CFA Level 1 - Quantitative Methods & Financial Reporting Analysis Flashcards

Question 1

Net Present Value (NPV) Formula & Decision Rule

Accepted Answer

The formula for NPV is:
$NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - CF_0$

**Decision Rule:** Accept projects with $NPV > 0$. For independent projects, accept all positive NPV projects. For mutually exclusive projects, select the project with the highest positive NPV.

Question 2

Internal Rate of Return (IRR) Definition & Decision Rule

Accepted Answer

The discount rate $r$ that equates the net present value of cash inflows to the initial cash outflow:
$\sum_{t=1}^{n} \frac{CF_t}{(1+IRR)^t} - CF_0 = 0$

**Decision Rule:** Accept projects if $IRR > r$ (required rate of return).

Question 3

Effective Annual Rate (EAR) Formulas

Accepted Answer

For discrete compounding with $m$ periods per year:
$EAR = \left(1 + \frac{r_s}{m}\right)^m - 1$

For continuous compounding:
$EAR = e^{r_s} - 1$

*Where $r_s$ is the stated annual interest rate.*

Question 4

Choosing Between Z-Test and T-Test for Population Means

Accepted Answer

- **Z-Test:** Use when population variance $\sigma^2$ is known, or when $\sigma^2$ is unknown but sample size $n \ge 30$ (Central Limit Theorem).
- **T-Test:** Use when population variance $\sigma^2$ is unknown and sample size $n < 30$ (assuming normal population).

Formula for t-statistic: $t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$ with $n - 1$ degrees of freedom.

Question 5

Type I Error vs. Type II Error

Accepted Answer

- **Type I Error ($\alpha$):** Rejecting a true null hypothesis ($H_0$). The probability of a Type I error is the significance level $\alpha$.
- **Type II Error ($\beta$):** Failing to reject a false null hypothesis ($H_0$).
- **Power of a Test:** $1 - \beta$ (probability of correctly rejecting a false null hypothesis).

Question 6

Standard Error of the Sample Mean

Accepted Answer

Measures the dispersion of sample means around the population mean:
$SE_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$

If population standard deviation $\sigma$ is unknown, substitute sample standard deviation $s$:
$SE_{\bar{x}} = \frac{s}{\sqrt{n}}$

Question 7

Chi-Square Test vs. F-Test Applications

Accepted Answer

- **Chi-Square ($\chi^2$) Test:** Used to test hypotheses concerning the variance of a single normal population ($df = n - 1$).
- **F-Test:** Used to test hypotheses comparing the equality of variances of two independent normal populations ($df_1 = n_1 - 1, df_2 = n_2 - 1$).

Question 8

Geometric Mean vs. Harmonic Mean Formulas

Accepted Answer

- **Geometric Mean (Compound Returns):** $R_g = \left[ \prod_{i=1}^n (1 + R_i) \right]^{\frac{1}{n}} - 1$
- **Harmonic Mean (Cost Averaging):** $\bar{X}_H = \frac{n}{\sum_{i=1}^n \frac{1}{X_i}}$

*Mathematical Order:* Harmonic Mean $\le$ Geometric Mean $\le$ Arithmetic Mean.

Question 9

Covariance and Correlation Coefficient

Accepted Answer

Correlation standardizes covariance between $-1$ and $+1$:
$ho_{X,Y} = \frac{	ext{Cov}(X,Y)}{\sigma_X \sigma_Y}$

*Note:* $ho_{X,Y} = 0$ indicates no linear relationship, but non-linear relationships may still exist.

Question 10

3-Step DuPont Model for ROE

Accepted Answer

Decomposes Return on Equity into profitability, efficiency, and leverage components:
$ROE = 	ext{Net Profit Margin} 	imes 	ext{Asset Turnover} 	imes 	ext{Financial Leverage}$
$ROE = \left(\frac{	ext{Net Income}}{	ext{Revenue}}ight) 	imes \left(\frac{	ext{Revenue}}{	ext{Avg Total Assets}}ight) 	imes \left(\frac{	ext{Avg Total Assets}}{	ext{Avg Equity}}ight)$

Question 11

5-Step DuPont Model for ROE

Accepted Answer

Isolates tax burden, interest burden, operating efficiency, total asset efficiency, and financial leverage:
$ROE = 	ext{Tax Burden} 	imes 	ext{Interest Burden} 	imes 	ext{EBIT Margin} 	imes 	ext{Asset Turnover} 	imes 	ext{Leverage}$
$ROE = \left(\frac{	ext{Net Income}}{	ext{EBT}}ight) 	imes \left(\frac{	ext{EBT}}{	ext{EBIT}}ight) 	imes \left(\frac{	ext{EBIT}}{	ext{Revenue}}ight) 	imes \left(\frac{	ext{Revenue}}{	ext{Avg Assets}}ight) 	imes \left(\frac{	ext{Avg Assets}}{	ext{Avg Equity}}ight)$

Question 12

LIFO vs. FIFO Financial Statement Effects (Rising Prices)

Accepted Answer

In an inflationary environment with stable/increasing quantities:
- **LIFO:** Higher COGS $\rightarrow$ Lower Net Income $\rightarrow$ Lower Income Taxes $\rightarrow$ Higher Operating Cash Flow (tax savings) $\rightarrow$ Lower Ending Inventory.
- **FIFO:** Lower COGS $\rightarrow$ Higher Net Income $\rightarrow$ Higher Income Taxes $\rightarrow$ Lower Operating Cash Flow $\rightarrow$ Higher Ending Inventory.

Question 13

LIFO Reserve and Inventory Conversion Formulas

Accepted Answer

To convert LIFO financial statements to FIFO:
- $	ext{Inventory}_{FIFO} = 	ext{Inventory}_{LIFO} + 	ext{LIFO Reserve}$
- $	ext{COGS}_{FIFO} = 	ext{COGS}_{LIFO} - (	ext{LIFO Reserve}_t - 	ext{LIFO Reserve}_{t-1})$
- $	ext{Retained Earnings}_{FIFO} = 	ext{Retained Earnings}_{LIFO} + 	ext{LIFO Reserve} 	imes (1 - t)$

Question 14

Deferred Tax Liabilities (DTL) vs. Deferred Tax Assets (DTA)

Accepted Answer

- **DTL (Accounting Income > Taxable Income):** Arises when tax expense is recognized before cash tax payment is due (e.g., accelerated tax depreciation vs. straight-line reporting). Results in future cash outflow.
- **DTA (Accounting Income < Taxable Income):** Arises when tax payable exceeds financial tax expense (e.g., warranty provisions or tax loss carryforwards). Results in future tax savings.

Question 15

Lower of Cost or NRV/Market (Inventory Valuation Rules)

Accepted Answer

- **IFRS:** Measured at lower of Cost or Net Realizable Value (NRV = Estimated Selling Price - Estimated Completion & Selling Costs). Write-downs can be reversed.
- **US GAAP:** Measured at lower of Cost or Market (Market = Replacement Cost, bounded between ceiling $NRV$ and floor $NRV - 	ext{normal profit margin}$). Reversals are prohibited.

Question 16

Cash Flow Statement Differences: IFRS vs. US GAAP

Accepted Answer

- **US GAAP:**
  - Operating: Interest Received, Dividends Received, Interest Paid.
  - Financing: Dividends Paid.
- **IFRS:**
  - Interest/Dividends Received: Operating or Investing.
  - Interest/Dividends Paid: Operating or Financing.

Question 17

Free Cash Flow to Firm (FCFF) from Operating Cash Flow

Accepted Answer

Calculated from Cash Flow from Operations (CFO):
$FCFF = CFO + Int 	imes (1 - 	ext{Tax Rate}) - FCInv$

*Where $Int$ is interest expense paid (under US GAAP) and $FCInv$ is fixed capital investment (CapEx).*

Question 18

5-Step Revenue Recognition Framework (IFRS 15 / ASC 606)

Accepted Answer

1. Identify the contract(s) with a customer.
2. Identify the separate performance obligations in the contract.
3. Determine the transaction price.
4. Allocate the transaction price to the performance obligations.
5. Recognize revenue when (or as) the entity satisfies a performance obligation.

Question 19

Financial Statement Impact of Capitalizing vs. Expensing Costs

Accepted Answer

- **Capitalizing an Expenditure:** Creates an asset. Lower current-period expense $\rightarrow$ Higher current Net Income $\rightarrow$ Higher CFO, Lower CFI $\rightarrow$ Smoother earnings over time.
- **Expensing an Expenditure:** Immediate income statement hit. Lower current Net Income $\rightarrow$ Lower CFO, Higher CFI $\rightarrow$ Higher future net income.

Question 20

Solvency Ratios: Debt-to-Equity and Interest Coverage

Accepted Answer

- **Debt-to-Equity:** $\frac{	ext{Total Debt}}{	ext{Total Equity}}$
- **Interest Coverage:** $\frac{	ext{EBIT}}{	ext{Interest Payments}}$
- **Financial Leverage:** $\frac{	ext{Average Total Assets}}{	ext{Average Total Equity}}$

CFA Level 1 - Quantitative Methods & Financial Reporting Analysis

Cards in this deck

Related Flashcard Sets

JLPT N5 - Essential Grammar & Kanji

Kubernetes Fundamentals & Container Orchestration

Pharmacology - Drug Classes & Mechanisms of Action

CompTIA Security+ (SY0-601) - Threats, Attacks & Vulnerabilities