1. CORPORATE FINANCIAL THEORY Lecture 3

2. Interest Rate Cash Flow Interest Rate and Cash Flow - REALITY Is not guaranteed Has many different sources

3. Beta and the COC Company cost of capital (COC) is based on the average beta of the assets The average beta of the assets is based on the % of funds in each asset Assets = debt + equity

4. Expected return (%) B debt B assets B equity R debt = 8 R assets = 12.2 R equity = 15 Beta and the COC

5. Company Cost of Capital simple approach  Company Cost of Capital (COC) is based on the average beta of the assets  The average Beta of the assets is based on the % of funds in each asset Assets = Debt + Equity

6. IMPORTANT E, D, and V are all market values of Equity, Debt and Total Firm Value Company Cost of Capital

7. Weighted Average Cost of Capital  WACC is the traditional view of capital structure, risk and return.

8. Weighted Average Cost of Capital without taxes & bankruptcy risk r DVDV rDrD rErE

9. r DVDV rDrD rErE WACC Weighted Average Cost of Capital without taxes & bankruptcy risk

10. DVDV rDrD rErE Includes Bankruptcy Risk Weighted Average Cost of Capital without taxes & bankruptcy risk r

11. r DVDV rDrD rErE Includes Bankruptcy Risk

12. r DVDV rDrD rErE WACC Weighted Average Cost of Capital without taxes & bankruptcy risk Includes Bankruptcy Risk

13. r DVDV WACC r*r* D*D* Weighted Average Cost of Capital without taxes & bankruptcy risk Includes Bankruptcy Risk

14. Company cost of capital (COC) is based on average beta of assets Average beta of assets is based on the % of funds in each asset Example 1/3 new ventures β = 2.0 1/3 expand existing business β = 1.3 1/3 plant efficiency β = 0.6 AVG β of assets = 1.3 Beta and the COC

15. Company Cost of Capital Beta and the COC

16. Project risk Allowing for Possible Bad Outcomes Example Project Z will produce one cash flow, forecasted at $1 million at year 1. It is regarded as average risk, suitable for discounting at 10% company COC:

17. Project risk Allowing for Possible Bad Outcomes Example, continued Company’s engineers are behind schedule developing technology for project. There is a small chance that it will not work. Most likely outcome still $1 million, but some chance that project Z will generate zero cash flow next year:

18. Project risk Allowing for Possible Bad Outcomes Example, continued If technological uncertainty introduces a 10% chance of zero cash flow, unbiased forecast could drop to $900,000:

19. Risk, DCF and CEQ Risk, Discounted Cash Flow (DCF), and Certainty Equivalents (CEQ)

20. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?

21. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?

22. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?

23. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project? Now assume that the cash flows change, but are RISK FREE. What is the new PV?

24. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?

25. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV? Since the 94.6 is risk free, we call it a Certainty Equivalent of the 100.

26. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project? DEDUCTION FOR RISK

27. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV? The difference between the 100 and the certainty equivalent (94.6) is 5.4%…this % can be considered the annual premium on a risky cash flow

28. Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?

29. Capital Budgeting & Risk Invest in highest NPV project Need Discount rate to get NPV Use CAPM to get discount rate Modify CAPM (account for proper risk) Modify Cash Flows

30. Capital Budgeting & Risk Sensitivity Analysis - Analysis of the effects of changes in sales, costs, etc. on a project. Scenario Analysis - Project analysis given a particular combination of assumptions. Simulation Analysis (Monte Carlo) - Estimation of the probabilities of different possible outcomes. Break Even Analysis - Analysis of the level of sales (or other variable) at which the company breaks even. Decision Trees – Binomial model in which outcomes are path dependent. Real Options – The value of flexibility.

31. Sensitivity Analysis Example Given the expected cash flow forecasts for Otobai Company’s Motor Scooter project, listed on the next slide, determine the NPV of the project given changes in the cash flow components using a 10% cost of capital. Assume that all variables remain constant, except the one you are changing.

32. Sensitivity Analysis Example - continued Possible Outcomes

33. Sensitivity Analysis Example - continued NPV Possibilities (Billions Yen)

34. Sensitivity Analysis NPV= 3.43 billion Yen

35. Sensitivity Analysis Example - continued Possible Outcomes

36. Sensitivity Analysis NPV Calculations for Optimistic Market Size Scenario NPV= +5.77 bil yen

37. Sensitivity Analysis Example - continued NPV Possibilities (Billions Yen)

38. Break Even Analysis Accounting break-even does not consider time value of money Otobai Motors has accounting break-even point of 60,000 units sold 60 200 Sales, thousands Accounting revenue and costs (Yen) Billions 60 40 20 Break -even Profit =0 Revenues Costs

39. Break Even Analysis Point at which NPV=0 is break-even point Otobai Motors has a break-even point of 85,000 units sold Sales, thousands PV (Yen) Billions 400 200 19.6 85 200 Break-even NPV = 0 PV inflows PV Outflows

40. Monte Carlo Simulation  Step 1: Modeling the Project  Step 2: Specifying Probabilities  Step 3: Simulate the Cash Flows  Step 4: Calculate NPV Modeling Process

41. Monte Carlo Simulation

42. Decision Trees NPV=0 Don’t test Test (Invest $200,000) Success Failure Pursue project NPV=$2million Stop project NPV=0

43. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) +150(.6) +30(.4) +100(.6) +50(.4) -550 NPV= ? -250 NPV= ? -150 0 or Turboprop Piston

44. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) +150(.6) +30(.4) +100(.6) +50(.4) -550 NPV= ? -250 NPV= ? -150 0 or 812 456 660 364 148 Turboprop Piston

45. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) +150(.6) +30(.4) +100(.6) +50(.4) -550 NPV= ? -250 NPV= ? -150 0 or 812 456 660 364 148 Turboprop Piston

46. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) -550 NPV= ? -250 NPV= ? -150 0 or 812 456 660 364 148 +150(.6) +30(.4) +100(.6) +50(.4) NPV=444.55 NPV=888.18 NPV=550.00 NPV=184.55 *450 331 Turboprop Piston

47. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) 812 456 660 364 148 +150(.6) 710.73 +30(.4) +100(.6) 403.82 +50(.4) -150 0 *450 331 or NPV=444.55 NPV=888.18 NPV=550.00 NPV=184.55 -550 NPV= ? -250 NPV= ? Turboprop Piston

48. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) 812 456 660 364 148 +150(.6) 710.73 +30(.4) +100(.6) 403.82 +50(.4) -550 NPV=96.12 -250 NPV=117.00 -150 0 *450 331 or NPV=444.55 NPV=888.18 NPV=550.00 NPV=184.55 Turboprop Piston

49. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) -550 NPV= ? -250 NPV= ? -150 0 or 812 456 660 364 148 +150(.6) +30(.4) +100(.6) +50(.4) *450 331 Turboprop Piston

50. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) 812 456 660 364 148 +150(.6) 710.73 +30(.4) +100(.6) 403.82 +50(.4) -550 NPV=96.12 -250 NPV=117.00 -150 0 *450 331 or NPV=444.55 NPV=888.18 NPV=550.00 NPV=184.55 Turboprop Piston

51. Flexibility & Real Options Decision Trees - Diagram of sequential decisions and possible outcomes.  Decision trees help companies determine their Options by showing the various choices and outcomes.  The Option to avoid a loss or produce extra profit has value.  The ability to create an Option thus has value that can be bought or sold.

52. Corporate Real Options 1. Option to expand (make follow up investment) 2. Option to abandon 3. Timing option (wait and invest later) 4. Flexible production facilities Value = NPV with option - NPV w/o option Value = Black Scholes approach

53. Corporate Real Options Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Use a discount rate of 10%

54. Corporate Real Options Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Year 0Year 1Year 2 120 (.6) 100 (.6) 90 (.4) NPV = 145 70 (.6) 50 (.4) 40 (.4)

55. Corporate Real Options Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Year 0Year 1Year 2 120 (.6) 100 (.6) 90 (.4) NPV = 162 150 (.4) Option Value = 162 - 145 = $17 mil

56. Corporate Real Options Reality Decision trees for valuing “real options” in a corporate setting can not be practically done by hand. We must introduce binomial theory & B-S models