notes/10 - Projects/CSC/Chapter 11/Formulas.md
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### Accounting Equation
$$\text{Assets} = \text{Equity} + \text{Liabilities}$$
$$\text{Equity} = \text{Assets} - \text{Liabilities}$$
---
### Gross Profit
$$\text{Gross Profit} = \text{Revenue} - \text{Cost of Sales}$$
> ⚠️ Other Income is added **AFTER** gross profit — never include it here
---
### Straight-Line Depreciation
$$\text{Annual Depreciation} = \frac{\text{Original Value} - \text{Residual Value}}{\text{Expected Life}}$$
---
### Carrying Amount (Book Value)
$$\text{Carrying Amount} = \text{Original Cost} - (\text{Annual Depreciation} \times \text{Years Elapsed})$$
> ⚠️ Land is **never** depreciated
---
### 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
---
### Share of Profit of Associates
$$\text{Share of Profit} = \text{Ownership \%} \times \text{Investee's Net Income}$$
> Used when ownership is **2050%** (equity method)
> **Non-cash item** — subtract when calculating cash-based ratios
---
## 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 |
---
## 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 |
---
## Ownership Thresholds
$$\text{Ownership} < 20\% \Rightarrow \text{Cost Method (record dividends received only)}$$
$$20\% \leq \text{Ownership} \leq 50\% \Rightarrow \text{Equity Method (record \% of profit/loss)}$$
$$\text{Ownership} > 50\% \Rightarrow \text{Full Consolidation}$$
---
## 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 |
---
## 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 × $n$).