Liabilities, Time Value of Money, and Bonds（负债、货币时间价值与债券）

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1. Financing the Business: Debt vs Equity（企业融资：债务与权益）

1.1 Assets Financed by Debt and Equity（资产由债务与权益共同筹资）

• Every asset must be financed by borrowing (debt) or owner investment (equity).
• 每一项资产都来自外部借款或所有者投入资本。

1.2 Debt: Funds from Creditors（债务：来自债权人的资金）

• Creates legal obligations to repay principal and interest.
• 形成必须按期偿还本息的法律义务。

1.3 Equity: Funds from Owners（权益：来自所有者的资金）

• Represents owners’ residual claim after liabilities.
• 代表清偿负债后所有者对资产的剩余权益。

1.4 Why Debt Is Riskier than Equity（债务为何更高风险）

• Fixed payments must be made even in loss years; default may lead to bankruptcy.
• 即使亏损也要支付利息，本息违约可能被债权人申请破产。

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2. Liabilities: Definition, Classification, Measurement（负债：定义、分类与计量）

2.1 Definition of Liabilities（负债的定义）

• Probable debts from past events, requiring future transfer of assets or services.
• 由过去事项形成、很可能导致未来经济利益流出的现时义务。

2.2 Current vs Noncurrent Liabilities（流动负债 vs 非流动负债）

• Current: due within one year or one operating cycle; noncurrent: due after that.
• 一年或营业周期内到期为流动负债，超过为长期负债。

2.3 Measurement at Current Cash Equivalent / PV（按当前现金等价/现值计量）

• Measure at amount a creditor would accept today to cancel debt.

• 计量金额 ≈ 未来现金流现值：

  • (PV = \sum \dfrac{CF_t}{(1+r)^t})。

2.4 Common Current Liability Accounts（常见流动负债账户）

• Accounts payable, accrued liabilities, notes payable, deferred/unearned revenues.
• 应付账款、应计负债、应付票据、递延（未实现）收入。

2.5 Contingent Liabilities / Provisions（或有负债 / 预计负债）

• Potential obligations depending on uncertain future events.
• 根据“发生概率 × 是否可估计金额”决定记录、披露或不处理。

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3. Liquidity and Payment Behavior（流动性与付款行为）

3.1 Current Ratio（流动比率）

• Formula 公式：(Current\ Ratio = \dfrac{Current\ Assets}{Current\ Liabilities})。
• Indicates short-term liquidity; too low = risk, too high = idle resources.

3.2 Working Capital（营运资本）

• (Working\ Capital = Current\ Assets - Current\ Liabilities)。
• Shows net short-term resources available for operations.

3.3 Accounts Payable Turnover（应付账款周转率）

• (A/P\ Turnover = \dfrac{Total\ Net\ Credit\ Purchases}{Average\ Accounts\ Payable})。
• Measures how quickly a firm pays suppliers; higher = faster payments.

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4. Notes Payable and Interest（应付票据与利息）

4.1 Interest as Revenue/Expense（利息：收入与费用）

• To lender: interest revenue; to borrower: interest expense.
• 同一笔利息在出借人是收入，在借入人是费用。

4.2 Interest Formula: Principal × Rate × Time（利息计算公式）

• (Interest = Principal \times Rate \times Time)。
• Time expressed in years or fraction of a year (e.g., (2/12) for two months).

4.3 Short-Term Interest Example: Starbucks Note（短期票据例子）

• Borrow (100{,}000) at 12% for 2 months → interest (= 100{,}000 \times 12% \times \dfrac{2}{12} = 2{,}000)。

4.4 Long-Term Notes at Present Value（长期票据按现值入账）

• Record note and related asset at PV of future payment using market rate.
• 例：(FV=200{,}000, i=12%, n=2 \Rightarrow PV = 200{,}000 \times 0.7972 = 159{,}440)。

4.5 Effective Interest Method & Year-1 Entry（实际利率法与第一年分录）

• Interest expense = carrying amount × market rate.
• Year 1: (159{,}440 \times 12% = 19{,}133)，借记 Interest expense，贷记 Notes payable。

4.6 Year-2 Interest and Settlement（第二年利息与清偿）

• New carrying amount = old carrying + interest; second-year interest ≈ 21,429。
• 到期借记 Notes payable 200,000，贷记 Cash 200,000。

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5. Long-Term Debt: Loans vs Bonds（长期债务：贷款与债券）

5.1 Small Long-Term Debt from Single Lenders（小额长期债务：单一贷款方）

• Banks, insurance companies, pension plans provide customized long-term loans.
• 适用于资金需求较小且条款可协商的情形。

5.2 Large Debt Needs via Bond Issues（大额资金需求：发行债券）

• Issue many bonds to public investors to raise large amounts at once.
• 需承销与监管，固定发行成本高，但可分散在众多投资者之间。

5.3 Long-Term Liabilities and Collateral（长期负债与资产抵押）

• Creditors often require pledged assets as security; disclosed in notes.
• 抵押限制企业资产使用，影响财务风险与弹性。

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6. Time Value of Money Basics（货币时间价值基础）

6.1 Money Growth and Compound Interest（货币增长与复利）

• Money today can earn interest → more money tomorrow.
• 例：(1{,}000) at 10% → (1{,}610.51) in 5 years, (10{,}834.71) in 25 years。

6.2 Four Key Variables: PV, FV, Rate, Time（四个关键变量）

• PV（现值）、FV（终值）、(r)（利率）、(n)（期数）。
• Knowing any 3 allows solving for the 4th.

6.3 Present Value Concept and Tools（现值概念与计算工具）

• (PV = \dfrac{FV}{(1+r)^n})。
• 计算工具：公式、PV 表、财务计算器、Excel。

6.4 PV of a Single Amount（单一金额的现值）

• 例：(FV=1{,}331, r=10%, n=3 \Rightarrow PV = 1{,}331 \div 1.1^3 = 1{,}000)。
• 折现率越高、期数越多，PV 越低。

6.5 PV Example Using Table（使用现值表的例题）

• 查得 10%/3 年系数 0.7513；(PV = 1{,}331 \times 0.7513 \approx 1{,}000)。

6.6 Future Value of a Single Amount（单一金额的未来值）

• (FV = PV \times (1+r)^n)。
• 例：(FV = 1{,}000 \times 1.1^3 = 1{,}331)。

6.7 FV Example Using Table（使用未来值表的例题）

• 查得 10%/3 年 FV 因子 1.331；(FV = 1{,}000 \times 1.331 = 1{,}331)。

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7. Annuities: PV and FV（年金：现值与未来值）

7.1 Definition and Structure of Annuity（年金的定义与结构）

• Series of equal payments at regular intervals (ordinary annuity if at period end).
• 常见于分期还款、租金、养老金等。

7.2 PV of an Annuity（年金的现值）

• (PV_{annuity} = Payment \times PVIFA(r,n))。
• 等价于每期现值之和：(\sum \dfrac{Payment}{(1+r)^t})。

7.3 PV Example: 3-Year $1,000 Annuity（例题：3 年每年 1,000 的年金现值）

• (r=10%, n=3, PVIFA=2.4869)。
• (PV = 1{,}000 \times 2.4869 = 2{,}486.90)。

7.4 FV of an Annuity（年金的未来值）

• (FV_{annuity} = Payment \times FVIFA(r,n))。
• 每笔付款各自复利至期末再求和。

7.5 FV Example: 3-Year $1,000 Ordinary Annuity（例题：普通年金未来值）

• (r=10%, n=3, FVIFA=3.3100)。
• (FV = 1{,}000 \times 3.3100 = 3{,}310)。
• 手动：(1{,}000(1.1^2 + 1.1 + 1) = 3{,}310)。

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8. Bond Valuation and Terminology（债券计价与相关术语）

8.1 Bond Cash Flows: Interest and Principal（债券的两类现金流）

• Periodic interest = face value × stated rate.
• 到期偿还面值（principal / face value）。

8.2 Effective vs Stated Interest Rate（有效利率 vs 票面利率）

• Stated rate决定票息金额；effective (market) rate决定折现和定价。
• 投资人实际收益率取决于市场利率。

8.3 Pricing at Par, Premium, Discount（按面值、溢价、折价发行）

• Stated = market → price = face (par)。
• Stated > market → price > face (premium)。
• Stated < market → price < face (discount)。

8.4 Key Terms: Face Value, Premium, Discount, Amortized Cost（关键术语）

• Face value：到期偿还本金。
• Premium/discount：购买价与面值差额。
• Amortized cost（摊余成本）= future cash flows discounted at effective rate.

8.5 Fair Value vs Amortized Cost（公允价值 vs 摊余成本）

• Fair value = market price at a given date; may differ from amortized cost.
• 摊余成本随利息费用调整，逐渐接近面值。

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9. Discount Bond Example and Carrying Amount（折价债券案例与账面价值）

9.1 Initial Purchase at Discount（折价初始购买）

• Face value 1,250, stated 4.7%, effective 10%。
• Fair value/price = 1,000 → purchased at discount of 250。

9.2 Pricing from PV of Interest and Principal（用利息与本金现值定价）

• Coupon each year: (59 = 1{,}250 \times 4.7%)。
• Price (= 59 \times PVIFA(10%,5) + 1{,}250 \times PVIF(10%,5) \approx 1{,}000)。

9.3 Carrying Amount After One Year（一年后的账面价值）

• Remaining 4 years:

  • (1{,}250 \times PVIF(10%,4))
  • (59 \times PVIFA(10%,4))

• Carrying amount ≈ 1,041 > initial 1,000。

9.4 Effective Interest Income & Discount Amortization（有效利息与折价摊销）

• Interest income = opening carrying amount × 10%。
• 折价摊销 = 利息收入 − 实收票息 59，使账面价值增加。

9.5 Trend Toward Face Value（账面价值趋近面值）

• Each year carrying amount increases until it reaches 1,250 at maturity.
• 体现 effective rate > stated rate 时折价债券“向面值拉升”的摊销路径。