Class 28 30 (Risk Analysis In Capital Budgeting)

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Class 28 30 (Risk Analysis In Capital Budgeting)

  1. 1. Risk analysis in capital budgeting Taken from Financial Management (Prasanna Chandra)
  2. 2. Sources of risk <ul><li>Project specific risk </li></ul><ul><li>Competitive risk </li></ul><ul><li>Industry specific risk </li></ul><ul><li>Market risk </li></ul><ul><li>International risk </li></ul>
  3. 3. Perspectives of risk <ul><li>Three different perspectives </li></ul><ul><ul><li>Standalone risk </li></ul></ul><ul><ul><li>Firm risk </li></ul></ul><ul><ul><li>Market risk </li></ul></ul>
  4. 4. 1. Sensitivity analysis or ‘what if’ analysis
  5. 5. <ul><li>Problem: ABC is considering the risk characteristics of a project . The firm has identified that the following factor, with their respective expected values, have a baring on the NPV of this project </li></ul><ul><li>Initial investment 30,000 </li></ul><ul><li>Cost of capital 10% </li></ul><ul><li>Quantity manufactured and sold (annually) 1,400 </li></ul><ul><li>Price per unit 30 variable cost 20 </li></ul><ul><li>fixed cost 3,000 depreciation 2,000 </li></ul><ul><li>Tax rate 50% Life of the project 5 Years </li></ul><ul><li>Net salvage value nil </li></ul><ul><li>Assume the underlying variable can take the values as shown below </li></ul><ul><li>underlying variable pessimistic optimistic </li></ul><ul><li>Quantity manufactured and sold 800 1800 </li></ul><ul><li>price Rs 20 Rs50 </li></ul><ul><li>Variable cost per unit 15 40 </li></ul><ul><li>Calculate the sensitivity of net present value to the variations in- </li></ul><ul><li>1. Sales 2. price 3. variable cost </li></ul>
  6. 6. <ul><ul><li>Limitations </li></ul></ul><ul><ul><ul><li>Possibility of change </li></ul></ul></ul><ul><ul><ul><li>Variables (changing) </li></ul></ul></ul><ul><ul><ul><li>Subjectivity </li></ul></ul></ul>
  7. 7. 2. Scenario analysis <ul><li>Example: different scenarios </li></ul><ul><li>moderate appeal at modest price </li></ul><ul><li>Strongly appeal at low but price sensitive </li></ul><ul><li>Small segment but high price </li></ul>
  8. 8. <ul><li>Here, σ 2 = variance; </li></ul><ul><li>σ = standard deviation, </li></ul><ul><li>NCF j = Net cash flow of j th event; ENCF = Expected net present value; </li></ul><ul><li>P j = Probability of j th event. </li></ul>
  9. 9. <ul><li>Problem: you are given three scenarios, and the probability of occurrence of NPV </li></ul><ul><li>Scenarios probability NPV </li></ul><ul><li>Best case .25 1,46,180 </li></ul><ul><li>Base case .50 5,809 </li></ul><ul><li>Worst case .25 (37,257) </li></ul><ul><li>Calculate expected NPV </li></ul><ul><li>Standard deviation </li></ul><ul><li>Coefficient of variation </li></ul>
  10. 10. 3. Decision tree Approach <ul><li>Delineate </li></ul><ul><ul><li>Decision points </li></ul></ul><ul><ul><li>Chance points </li></ul></ul>
  11. 11. Incorporating Project Risk into Capital Budgeting Decisions <ul><li>Modification in the conventional methods </li></ul>
  12. 12. 1. Risk adjusted discount rate <ul><li>Discount rate should be adjusted with level of risk </li></ul><ul><ul><li>R k = i + n + d k </li></ul></ul><ul><ul><li>i = risk free rate of interest </li></ul></ul><ul><ul><li>n = adjustment for normal risk </li></ul></ul><ul><ul><li>d k = adjustment for the differential risk of project </li></ul></ul><ul><ul><li>Example: replacement investment cost of capital </li></ul></ul><ul><ul><li>expansion investment CoC + 3% </li></ul></ul><ul><ul><li>investment in related line CoC + 6% </li></ul></ul><ul><ul><li>investment in new line CoC + 10% </li></ul></ul>
  13. 13. 2. Certainty equivalent method <ul><li>NPV = α t Ĉ t </li></ul><ul><li>(1+i) t </li></ul><ul><li>α t = Certainty equivalent coefficient (CEC) </li></ul><ul><li>Ĉ t = expected cash flow for year t </li></ul><ul><li>i = risk free interest rate </li></ul><ul><li>I = initial investment </li></ul>Σ - I
  14. 14. <ul><li>A project involves an outlay of Rs. 5,00,000. Its expected cash inflow at the end of year 1 is Rs. 2,00,000. Thereafter it decreases every year by Rs 10,000. It has an economic life of 6 years. The certainty equivalent factor is α t = 1 - .05t. Calculate the net present value of the project of the risk free rate of return is 10 percent. </li></ul>
  15. 15. <ul><li>Problem: There is a proposal for manufacturing a new product. The initial investment is estimated to be 50 million and the cash inflows for the year 1 through 3 would have the following distributions. </li></ul><ul><li>Year 1 cash flow 15 20 30 </li></ul><ul><li>Probability 0.4 0.3 0.3 </li></ul><ul><li>Year 2 cash flow 20 25 30 </li></ul><ul><li>Probability 0.4 0.4 0.2 </li></ul><ul><li>Year 3 cash flow 25 30 40 </li></ul><ul><li>Probability 0.3 0.5 0.2 </li></ul><ul><li>Calculate expected NPV, standard deviation, and coefficient of variation considering cost of capital to be 10%. </li></ul>

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