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One basic theory behind the risk and return calculation and the portfolio risk and return calculation is that the investors want to maximize the returns from a set of investment instrument for a given level of risk. Rational investors are risk-averse. Jones (2002) states if it is seen that two investment assets having same return differ in risk level the investor would choose the investment asset with lower risk. Though all people are not rational and risk-averse for simplicity the theory follows the rational investors.

There are differences in the definition of risk in most of the financial literature. But the most common thing is risk and uncertainty- the two terms are used interchangeably. For most of the cases, risk means the uncertainty of future outcome. Alternatively, it can be said that risk is the probability of the adverse or negative outcome (Gitman, 2015).

Expected return of an Asset = ∑ (Probability × Return)

= (0.35×6) + (.30×5) + (.20×16) + (.15×12)

=.086 or 8.6%

Variance = ∑ (Probability × Deviation squared)

Standard Deviation= √ [∑ (Probability × Deviation squared)]

One of the best measures of risk is variance or standard deviation of expected returns. Mathematically expected return of an individual asset is the sum of the product of probabilities of various returns on certain asset. It is the best known measure of expected return so far. Probabilities are used because these are the numbers which represent the chances of occurrence of different outcomes (Jones, 2002). The range of probability is 0 to 1. Sum of the probability of all outcomes is 1. When probabilities are allocated to various random variables it is called probability distribution.

Risk is the dispersion of return from its expected value. The theory is that the more dispersed the return is the greater the uncertainty of future returns. Dispersion of outcomes measures the variability around the expected outcomes. Variance is the weighted dispersion of all outcomes around the value.

Deviation

Deviation squared

Probability

Probability × Deviation squared

(.06-.086) = -0.26

0.000676

0.35

0.000237

(.05-.086) = -0.036

0.001296

0.30

0.000389

(.16-.086) = 0.074

0.005476

0.20

0.001095

(.12-.086) = 0.034

0.001156

0.15

0.000173

Variance = 0.001894

Standard Deviation = 0.0435

Return on Security Asset

Investors can simply evaluate the investments by comparing the historical returns. The purpose of the investment is to defer the current consumption and add wealth in order to consume more in future. So return on an investment somewhat refers change in wealth resulting from the investment (Northington & Gerard, 2011). Change in wealth occurs through cash inflows such as profit, interest, and dividends or caused by a change in the price of assets. When the gain is calculated any investor compares the investment value of beginning with the ending investment value. When an investor has higher-end investment value than the beginning investment value he recognizes it as gain from investment. An investor also calculates the holding period return. Holding period return is expressed in percentage term.

Problem 7-2: Holding period Gain and return

Holding period Gain = Ending value investment- Beginning value investment

= 1371.92 – 1315.6 = 56.32

Ending investment = Number of shares × Price per share

= (16 × 54.12) + (10 × 50.60)

= 1371.92

Beginning investment= (26 × 50.60)

= 1315.6

Holding period return=

= 1371.92÷1315.6

= 1.042

Market portfolio Theory and CAPM

The capital market theory implies that the investors cannot expect compensation for the risk that could be diversified away. Diversifiable risk portion in a market is called unsystematic risk. Capital Market line represents the risk of an investor that emerged from the volatility of the investment. But the limitation of CML it fails to explain the risk-return tradeoff for individual risky assets. CAPM model extends the capital market model in a way that allows evaluation of both diversified portfolios and individual securities (Gitman, 2015).

CAPM model identifies the non-diversifiable risk as the systematic risk which is represented by Beta (ɓ) coefficient. It measures the systematic risk of an individual security and assigns a value to it and Beta measures the extent the reaction of the market movements on an individual security mathematically it is the coefficient of market risk premium. The market risk premium is the difference between the risk-free rate and market rata and it represents the premium rate for which an investor will invest in risky assets.

Problem 7-3: Capital Asset pricing model (CAPM)

According to CAPM model the required rate of returns of the stocks is,

E(R) = Risk Free Rate + Beta [(Expected Market Rate- Risk Free Rate)]

Stock

Beta

Expected Return

A

0.70

10.3%

B

0.85

11.65

C

1.50

17.5

Risk Free Rate

4%

Market Rate

13%

Break-Even Analysis

Break-Even analysis is a commonly used tool which analyzes the relationship between sales volume and profitability. In break-even analysis Fixed cost and variable costs are needed. Variable cost changes with the change of quantity produced. The fixed asset has no relationship with production or sales. Fixed cost can’t be changed in zero production while variable cost is zero (Ross, Westerfield & Jordan, 2008). In the given problem it is shown that how sales unit is calculated from given level of EBIT and fixed and variable cost.

Problem 7-4: Break-even point and selling price

A) We know that,

EBIT = (sales- Variable cost-Fixed cost)

450000= (Sales- .54*sales – 550000)

1000000= .46*sales

Sales = 2173913

Average selling Price = 2173913÷400000

= 5.43

Sales = 400000 × 5.43 = 2173913

Total Variable cost = 2173913 × .54 = 1173913

Revenue before FC = 1000000

Total Fixed cost = 550000

EBIT = 450000

Operating leverage

Operating leverage is the degree to which a firm is obliged to its fixed production cost. A firm with lower operating leverage needs a lower volume of sales to cover its fixed obligation than the firm with higher operating leverage. The implication of operating leverage is that it can measure the sensitivity of percentage change of Sales in its EBIT and operating cash flows (Ross et al., 2008). The degree of operating leverage helps to measure this percentage change. In the given problem it is shown that how break-even level of output is calculated and how Degree of operating leverage and percentage change in EBIT can be calculated from a given level of change in sales.

Problem 7-5: Operating Leverage

Break-Even level of Output = Fixed cost÷ (Price- Variable Cost)

Break-Even for Jeddah Manufacturers = 300000 ÷ (800-550)

= 1200

Dollar sales Volume = 1200×800

= 960000

Operating Cash Flow = EBIT+ Depreciation-Taxes

Degree of operating leverage = 1+ FC/OCF

= 1+ 300000/950000

= 1.315

OCF = Operating Cash Flow = -Fixed cost + (Price – Variable Cost) × Quantity

= -300000 + (800-550) × 5000

= 9500000

Change in OCF = DOL× Percentage change in Quantity

= 1.315 × .15

= 19.72%

So if Sales Increase 15% EBIT will be increased by 19.72%.

References

Gitman, L. (2015). Principles of Managerial Finance (7th ed.). New York: PEARSON.

Jones, C. (2002). Introduction to Financial Management (10th ed.). Boston: Richard D.

Northington, S., & Gerard, G. (2011). Finance. New York: Ferguson’s.

Ross, S., Westerfield, R., & Jordan, B. (2008). Corporate finance fundamentals. Boston: McGraw Hill.

August 18, 2023

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