### Accounting Equation

$$\text{Assets} = \text{Equity} + \text{Liabilities}$$

$$\text{Equity} = \text{Assets} - \text{Liabilities}$$

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### Gross Profit

$$\text{Gross Profit} = \text{Revenue} - \text{Cost of Sales}$$

> ⚠️ Other Income is added **AFTER** gross profit — never include it here

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### Straight-Line Depreciation

$$\text{Annual Depreciation} = \frac{\text{Original Value} - \text{Residual Value}}{\text{Expected Life}}$$

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### Carrying Amount (Book Value)

$$\text{Carrying Amount} = \text{Original Cost} - (\text{Annual Depreciation} \times \text{Years Elapsed})$$

> ⚠️ Land is **never** depreciated

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### Declining Balance Depreciation

$$\text{Depreciation}_n = \text{Remaining Balance}_{n-1} \times \text{Fixed Rate}$$

> Fixed Rate is typically 2× the straight-line rate
> Depreciation is **higher** in early years, **lower** later

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### Share of Profit of Associates

$$\text{Share of Profit} = \text{Ownership \%} \times \text{Investee's Net Income}$$

> Used when ownership is **20–50%** (equity method)
> **Non-cash item** — subtract when calculating cash-based ratios

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## Yield Relationships

| Bond Price vs Par | Relationship |
|---|---|
| Price **< Par** (Discount) | Coupon Rate < Current Yield < YTM |
| Price **> Par** (Premium) | Coupon Rate > Current Yield > YTM |
| Price **= Par** | Coupon Rate = Current Yield = YTM |

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## Volatility Rules

| Rule | Relationship |
|---|---|
| Interest rates vs price | Rates ↑ → Prices ↓ &nbsp;&nbsp;\|&nbsp;&nbsp; Rates ↓ → Prices ↑ |
| Maturity & volatility | Longer maturity = **more** price volatility |
| Coupon & volatility | Lower coupon = **more** price volatility |
| Duration | Higher duration = **more** price sensitivity |

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## Ownership Thresholds

$$\text{Ownership} < 20\% \Rightarrow \text{Cost Method (record dividends received only)}$$

$$20\% \leq \text{Ownership} \leq 50\% \Rightarrow \text{Equity Method (record \% of profit/loss)}$$

$$\text{Ownership} > 50\% \Rightarrow \text{Full Consolidation}$$

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## Yield Curve Theories

| Theory | Key Idea | Explains All Curves? |
|---|---|---|
| **Expectations** | Long rates = expected future short rates | Partially |
| **Liquidity Preference** | Investors prefer short-term; demand premium for long | Normal only |
| **Market Segmentation** | Supply & demand by maturity segment | Yes — all shapes |

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## Common Exam Traps

> **Gross Profit trap** — Other Income is added *after* gross profit. Never include it in Revenue − Cost of Sales.

> **Dividends paid vs received** — Dividends *paid* to shareholders = **Financing Activities**. Dividends *received* from associates = **Investing Activities**.

> **Depreciation is non-cash** — Add back to profit in Operating Activities on the cash flow statement.

> **Current yield vs YTM** — Current yield ignores capital gain/loss. YTM includes everything. Equal only when bond trades at par.

> **Semi-annual adjustments** — Divide coupon by 2, multiply periods by 2, divide annual rate by 2.

> **Carrying amount** — End of Year 2 = subtract *2 years* of depreciation. End of Year $n$ = Cost − (Dep × $n$).