CHAPTER 3 RISK AND RETURN

©Correia, Flynn, Uliana & Wormald 2 Learning Objectives By the end of the chapter, you should be able to; n Distinguish between business risk, financial risk and investment risk n Calculate the following indicators of return u Earnings before interest and tax u Percentage return to shareholders u Expected return based on probabilities n Calculate the following indicators of risk u Degree of operating leverage u Degree of financial leverage u Variance of returns u Standard deviation of returns u Coefficient of variation u Z score n Understand the risks and returns of financial markets

©Correia, Flynn, Uliana & Wormald 3 Overview   Introduction   The concept of risk   Business risk   Financial risk   Total Company risk   Measuring expected return and risk   Measuring expected return for a single share   Measuring risk for a single share   The Mean-Variance Rule   Interpreting the summary statistics   Properties of a normal distribution   Comparison of single shares   Risks and returns in financial markets   Summary

©Correia, Flynn, Uliana & Wormald 4 There is a trade-off between risk and return Return Risk

©Correia, Flynn, Uliana & Wormald 5 What is Risk? n The word risk is usually used in a context of potential hazard of possibility of an unfortunate outcome resulting from a given action. n In financial management, risk also indicates the expectation that the actual outcome of the project may differ from the expected outcome. n The term risk and uncertainty are used interchangeably

©Correia, Flynn, Uliana & Wormald 6 What is Business Risk? n Business risk refers to the nature of the business itself and the uncertainty that surrounds the business operating environment n This is reflected in variability of sales and costs and the nature of the firm’s cost structure

©Correia, Flynn, Uliana & Wormald 7 Variability of Costs Relationship between fixed and variable costs Fixed costs remain constant regardless of the sales volume. NB: For a given range. Variable costs are directly related to the sales volume.

©Correia, Flynn, Uliana & Wormald Variability of Costs (continued) 8 The break even point is where Sales Revenue is equal to total costs (fixed + variable costs). Neither profit nor loss is made. Note how the Total Cost line does not begin at zero. Why?

©Correia, Flynn, Uliana & Wormald 9 Business Risk n Example: Leverage Ltd has the following budgeted information F Fixed costs (FC) R10m p.a. F Variable cost (VC) R400 per unit F Selling price (S) R1000 per unit F Expected demand units (minimum)

©Correia, Flynn, Uliana & Wormald 10 Break-even n Break even (units) = units What is the break even?

©Correia, Flynn, Uliana & Wormald 11 What is the effect of volume on EBIT? (Earnings before Interest & Tax)

©Correia, Flynn, Uliana & Wormald 12 Business Risk & Operating Leverage n How do we measure operating leverage? n This means an increase in sales of 10% will lead to an increase of 10% x 2.25 that is 22.5% in EBIT. n In our example, sales increased by 33.3% and EBIT increased by 33.3% x 2.25 = 75%.

©Correia, Flynn, Uliana & Wormald 13 Business risk n Assume now that Leverage Ltd decides to install machinery which will increase fixed costs by R5m per year and reduce variable costs by R150 to R250 per unit n The new break-even units will be: units. [ /(1000 – 250)]

©Correia, Flynn, Uliana & Wormald 14 Business risk n How will EBIT change now? n DOL = 22.5/7.5 = 3. A 33.3% increase in sales has resulted in 100% increase in EBIT.

©Correia, Flynn, Uliana & Wormald 15 Business risk n The riskier option offers greater potential losses if sales volumes are low and greater profits when sales volumes are high. n Thus, total business risk is therefore a function both sales and costs

©Correia, Flynn, Uliana & Wormald 16 Financial Risk n Financial Risk is due to financing with debt. Why? n Interest must be paid regardless of the performance of the firm. n How do we measure financial risk? n Degree of Financial Leverage (DFL)

©Correia, Flynn, Uliana & Wormald 17 Total company risk n Operating leverage and financial leverage work together to create what is referred to as Degree of Combined Leverage (DCL) n The degree of combined leverage is Or DCL = Contribution/Net income before tax

©Correia, Flynn, Uliana & Wormald 18 Total company risk n Example from the Textbook n

©Correia, Flynn, Uliana & Wormald 19 Measuring Returns Returns from an investment (such as shares) can be measured. Returns consist of two components: 1 – Dividends received 2 – Capital Appreciation

©Correia, Flynn, Uliana & Wormald 20 Expected Return The inclusion of probabilities allows for the approximation of an expected return.

©Correia, Flynn, Uliana & Wormald 21 Measuring Expected Return Probabilities add up to 100% All events are mutually exclusive

©Correia, Flynn, Uliana & Wormald 22 Mean-Variance Rule X is preferred to Z. W is preferred to Y. Why? Superior returns in each case for the same risk. X is superior to Y, as it offers the same return for a lower level of risk.

©Correia, Flynn, Uliana & Wormald 23 Measuring Risk n A more scientific approach is to examine the share's standard deviation of returns. n Standard deviation is a measure of the dispersion of possible outcomes. n The greater the standard deviation, the greater the uncertainty, and therefore, the greater the RISK.

©Correia, Flynn, Uliana & Wormald 24 Measuring Risk – Standard Deviations The above calculation is explained further on page 3.10 and 3.11 of Financial Management 7 th Edition and in later slides. The standard deviation formula:

©Correia, Flynn, Uliana & Wormald The Normal Distribution 25 Mean = 12% (The expected rate of return) What does the peak of the graph denote? One Standard Deviation: 68.3% chance that the return will be between –1σ and +1σ Two Standard Deviations: 95.5% chance that the actual return will fall between +2σ and –2σ

©Correia, Flynn, Uliana & Wormald 26 Measuring Risk for a Single Share Probability x Return = 10 % x 50% = 5.0%

©Correia, Flynn, Uliana & Wormald 27 Measuring Risk for a Single Share Follow the steps sequentially to ensure accuracy.

©Correia, Flynn, Uliana & Wormald 28 n Risk may be expressed as n Standard Deviation = Variance (0.5) = = 14.4% = (R i - R*) P(R i ) 2   n i=1 Measuring Risk for a Single Share

©Correia, Flynn, Uliana & Wormald 29 Equal Expected Returns Comparison of single shares Example: Choosing between two alternative identical expected returns Answer: Trinpak has a much tighter distribution than Claycor. Based on the mean variance rule, investors are likely to invest in Trinpak than Claycor. The demand for Trinpak will force its price upwards and downwards for Claycor until an equilibrium is reached.

©Correia, Flynn, Uliana & Wormald 30 Different Expected Returns Comparison of single shares n Example: Selecting between two alternatives: different expected returns In this case, some basis of comparison is required. Two indicators (the coefficient of variation and the z-score) may be used.

©Correia, Flynn, Uliana & Wormald 31 Coefficient of Variation The results indicate that Atlas exposes the investor to 0.5 units of risk for each expected unit of return while Brenco exposes the investor to only 0.4 units of risk for every unit of return. On this basis, Brenco seems to be a better investment.

©Correia, Flynn, Uliana & Wormald 32 The Z-Score The Z Score is a statistical number. Used to find the probability of a return falling below a given level.

©Correia, Flynn, Uliana & Wormald 33 The Z-Score Example: Atlas Brenco Atlas Brenco Z-score at 0% = -2 0 – 20 = Table E reading % probability 2.28% 0.62% (0.5 – Table reading)

©Correia, Flynn, Uliana & Wormald 34 Using Table E to determine probabilities - Atlas

©Correia, Flynn, Uliana & Wormald 35 Covariance & Correlation n Covariance measures how share returns move together n Cov(x, y) > 0, x and y will tend to move in the same direction n Cov(x, y) < 0, x and y will tend to move in opposite directions n Cov(x, y) = 0,x and y are independent.

©Correia, Flynn, Uliana & Wormald 36 Correlation Co-efficient n The Correlation co-efficient measures the strength of the relationship between x and y n The correlation co-efficient is between -1 and +1. n Example: Correlation of Share price movements

©Correia, Flynn, Uliana & Wormald 37 Do investors require a higher return for higher levels of risk? What is the evidence? n The evidence supports the risk-return relationship in South Africa. n Investing in ordinary shares which involves higher risk has offered higher returns than bonds. n Bills which have the lowest level of risk, offered investors the lowest returns.

©Correia, Flynn, Uliana & Wormald 38 Real returns from equities and bonds Returns are after adjusting for inflation