Chapter 7. Investment analysis in conditions of risk Summary (2016)Resumen Inglés
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Chapter 7: Investment analysis in
conditions of risk
1. Risk in investment analysis
Deterministic: we know with certainty all the parameters of an investment project
Probabilistic: the parameters of an investment project can be estimated in terms of
probabilities, different scenarios, etc
Total uncertainty: total uncertainty about the parameters of an investment
Risk results from the uncertainty surrounding the variables of the investment project. Most
companies prepare a capital budget and require appropriation requests for each investment
*Only 85% of the approved investment projects generate positive NPVs 2. Simple methods of adjusting for risk Risk adjusted cash flows (Method of risk adjustment coefficient of cash flows) It consists in adjusting net cash flows by a coefficient between 0 and 1, depending on the degree of risk of each cash flow Risk premium added to the cost of capital “r”: It consists in adding up to the calculative interest rates some risk premium (p) depending on the degree of considered future risk Comparison between the 2 methods Both are very subjective and approximate Difference: Adjusted cash flow: it considers cash flows separately, period by period. It doesn’t consider the project as a whole.
Adjusted cost of capital: it considers the project as a whole, increasing the discount rate by a premium suggesting that risk premium may mitigate the risk.
3. Means / Variance alternative Probabilistic approach (the mean/variance criteria) treats net cash flows as random variables distributed according to some probability distribution function. Estimated cash flows correspond to an average or expected value of a random variable that measures cash flows.
The risk variation associated with the variable value is introduced by means of variance.
Variance of the expected cash flow is a measures of riskiness associated with a given distribution of cash flows.
Expected value of NPV Assume Ct is a random variable with the following distribution of probabilities: Given that the expected value of a sum of random independent or dependent variables is equal to the sum of the expected values of each of these variables, we have: The NPV variance (σ2 NPV) F.S.HILLIER applied the variance criteria distinguishing 3 cases: 1. Independent cash flows 2. Perfectly correlated cash flows Ci and Cj are perfectly correlated if their correlation coefficient = 0 3. Some cash flows are perfectly correlated, while other cash flow are independent Independent cash flow: Ci’. Perfectly correlated: Ci’’. In this case, Ci=Ci’ + Ci’’ Standard Deviation of NPV (σ NPV) Square root of the Variance Variation coefficient (v) This coefficient measures the risk associated with each unit of benefit when we calculate the degree of relative dispersion of the set of values of a random variable in respect to the mean value. So, how risky am I to not obtain what I forecasted.
If Standard Deviation increases v increases. This means that there are less possibilities to obtain the expected/forecasted NPV.
If v is close to 0, the deviation of NPV is small and this means there are possibilities to obtain the expected/forecasted NPV.
Example 1: Company A would like to determine the NPV of the following project, assuming r=10% and independent cash flows: SOLUTION 4. Sequential investment decisions It is common that investment projects: - Are contemplated within a period before deciding to invest or not Are related in time: any decision is conditioned by the previous one Can be expanded if cash flows are meeting expectations, and abandoned if something goes wrong.
Decision trees Decision trees are also called flow charts/diagrams, because the streams of cash receipts and payments flow through their branches that are related to the possible investment decisions.
They are formal methods of analysis that allow visualizing the overall decision process. They display the link between today’s decisions and future outcomes.
Options to modify the projects are known as real options: - Expansion options Abandonment options Timing options Flexibility in production options Example 2: A company has to choose between 2 production alternatives: “large production” LP and “small production” SP.
Once made, the decision has to be maintained during 2 years, and for each of these years 2 market scenarios are possible: “low demand” LD and “high demand” HD. The probability of the LD in the first year is 30%. The probability of having the same demand during the 2nd year is 75%.
Initial investments are of 30 and 10 millions of m.u., respectively, for large and small production.
The respective net cash flows for all 4 possible combinations are: a) Which decision is optimal using NPV criteria and cost of capital equal to 10%? b) Would it be different if we take into account the riskiness of each alternative? Similarly, we compute the expected NPVs of the nodes 2 and 3 Node 1 is a Decision type, we can choose the highest NPV option between Nodes 2 and 3, which is Node 3 and corresponds to the option of a LP Choosing LP option, we obtain the highest expected NPV.
But what about the riskiness of each alternative? 2 possible decisions may be subject to different degrees of risk that may modify the decision of the financial manager of the company.
We can determine the respective variances in order to analyse the risk of each decision.
As an example of calculus for the LP The degree of risk tolerance of a given investor influences the choice of investment alternative.