Risk in Investment Decisions

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Osborn Lambert
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1 Learning Objectives: To provide conceptual understanding of risk & uncertainty. To bring out various approaches to risk measurement. To focus on methods of adjusting risks in investment decisions. Structure: Introduction Concept of Certainty, Risk & Uncertainty Factors of Risk Measurement of Risk Utility Theory & Risk Analysis Risk Analysis approaches Methods of Adjusting Risk

2 Introduction In the last chapters we saw the capital budgeting without referring to the risk element. The rule was that proposals with positive net present value can be accepted. These models do not refer to the risk elements in investment decisions & hence are not adequate for investment analysis in the real world. The fact that Finance Manager does not know before he makes the investment, as to what would be the gains from the project, indicates uncertainty attached to every investment decision..

3 Introduction The uncertainty is attached to every investment project and different projects have varying degrees of risk. A finance manager must take cognizance of risk factors while taking investment decision. So the questions may pop up in our minds are, what is risk?, uncertainty? Let s find out the answers to these questions in this chapter along with proper understanding of methods to measure and reduce the intensity of risk. The aim is to arrange for additional adjustments to cover risks.

4 Concept of Risk, Certainty & Uncertainty The certainty is state of nature which arises when outcomes are known and determinate. e.g. investment in five years 7% tax free Government Bonds. The return on 7% can be estimated quite precisely. This is so because we assume that Government of India is one of the most stable forces in this country and investment decision would certainly result in returns at 7% p.a. until maturity and full refund of capital thereafter. The outcome here has a probability of 1.0.

5 Concept of Risk, Certainty & Uncertainty Risk involves situations in which the probabilities of an event occurring are known and these probabilities are objectively or subjectively determinable. It is the inability to predict with perfect knowledge the course of future events that introduces risk. When events become more predictable the risk is reduced and vice versa. Hence Proposal B is riskier than Proposal A in the next graph. In contrast, when an event is not repetitive and unique in character and finance manager is not sure about probabilities themselves, uncertainty is said to prevail. Uncertainty is a subjective phenomenon. Since there is no frequency distribution under uncertainty, acceptable methods cannot be evolved to handle for handling uncertainty.

6 P R O B A B I L I T Y OF O C C U R E N C Concept of Risk, Certainty & Uncertainty Proposal A Proposal B E Annual Cash Flow [Rs.]

7 Factors of Risk After understanding the difference among risk, uncertainty and certainty, now let's look at the main factors of risks. The first step in risk analysis is to uncover the major factors that contribute to the variability of results from investment or risk in investment.. a. Size of investment larger the project, greater the investments and resulting risks. b. Reinvestment of Cash Flows models assume that cash inflows in future can be used by the company to earn similar rate of return from reinvestment. This is not certain. c. Variability of Cash Flows reliance on single estimate is risky. Range of estimates is desirable. d. Life of the Project cannot be determined precisely and has to be determined by technical experts.

8 Measurement of Risk So far we have learnt that every opportunity of investment is followed by risk. So risky proposition in business is presumed to be one with a wide range of possible outcomes. There are certain methods to understand what and how much is the risk involved in a particular investment decision.. This chart presents the different methods. Probability Distribution Coefficient of Variation Methods of Risk Measurement Standard Deviation

9 Measurement of Risk Probability Distribution : If a range of possible outcomes for a cash flow in a year one is Coefficient of Variation arranged in the form of a frequency distribution, it is known as a probability Methods of Risk Measurement distribution. Probabilities Probability Distribution Standard Deviation normally are stated as decimal fractions but they can also be expressed in percentage terms.

10 Measurement of Risk Standard Deviation : Probability Distribution provides the basis for measuring the risk of project. The rule is higher the probability smaller the risk & vice versa. To measure the rightness or the probability distribution, the most widely used statistical technique of standard deviation is employed. Probability Distribution Coefficient of Variation Methods of Risk Measurement Standard Deviation

11 Measurement of Risk Coefficient of Variation as a Relative Measure of Risk: The size difficulty can be eliminated by using this third measure. It measures the relative variability of returns. Generally larger the coefficient of variation, greater is the risk. Probability Distribution Coefficient of Variation Methods of Risk Measurement Standard Deviation

12 Utility Theory & Risk Analysis in Investment Decisions Even after using different methods of measurement of risks it may be difficult to know whether to accept the risk or not. The decision is to be based ultimately on management s subjective evaluation of risk. Utility theory has been developed to measure an individual s attitude towards varying amounts of gains and losses. The same has been developed by Milton Friedman and L.J. Savage. The core of this theory is the concept of diminishing marginal utility of money.

13 Utility Theory & Risk Analysis According to this concept, marginal utility goes on diminishing successively in correspondence with increasing money income. In short, increase in income will mean lower utility from additional income. Investors with diminishing marginal utility of money will get more pain from a rupee lost than pleasure from rupee gained. They cannot, therefore, be apathetic to risk and will require a higher return as a compensation for bearing risk.

14 Utility Theory & Risk Analysis This is why a prudent finance manager considers both risk factors and utility function together while choosing worthwhile capital investment projects. This chart represents the theory. As earnings go on increasing, the value of total utility declines Earnings

15 Risk Analysis Approaches To handle risk dimensions within investment decision process, there are two approaches adopted. Those are; a. Simulation Approach b. Sensitivity Analysis Let s look each one of them in brief. Simulation Approach : This approach is used by those who are interested in gauging the effects of the uncertainty surrounding of significant factors that enter into the valuation of a specific decision on the expected returns..

16 Risk Analysis Approaches Simulation Approach :This model considers following variables which are subject to random variations. Risk analysis based on this approach involves five steps. Simulation Approach Market Related Factors Market Price Market Growth Rate Selling Price of Product Market Share Captured By Firm Investment Related Factors Investment Outlay Useful Life of Investment Residual Value Cost Related Factors Variable Operating Unit Cost Fixed Cost

17 Risk Analysis Approaches Sensitivity Analysis : This is a meaningful technique used to locate and assess the potential impact of risk on a project s profitability. It does not attempt to quantify risk, but rather provides insight into how the final outcome of an investment decision is likely to affected by possible variations in the underlying factors. It attempts to answer what is the NPV if selling price falls by 10%, what is the IRR if the project s life is only three years and not five years as expected, what is the level of sales revenue required to break-even in the net present value terms.

18 Risk Analysis Approaches Discount Rate NPV Price 8000 Fixed Cost 6000 Market Size Deviation from Expected Value Sensitivity Graph

19 Methods of Adjusting Risk When a finance manager being a risk averter when given choice between two projects promising the same rate of return but different in risk, he would prefer the one with least perceived risk. There are several methods of adjusting risk in investment decisions. Those are broadly classified into two groups. Informal Method & Formal Method

20 Methods of Adjusting Risk Methods of Adjusting Risk Informal Method Formal Method Risk Adjusted Discount Rate Certainty Equivalent Approach

21 Methods of Adjusting Risk Informal Method This is the most common method of adjusting the risk. By using this method finance manager decides about risk in project on subjective basis. The manner of fixing the standard is strictly internal and known to finance manager and is not specified.

22 Methods of Adjusting Risk Formal Method Risk Adjusted Discount Rate It is a popular approach to adjusting the risk in the use of different discount rates for proposals with different risk level. More risk higher the discount rate. Certainty Equivalent Approach This approach is based on the premise that investors prefer certainty of return. Therefore they accept riskier project only when higher returns are assured. With more risk, cash flows are adjusted downwards.

23 The end! Next Chapter Four Cost of Capital Good Luck!

Chapter 14 Solutions Solution 14.1

Chapter 14 Solutions Solution 14.1 a) Compare and contrast the various methods of investment appraisal. To what extent would it be true to say there is a place for each of them As capital investment decisions