Unit4 - Subjective Questions

In financial management, Return represents the reward for investing. It is the gain or loss on an investment over a specified period, expressed as a percentage of the investment's cost.

The total return of an asset generally consists of two components:

1. Current Income (Yield): The periodic cash flow received from the investment, such as dividends for stocks or interest for bonds.
2. Capital Appreciation (Capital Gain/Loss): The change in the market price of the asset over the holding period (i.e., the difference between the selling price and the purchase price).

The formula for Total Return () is:

• = Dividend/Interest income
• = Price at the end of the period
• = Price at the beginning of the period

The Expected Return is the weighted average of all possible returns, where the weights correspond to the probability of each return occurring. It represents the mean value of the probability distribution of future returns. While the actual return may differ, the expected return provides a central tendency for decision-making.

Calculation:
It is calculated by summing the product of each possible return and its associated probability.

The formula is:

Where:

• = Expected return
• = Possible return in scenario
• = Probability of scenario occurring
• = Total number of possible scenarios

Risk in finance refers to the variability or uncertainty of returns associated with an investment. It is the possibility that the actual return will deviate from the expected return.

Types of Risk:

1. Systematic Risk (Market Risk):

   • Refers to the risk inherent to the entire market or market segment.
   • It is caused by macro-economic factors like inflation, interest rate changes, or political instability.
   • Crucial Characteristic: It is non-diversifiable (cannot be eliminated by holding a variety of assets).

2. Unsystematic Risk (Specific Risk):

   • Refers to risk specific to a company or industry.
   • It is caused by factors like management strikes, lawsuits, or competition.
   • Crucial Characteristic: It is diversifiable (can be reduced or eliminated through portfolio diversification).

Standard Deviation () is the most common statistical measure used to quantify the risk of a single asset. It measures the dispersion (variability) of returns around the expected return (mean). A higher standard deviation implies higher volatility and, consequently, higher risk.

Formula:

Steps to Calculate:

1. Calculate Expected Return (): Multiply each possible return by its probability and sum them up.
2. Determine Deviations: Subtract the expected return from each possible return ().
3. Square the Deviations: Square the result from step 2 ().
4. Weight by Probability: Multiply the squared deviations by their respective probabilities.
5. Calculate Variance: Sum the weighted squared deviations to get the Variance.
6. Calculate Standard Deviation: Take the square root of the Variance.

The Coefficient of Variation (CV) is a relative measure of risk. It represents the amount of risk (standard deviation) per unit of expected return.

Formula:

Utility in Comparison:
Standard deviation alone can be misleading if two assets have significantly different expected returns. The CV allows for a fair comparison by standardizing the risk.

• Example: If Asset A has a return of 10% and risk of 5%, and Asset B has a return of 20% and risk of 8%, Asset B has higher absolute risk. However, Asset A has a CV of 0.5, while Asset B has a CV of 0.4. Asset B offers a better risk-return trade-off because it has less risk per unit of return.

Leverage in financial management refers to the ability of a firm to use fixed-cost assets or funds to magnify the returns to its owners. It acts as a mechanical lever: a small change in one variable (like Sales) results in a larger change in another variable (like EBIT or EPS).

Implication for Risk and Return:
Leverage is often described as a "double-edged sword":

• Return: Ideally, leverage increases shareholder returns. If the firm earns more on the fixed-cost assets/funds than the cost of using them, the surplus increases the return to owners.
• Risk: Leverage increases the variability of returns. If the firm fails to cover the fixed costs, losses are also magnified. Therefore, high leverage implies high risk alongside the potential for high returns.

Operating Leverage measures the sensitivity of a firm's Operating Profit (EBIT - Earnings Before Interest and Taxes) to changes in its Sales revenue. It reflects the extent to which a firm uses fixed operating costs in its operations.

Source of Operating Leverage:
Operating leverage is created by the presence of Fixed Operating Costs (such as rent, depreciation, and salaries) in the firm's cost structure.

• If a firm has high fixed costs compared to variable costs, a small percentage increase in sales will result in a much larger percentage increase in EBIT, because the fixed costs remain constant regardless of the volume of sales.
• Conversely, if sales drop, EBIT will drop disproportionately.

The Degree of Operating Leverage (DOL) quantifies the responsiveness of Operating Profit (EBIT) to changes in Sales. It indicates how many percentage points EBIT will change for a 1% change in Sales.

Formula:
At a specific level of output, DOL can be calculated as:

Also represented as:

Where:

• = Quantity sold
• = Selling price per unit
• = Variable cost per unit
• = Total fixed operating costs
• = Sales - Variable Costs

Financial Leverage measures the sensitivity of a firm's Earnings Per Share (EPS) to changes in its Operating Profit (EBIT). It arises from the presence of fixed financial charges, such as interest on debt and preference dividends.

Relation to "Trading on Equity":
Financial leverage is often referred to as "Trading on Equity." This concept implies that a company uses equity as a base to borrow funds (debt). If the company can earn a return on assets (ROA) that is higher than the interest rate paid on the debt, the excess earnings belong to the equity shareholders, thereby boosting the EPS and Return on Equity (ROE). However, if the ROA is lower than the interest rate, it destroys shareholder value.

The Degree of Financial Leverage (DFL) quantifies the responsiveness of Earnings Per Share (EPS) to changes in Operating Profit (EBIT). It indicates the percentage change in EPS resulting from a 1% change in EBIT.

Formula:

For calculation at a specific level of EBIT:

Or, if Preference Dividend () is involved:

Where:

• = Interest Expense
• = Earnings Before Tax
• = Tax rate

1. Business Risk:

• Definition: The risk associated with the firm's operations and its ability to cover operating costs.
• Associated Leverage: Operating Leverage.
• Cause: Driven by the firm's industry, competition, product demand, and the proportion of fixed operating costs (Cost Structure).
• Independence: It exists even if the firm has no debt.

2. Financial Risk:

• Definition: The additional risk placed on common stockholders as a result of using debt and preference shares.
• Associated Leverage: Financial Leverage.
• Cause: Driven by the firm's capital structure (Debt-Equity mix) and the obligation to pay fixed financial charges (Interest).
• Dependence: It only exists if the firm uses debt financing.

Combined Leverage (also known as Total Leverage) is the total risk of the firm resulting from the combined effect of both Operating and Financial Leverage. It looks at the entire income statement from top to bottom.

Measurement:
It measures the sensitivity of Earnings Per Share (EPS) to changes in Sales. It answers the question: "If Sales change by 1%, by what percentage will EPS change?"

A high degree of combined leverage indicates that a small change in sales volume will result in a massive change in the returns available to shareholders, implying high total risk.

Combined Leverage is the product of Operating Leverage and Financial Leverage. The magnification of sales into EBIT (Operating) is further magnified from EBIT into EPS (Financial).

Relationship:

Derivation/Formula:
Since and

Multiplying them:

Calculation Formula:
Using absolute values:

Holding Period Return (HPR) is the total return earned on an asset or investment portfolio over the period for which the asset was held. It is a useful measure for comparing the performance of investments held for different durations.

Formula:

Example:
Suppose you bought a stock for 5 in dividends, and the price rose to $110.

• Beginning Value = $100
• End Value = $110
• Income = $5

The Risk-Return Trade-off is a fundamental principle in finance which states that the potential return rises with an increase in risk. In other words, to persuade investors to accept a higher risk, an investment must offer a higher expected return.

• Low levels of uncertainty (Low Risk) are associated with low potential returns (e.g., Government Bonds).
• High levels of uncertainty (High Risk) are associated with high potential returns (e.g., Small-cap Stocks, Cryptocurrencies).

Investors are generally assumed to be risk-averse; they will not accept additional risk unless compensated with a 'risk premium' over the risk-free rate.

Impact on Break-even Point:
High fixed operating costs raise the firm's Break-even Point (the level of sales where total revenue equals total costs). The firm must sell a larger quantity of goods just to cover its costs before it starts generating any profit.

Impact on Risk Profile:

• Higher Business Risk: A higher break-even point means the firm is more vulnerable to economic downturns. If sales decline slightly, the firm may plunge into losses quickly compared to a firm with low fixed costs.
• Higher Volatility: It increases the Degree of Operating Leverage (DOL), meaning EBIT becomes very volatile in response to sales fluctuations.

Comparison of Operating and Financial Leverage:

Calculation:

Interpretation:
A Degree of Combined Leverage of 3.5 means that for every 1% change in Sales, the firm's Earnings Per Share (EPS) will change by 3.5% in the same direction.

• If Sales increase by 10%, EPS will increase by 35% ().
• If Sales decrease by 10%, EPS will decrease by 35%.

This indicates the total leverage risk exposure of the firm.

Favourable (Positive) Leverage:
This occurs when the firm earns a return on the invested funds (Return on Investment/Assets) that is higher than the fixed cost of those funds (Interest rate). In this scenario, the surplus return goes to the equity shareholders, increasing EPS and ROE. This is the goal of financial leverage.

Unfavourable (Negative) Leverage:
This occurs when the firm earns a return on invested funds that is lower than the fixed cost of funds. Here, the firm is paying more in interest than it is earning from the operations funded by that debt. This erodes shareholder value and reduces EPS.

While both Range and Standard Deviation measure dispersion (spread) of returns:

1. Sensitivity to Outliers: The Range considers only the two extreme values (Highest Return - Lowest Return). It ignores all the data points in between. A single outlier can distort the perception of risk.
2. Probability Weighting: Standard Deviation considers every possible outcome and its probability. It measures how far, on average, the returns deviate from the mean.
3. Statistical Robustness: Standard deviation is mathematically more robust and is used in further financial calculations (like Beta, Correlation, and Normal Distribution analysis), whereas Range is a crude, static measure.