CFA Level 1 - Quantitative Methods & Financial Statement Analysis Flashcards

Question 1

What is the formula for Present Value (PV)?

Accepted Answer

The Present Value (PV) formula calculates the current worth of a future sum of money or stream of cash flows given a specified rate of return.
$PV = \frac{FV}{(1+r)^n}$
Where:
$FV$ = Future Value
$r$ = Discount rate per period
$n$ = Number of periods

Question 2

What is the formula for Future Value (FV)?

Accepted Answer

The Future Value (FV) formula calculates the value of an asset or cash at a specified date in the future, based on a given rate of return.
$FV = PV 	imes (1+r)^n$
Where:
$PV$ = Present Value
$r$ = Interest rate per period
$n$ = Number of periods

Question 3

Differentiate between the Stated Annual Rate (SAR) and the Effective Annual Rate (EAR).

Accepted Answer

The **Stated Annual Rate (SAR)** (or nominal rate) is the interest rate before taking inflation or compounding into account. The **Effective Annual Rate (EAR)** is the actual annual rate of return earned or paid, considering the effect of compounding more frequently than once a year.
$EAR = (1 + \frac{SAR}{m})^m - 1$
Where $m$ is the number of compounding periods per year.

Question 4

Explain the difference between an annuity and a perpetuity.

Accepted Answer

An **annuity** is a series of equal payments or receipts occurring at regular intervals for a finite period. A **perpetuity** is a special type of annuity that involves an infinite series of equal payments or receipts occurring at regular intervals.
PV of Perpetuity = $\frac{PMT}{r}$

Question 5

What is Net Present Value (NPV) and its decision rule?

Accepted Answer

**Net Present Value (NPV)** is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. It's used in capital budgeting to analyze the profitability of a projected investment.
Decision Rule: Accept projects with $NPV > 0$. Reject projects with $NPV < 0$. Indifferent if $NPV = 0$.

Question 6

What is the Internal Rate of Return (IRR) and its decision rule?

Accepted Answer

The **Internal Rate of Return (IRR)** is the discount rate that makes the Net Present Value (NPV) of all cash flows from a particular project equal to zero. It represents the project's expected rate of return.
Decision Rule: Accept projects where $IRR >$ required rate of return (hurdle rate). Reject if $IRR <$ hurdle rate.

Question 7

Define the Null Hypothesis ($H_0$) and Alternative Hypothesis ($H_a$).

Accepted Answer

The **Null Hypothesis ($H_0$)** is a statement of no effect or no difference, often representing the status quo or a belief to be tested. The **Alternative Hypothesis ($H_a$)** is what the researcher is trying to prove, suggesting an effect or difference exists.

Question 8

Differentiate between Type I and Type II errors in hypothesis testing.

Accepted Answer

A **Type I Error** occurs when the null hypothesis is true, but we incorrectly reject it (false positive). Its probability is denoted by $\alpha$ (significance level). A **Type II Error** occurs when the null hypothesis is false, but we fail to reject it (false negative). Its probability is denoted by $\beta$.

Question 9

How is the p-value interpreted in hypothesis testing?

Accepted Answer

The **p-value** is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true.
Interpretation: If $p-value < \alpha$ (significance level), reject $H_0$. If $p-value \ge \alpha$, fail to reject $H_0$.

Question 10

What is the significance level ($\alpha$) in hypothesis testing?

Accepted Answer

The **significance level ($\alpha$)** is the maximum probability of making a Type I error that a researcher is willing to accept. Common values are 0.01, 0.05, or 0.10. It defines the critical region for the test.

Question 11

Outline the general steps involved in hypothesis testing.

Accepted Answer

1. State the null ($H_0$) and alternative ($H_a$) hypotheses.
2. Select the appropriate test statistic.
3. Specify the significance level ($\alpha$).
4. State the decision rule.
5. Collect data and calculate the test statistic.
6. Make a statistical decision (reject or fail to reject $H_0$).
7. Make an economic or investment decision.

Question 12

When would you use a t-test versus a z-test?

Accepted Answer

A **z-test** is used when the population variance is known, or when the sample size is large (typically $n \ge 30$). A **t-test** is used when the population variance is unknown and the sample size is small (typically $n < 30$), assuming the population is normally distributed.

Question 13

State the fundamental accounting equation.

Accepted Answer

The fundamental accounting equation is:
$Assets = Liabilities + Equity$
This equation must always balance, reflecting the dual-aspect concept of accounting.

Question 14

What are the main classifications of assets on the balance sheet?

Accepted Answer

Assets are classified into:
*   **Current Assets:** Expected to be converted to cash or used up within one year or one operating cycle (e.g., Cash, Accounts Receivable, Inventory).
*   **Non-current Assets (Long-term Assets):** Assets not expected to be converted to cash or used up within one year (e.g., Property, Plant & Equipment, Intangible Assets, Long-term Investments).

Question 15

What are the main classifications of liabilities on the balance sheet?

Accepted Answer

Liabilities are classified into:
*   **Current Liabilities:** Obligations due within one year or one operating cycle (e.g., Accounts Payable, Short-term Debt, Unearned Revenue).
*   **Non-current Liabilities (Long-term Liabilities):** Obligations due beyond one year (e.g., Bonds Payable, Long-term Notes Payable, Deferred Tax Liabilities).

Question 16

What are the primary components of Shareholders' Equity?

Accepted Answer

Shareholders' Equity typically includes:
*   **Contributed Capital:** Common Stock, Preferred Stock, Additional Paid-in Capital.
*   **Retained Earnings:** Accumulated net income less dividends.
*   **Other Comprehensive Income (OCI):** Gains/losses not recognized in net income (e.g., unrealized gains/losses on available-for-sale securities).
*   **Treasury Stock:** Shares repurchased by the company.

Question 17

Compare GAAP and IFRS rules for inventory valuation methods (LIFO/FIFO).

Accepted Answer

*   **GAAP:** Permits the use of LIFO (Last-In, First-Out), FIFO (First-In, First-Out), and Weighted-Average methods. LIFO is commonly used in the US to reduce taxable income during periods of rising costs.
*   **IFRS:** Prohibits the use of LIFO. Only permits FIFO and Weighted-Average methods. This generally results in higher reported inventory values and lower Cost of Goods Sold (COGS) during inflation compared to LIFO under GAAP.

Question 18

How do GAAP and IFRS differ regarding the revaluation of Property, Plant, and Equipment (PP&E)?

Accepted Answer

*   **GAAP:** Generally prohibits the upward revaluation of PP&E to fair value. Assets are typically carried at historical cost less accumulated depreciation.
*   **IFRS:** Permits the revaluation model, allowing PP&E to be carried at a revalued amount (fair value at the date of revaluation less subsequent depreciation). Revaluation gains are recognized in Other Comprehensive Income (OCI) unless they reverse a previous revaluation loss recognized in profit or loss.

Question 19

What are the three main sections of the Cash Flow Statement?

Accepted Answer

The three main sections are:
1.  **Operating Activities (CFO):** Cash flows from the primary revenue-generating activities of the business.
2.  **Investing Activities (CFI):** Cash flows from the acquisition and disposal of long-term assets and investments.
3.  **Financing Activities (CFF):** Cash flows from debt and equity transactions (e.g., issuing/repurchasing stock, borrowing/repaying debt, paying dividends).

Question 20

Explain the difference between the direct and indirect methods for preparing the operating activities section of the Cash Flow Statement.

Accepted Answer

Both methods yield the same net cash flow from operating activities.
*   **Direct Method:** Shows major classes of gross cash receipts and gross cash payments (e.g., cash received from customers, cash paid to suppliers).
*   **Indirect Method:** Starts with net income and adjusts for non-cash items and changes in working capital accounts to arrive at cash flow from operations.
IFRS encourages the direct method but permits the indirect. GAAP encourages the direct method but the indirect method is almost universally used in practice.

Question 21

Define Free Cash Flow to Firm (FCFF).

Accepted Answer

**Free Cash Flow to Firm (FCFF)** represents the total cash flow generated by a company's operations that is available to all providers of capital (both debt and equity holders) after accounting for capital expenditures.
$FCFF = Net Income + Non-cash Charges + Interest Exp(1-t) - FCInv - WCInv$
Where: $FCInv$ = Fixed Capital Investment, $WCInv$ = Working Capital Investment.

Question 22

Define Free Cash Flow to Equity (FCFE).

Accepted Answer

**Free Cash Flow to Equity (FCFE)** represents the cash flow available to a company's common equity holders after all operating expenses, interest, and principal payments have been paid, and necessary investments in working capital and fixed capital have been made.
$FCFE = FCFF - Interest Exp(1-t) + Net Borrowing$
Alternatively: $FCFE = Net Income - FCInv - WCInv + Net Borrowing$

Question 23

What is the Sharpe Ratio and its formula?

Accepted Answer

The **Sharpe Ratio** measures the excess return (or risk premium) per unit of total risk (standard deviation) in an investment or portfolio. It helps investors understand the return of an investment compared to its risk.
$Sharpe Ratio = \frac{R_p - R_f}{\sigma_p}$
Where:
$R_p$ = Portfolio return
$R_f$ = Risk-free rate
$\sigma_p$ = Standard deviation of portfolio returns

Question 24

Explain the 3-step DuPont Analysis breakdown of Return on Equity (ROE).

Accepted Answer

The 3-step DuPont Analysis breaks down Return on Equity (ROE) into three components:
$ROE = Net \ Profit \ Margin 	imes Asset \ Turnover 	imes Financial \ Leverage$
$ROE = (\frac{Net \ Income}{Sales}) 	imes (\frac{Sales}{Average \ Total \ Assets}) 	imes (\frac{Average \ Total \ Assets}{Average \ Shareholder \ Equity})$
This shows how profitability, asset efficiency, and financial leverage contribute to ROE.

Question 25

Compare GAAP and IFRS treatment of development costs for internally generated intangible assets.

Accepted Answer

*   **GAAP:** Generally requires all research and development (R&D) costs to be expensed as incurred, with limited exceptions (e.g., software development costs after technological feasibility is established).
*   **IFRS:** Requires research costs to be expensed. However, development costs (after certain criteria for technical and commercial feasibility are met) **must be capitalized** as an intangible asset and amortized over its useful life. This can lead to higher assets and net income under IFRS compared to GAAP for companies with significant development activities.

CFA Level 1 - Quantitative Methods & Financial Statement Analysis

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