross profit
Revenue minus cost of goods sold.
Operating expense
A cost of ordinary operations outside cost of goods sold.
Net income
Revenue and gains minus all expenses and losses included in the statement.
Net profit margin
Net income expressed as a percentage of revenue.

Formulas & rules

  • Gross profit

    Gross profit = revenue − cost of goods sold

  • Operating income

    Operating income = gross profit − operating expenses

  • Net income

    Net income = operating income + other revenues − other expenses

  • Net margin

    Net profit margin = net income ÷ revenue × 100

    Revenue must be nonzero.

Worked examples

Example 1Follow the income statement

Calculate the food cart's gross profit, operating income, and net income.

Solution

  1. 1Gross profit: $5,000 − $1,800 = $3,200.
  2. 2Operating income: $3,200 − $2,200 = $1,000.
  3. 3Net income: $1,000 − $200 = $800.

Answer: Gross profit is $3,200, operating income is $1,000, and net income is $800.

Example 2Put profit into perspective

Find the cart's net profit margin and cost-of-goods-sold percentage.

Solution

  1. 1Net income divided by revenue: $800 ÷ $5,000 = 0.16.
  2. 2Convert to percent: 0.16 × 100 = 16%.
  3. 3Cost-of-goods-sold percentage: $1,800 ÷ $5,000 × 100 = 36%.

Answer: Net profit margin is 16%; cost of goods sold is 36% of revenue.

Practice exercises 16.1

  1. Operating expenses rise by $150 with everything else unchanged. Find new net income and margin.
  2. Find total listed expenses in Figure 16.1.
  3. At the same total expense dollars, what revenue would make net income zero?
  4. An owner puts $500 into the business. Should it increase the statement's sales revenue?
  5. The business earns $300 from a customer who will pay next month. Under the stated accrual approach, what happens now?

Recap quiz 16.1

1. Revenue less cost of goods sold is:
2. An income statement covers:
3. $800 net income on $5,000 revenue gives a margin of:

Section 16.1 recap

  • Read down the statement from revenue through gross profit to net income.
  • Profit measures performance under an accounting method, not simply cash collected.
Answer key with explanations: Section 16.1

Practice exercises

  1. New net income = $800 − $150 = $650. Margin = $650 ÷ $5,000 × 100 = 13%.
  2. $1,800 + $2,200 + $200 = $4,200. Revenue of $5,000 less $4,200 equals the stated $800 net income.
  3. Revenue must equal $4,200 in expenses. This is a fixed-dollar illustration, not a claim that costs would stay unchanged at every sales level.
  4. No. Owner investment is financing, not earned revenue. Revenue stays $5,000; the contribution increases cash and equity by $500.
  5. Record $300 revenue and $300 accounts receivable now, with no immediate cash increase. If no associated expenses change, net income rises by $300.

Recap quiz

  1. Gross profit: Gross profit = $5,000 − $1,800 = $3,200 in the example.
  2. A period of time: Income statements measure activity during a stated period.
  3. 16%: $800 ÷ $5,000 × 100 = 16%.
16.2

Balance Sheets and Financial Position

Learning objectives

After this section you will be able to:

  1. Apply the accounting equation.
  2. Calculate working capital and the current ratio.
  3. Explain how transactions affect assets, liabilities, and equity.

Real-life situation

A repair shop's financial snapshot

A hypothetical neighborhood repair shop lists its resources and obligations at month-end. Equipment is shown at its net book amount, and no other accounts are omitted from this simplified balance sheet.

ClassificationAccountAmount
Current assetCash$3,000
Current assetAccounts receivable$2,000
Current assetInventory$5,000
Noncurrent assetEquipment, net$10,000
Current liabilityAccounts payable$4,000
Noncurrent liabilityLong-term loan$6,000
EquityOwner's equity$10,000
Figure 16.2 Hypothetical balance sheet at month-end

The concept

A balance sheet reports financial position at one date. Assets are resources controlled by the business; liabilities are obligations; equity is the residual after liabilities. The accounting equation must balance: assets = liabilities + equity.

Current assets are expected to turn into cash, be sold, or be used within a year or the normal operating cycle if longer. Current liabilities are due in that horizon. Classification matters: a loan's amount due soon belongs in current liabilities even if the original loan was long-term.

Working capital is current assets minus current liabilities. The current ratio divides those amounts instead. Both describe short-term financial position, but neither guarantees bill-paying ability: inventory may sell slowly, and customers may pay late.

Every transaction has effects that preserve the equation. Paying an existing payable reduces cash and liabilities; it does not create a second expense if that expense was already recorded. Borrowing cash increases both assets and liabilities without creating revenue.

Balance Sheets and Financial Position: solution map

  1. 1

    Identify the question

    Find total assets, liabilities, and equity from Figure 16.2.

  2. 2

    Calculation 1

    Current assets: $3,000 + $2,000 + $5,000 = $10,000.

  3. 3

    Calculation 2

    Total assets: $10,000 + $10,000 = $20,000.

  4. 4

    Calculation 3

    Total liabilities: $4,000 + $6,000 = $10,000.

  5. 5

    Calculation 4

    Equity: $20,000 − $10,000 = $10,000.

  6. 6

    Calculation 5

    Check: $20,000 = $10,000 + $10,000.

  7. 7

    Interpret and check

    Assets are $20,000, liabilities are $10,000, and equity is $10,000.

Figure 16.2.V Balance Sheets and Financial Position: solution map. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • asset

    Something valuable that a person or business owns, like cash, equipment, or a building.

  • liability

    Money or obligations a person or business owes to others.

  • equity

    What is left of an asset after debts are subtracted; in a home, value minus what you still owe.

Key terms

Asset
A resource controlled by a business as a result of past events.
Liability
An obligation the business must settle.
Equity
The residual interest after liabilities are subtracted from assets.
Current asset
An asset expected to be realized, sold, or used in the short-term classification horizon.
Working capital
Current assets minus current liabilities.
Current ratio
Current assets divided by current liabilities.

Formulas & rules

  • Accounting equation

    Assets = liabilities + equity

  • Residual equity

    Equity = assets − liabilities

  • Working capital

    Working capital = current assets − current liabilities

  • Current ratio

    Current ratio = current assets ÷ current liabilities

    Requires nonzero current liabilities.

Worked examples

Example 1Check the snapshot

Find total assets, liabilities, and equity from Figure 16.2.

Solution

  1. 1Current assets: $3,000 + $2,000 + $5,000 = $10,000.
  2. 2Total assets: $10,000 + $10,000 = $20,000.
  3. 3Total liabilities: $4,000 + $6,000 = $10,000.
  4. 4Equity: $20,000 − $10,000 = $10,000.
  5. 5Check: $20,000 = $10,000 + $10,000.

Answer: Assets are $20,000, liabilities are $10,000, and equity is $10,000.

Example 2Measure short-term resources

Find working capital and current ratio, then pay $1,000 of accounts payable in cash.

Solution

  1. 1Original working capital: $10,000 − $4,000 = $6,000.
  2. 2Original current ratio: $10,000 ÷ $4,000 = 2.5 to 1.
  3. 3After payment, current assets are $9,000 and current liabilities are $3,000.
  4. 4New working capital: $9,000 − $3,000 = $6,000.
  5. 5New current ratio: $9,000 ÷ $3,000 = 3 to 1.

Answer: Working capital stays $6,000, but the ratio rises from 2.5 to 3; cash nevertheless falls.

Practice exercises 16.2

  1. What percent of the original assets is financed by liabilities?
  2. Collect $500 of existing accounts receivable. Find new cash, receivables, and total current assets.
  3. Buy $600 of inventory on account. Find new total assets and liabilities.
  4. Why might $10,000 of current assets fail to cover an immediate $4,000 cash bill?
  5. Reclassify $1,000 of the long-term loan as due within a year. Find the current ratio.

Recap quiz 16.2

1. Assets of $20,000 less liabilities of $10,000 imply equity of:
2. A balance sheet is measured:
3. Collecting an existing receivable generally:

Section 16.2 recap

  • Keep the accounting equation balanced and distinguish totals from classifications.
  • Ratios summarize financial position but do not replace a cash-timing analysis.
Answer key with explanations: Section 16.2

Practice exercises

  1. $10,000 ÷ $20,000 × 100 = 50%. This is a debt-to-assets percentage, not the current ratio.
  2. Cash becomes $3,500 and receivables become $1,500. Their combined amount is unchanged, so current assets remain $10,000.
  3. Assets rise to $20,600 and liabilities to $10,600. Equity stays $10,000, so $20,600 = $10,600 + $10,000.
  4. Only $3,000 is cash; the other $7,000 is receivables and inventory. The shop could be $1,000 short immediately despite $6,000 positive working capital.
  5. Current liabilities become $4,000 + $1,000 = $5,000. Current ratio = $10,000 ÷ $5,000 = 2. Total liabilities do not change.

Recap quiz

  1. $10,000: Equity = $20,000 − $10,000 = $10,000.
  2. At a stated date: It is a snapshot of financial position.
  3. Changes one asset into another: Cash rises while accounts receivable falls by the same amount.
16.3

Cash Flow and the Connections Between Statements

Learning objectives

After this section you will be able to:

  1. Classify operating, investing, and financing cash flows.
  2. Reconcile a simplified net income amount to operating cash flow.
  3. Calculate the change in cash and ending cash balance.

Real-life situation

Profit and cash tell different stories

A hypothetical workshop reports $800 net income. Depreciation is $200, receivables increase $500, and operating accounts payable increase $300; all other reconciliation adjustments are zero.

Follow the cash

  • Net income: $800
  • Add depreciation: $200
  • Subtract receivables increase: $500
  • Add operating payables increase: $300
  • Cash equipment purchase: $1,200
  • Cash borrowed: $600
  • Beginning cash: $3,000
Figure 16.3 Simplified monthly cash flow information

The concept

A cash flow statement explains the change in cash over a period. Operating activities relate to the business's main earning activities. Investing activities include buying and selling long-lived assets. Financing activities include borrowing, repaying loan principal, and owner capital transactions.

Under a simplified indirect reconciliation, begin with net income and adjust for noncash items and timing differences. Depreciation reduces accounting income without being a current-period cash payment, so add it back. This does not mean equipment was free; its purchase cash flow is shown separately.

An increase in receivables means some recorded revenue has not yet been collected, so subtract that increase. An increase in operating payables means some recorded operating costs have not yet been paid, so add it. These sign rules require consistent account definitions and can be complicated by transactions omitted from a beginner model.

The three statements connect: net income affects equity, the balance sheet reports ending cash, and the cash flow statement explains how cash changed. Borrowing can raise cash without raising profit, while profitable sales on account can raise profit without immediate cash. No single statement tells the entire story.

Distinguish profit from cash movements

  1. 1

    Starting information

    $3,000 beginning cash; $800 net income

  2. 2

    Investing cash movement

    $1,200 equipment purchase

  3. 3

    Financing cash movement

    $600 borrowed; apply operating adjustments in the example

Figure 16.3.V Distinguish profit from cash movements. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • revenue

    The total money a business brings in from sales, before any costs are paid.

  • expense

    Money a business spends to run, such as rent, supplies, or wages.

  • net profit

    The final profit after every cost is paid — sometimes called the bottom line.

Key terms

Operating cash flow
Cash generated or used by the main operating activities.
Investing cash flow
Cash flows from long-lived assets and other investing activities.
Financing cash flow
Cash flows involving borrowing and owner capital.
Noncash expense
An expense not requiring a cash payment in the same period.
Indirect reconciliation
Adjusting net income to explain operating cash flow.

Formulas & rules

  • Simplified operating cash

    Operating cash = net income + depreciation − receivables increase + operating payables increase

    All other adjustments are zero in this model.

  • Net cash change

    Cash change = operating cash + investing cash + financing cash

  • Ending cash

    Ending cash = beginning cash + cash change

Worked examples

Example 1Reconcile profit to operating cash

Use the reconciliation data in Figure 16.3.

Solution

  1. 1Begin with $800 net income.
  2. 2Add noncash depreciation: $800 + $200 = $1,000.
  3. 3Subtract the receivables increase: $1,000 − $500 = $500.
  4. 4Add the operating payables increase: $500 + $300 = $800.

Answer: Operating cash flow is $800; matching net income here is a coincidence of the adjustments.

Example 2Find ending cash

Include a $1,200 cash equipment purchase, $600 cash borrowing, and $3,000 beginning cash.

Solution

  1. 1Operating cash flow is +$800.
  2. 2Investing cash flow is −$1,200 for equipment.
  3. 3Financing cash flow is +$600 from borrowing.
  4. 4Net cash change: $800 − $1,200 + $600 = $200.
  5. 5Ending cash: $3,000 + $200 = $3,200.

Answer: Cash rises $200 to $3,200, even though net income is $800.

Practice exercises 16.3

  1. Receivables increase $700 instead of $500. Recompute operating cash flow.
  2. Classify a $400 cash repayment of loan principal and show its effect on the original ending cash.
  3. If there were no equipment purchase, find net cash change using the original other figures.
  4. Why is depreciation added back rather than treated as extra earned cash?
  5. An owner contributes $250 cash after the original transactions. Find financing cash flow and ending cash.

Recap quiz 16.3

1. A cash equipment purchase is generally:
2. Why subtract an increase in receivables from net income?
3. Beginning cash $3,000 plus net cash change $200 equals:

Section 16.3 recap

  • Separate performance, financial position, and cash movement.
  • Cash borrowing is not profit, and depreciation is not a current cash payment.
Answer key with explanations: Section 16.3

Practice exercises

  1. $800 + $200 − $700 + $300 = $600. The additional $200 uncollected revenue lowers operating cash by $200.
  2. Loan principal repayment is a financing outflow. Original ending cash $3,200 − $400 = $2,800; principal repayment is not itself an income-statement expense.
  3. $800 + $0 + $600 = $1,400. Ending cash would be $3,000 + $1,400 = $4,400.
  4. Net income already subtracts the $200 noncash expense. Adding $200 reverses that subtraction in the cash reconciliation; it does not create a new receipt.
  5. Financing cash = $600 + $250 = $850. Total cash change = $800 − $1,200 + $850 = $450, so ending cash is $3,450.

Recap quiz

  1. An investing outflow: Cash paid for a long-lived operating asset belongs in investing activities in this model.
  2. Some recorded revenue has not been collected: Accrual revenue can precede the related cash receipt.
  3. $3,200: $3,000 + $200 = $3,200.

Chapter 16 Organizer and Review

Chapter Organizer

Every section at a glance: key formulas, key terms, and the main idea.

  • 16.1 Income Statements: From Revenue to Profit

    Key formulas

    • Gross profit: Gross profit = revenue − cost of goods sold
    • Operating income: Operating income = gross profit − operating expenses
    • Net income: Net income = operating income + other revenues − other expenses
    • Net margin: Net profit margin = net income ÷ revenue × 100

    Key terms

    Revenue, Cost of goods sold, Gross profit, Operating expense, Net income, Net profit margin

    Remember

    Read down the statement from revenue through gross profit to net income.

  • 16.2 Balance Sheets and Financial Position

    Key formulas

    • Accounting equation: Assets = liabilities + equity
    • Residual equity: Equity = assets − liabilities
    • Working capital: Working capital = current assets − current liabilities
    • Current ratio: Current ratio = current assets ÷ current liabilities

    Key terms

    Asset, Liability, Equity, Current asset, Working capital, Current ratio

    Remember

    Keep the accounting equation balanced and distinguish totals from classifications.

  • 16.3 Cash Flow and the Connections Between Statements

    Key formulas

    • Simplified operating cash: Operating cash = net income + depreciation − receivables increase + operating payables increase
    • Net cash change: Cash change = operating cash + investing cash + financing cash
    • Ending cash: Ending cash = beginning cash + cash change

    Key terms

    Operating cash flow, Investing cash flow, Financing cash flow, Noncash expense, Indirect reconciliation

    Remember

    Separate performance, financial position, and cash movement.

Cumulative Review

Mixed practice from this chapter and the two chapters before it.

  1. Section 16.1

    The business earns $300 from a customer who will pay next month. Under the stated accrual approach, what happens now?

    Show answer

    Record $300 revenue and $300 accounts receivable now, with no immediate cash increase. If no associated expenses change, net income rises by $300.

  2. Section 16.2

    Reclassify $1,000 of the long-term loan as due within a year. Find the current ratio.

    Show answer

    Current liabilities become $4,000 + $1,000 = $5,000. Current ratio = $10,000 ÷ $5,000 = 2. Total liabilities do not change.

  3. Section 16.3

    An owner contributes $250 cash after the original transactions. Find financing cash flow and ending cash.

    Show answer

    Financing cash = $600 + $250 = $850. Total cash change = $800 − $1,200 + $850 = $450, so ending cash is $3,450.

  4. Review of Section 14.3

    What payment lowers the first month's balance from $1,000 to $850 at 2% monthly interest?

    Show answer

    Interest is $20, so the amount before payment is $1,020. Required payment = $1,020 − $850 = $170.

  5. Review of Section 15.3

    Reproduce month 2 in Figure 15.3.

    Show answer

    Interest = $179,820.81 × 0.005 = $899.10405 → $899.10. Principal = $1,079.19 − $899.10 = $180.09. Balance = $179,820.81 − $180.09 = $179,640.72.

All prices, stores, people, and accounts in this chapter are hypothetical and for teaching only. Product references are generic categories; no brand endorses or is endorsed by this textbook.