Understanding Corporate Financial Theory and Cost of Capital

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Explore the concepts of corporate financial theory, interest rates, cash flows, beta, cost of capital, and more in this insightful lecture series. Understand how different factors influence the company's cost of capital and make informed financial decisions.

  • Financial Theory
  • Cost of Capital
  • Corporate Finance
  • Interest Rates
  • Beta
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  1. CORPORATE FINANCIAL THEORY Lecture 4

  2. Interest Rate and Cash Flow - REALITY Is not guaranteed C = PV r 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 D E = + assets debt equity V V

  4. Beta and the COC 20 Expected return (%) Requity = 15 Rassets = 12.2 Rdebt = 8 0 0 0.2 Bdebt 0.8 Bassets 1.2 Bequity

  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 ( ) ( ) = + % % assets r Debt r equity r Debt equity = = Cost of Capital COC assets r

  6. Company Cost of Capital IMPORTANT ( ) V ( ) V = + assets r debt r equity r D E E, D, and V are all market values of Equity, Debt and Total Firm Value = + V D E Interest = = Market Value of Debt D r debt ( ) ( ) = = Market Value of Equity shares # Price per Share E = YTM CAPM = on bonds r = debt r + ( ) equity r B r r f m f

  7. Weighted Average Cost of Capital WACC is the traditional view of capital structure, risk and return. D E ( ) = = + 1 WACC r T r r A c D E V V

  8. Weighted Average Cost of Capital without taxes & bankruptcy risk r rE rD D V

  9. Weighted Average Cost of Capital without taxes & bankruptcy risk r rE WACC rD D V

  10. Weighted Average Cost of Capital without taxes & bankruptcy risk r rE rD Includes Bankruptcy Risk D V

  11. Weighted Average Cost of Capital without taxes & bankruptcy risk r rE rD Includes Bankruptcy Risk D V

  12. Weighted Average Cost of Capital without taxes & bankruptcy risk r rE WACC rD Includes Bankruptcy Risk D V

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

  14. Beta and the COC 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 = 2.0 1/3 expand existing business = 1.3 1/3 plant efficiency = 0.6 AVG of assets = 1.3

  15. Beta and the COC Company Cost of Capital Category Discount Rate Speculativ ventures e 30% New products 20% Expansion of existing business (Company 15% COC) improvemen Cost known tech t, nology 10%

  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: , 1 000 000 , C = = = 1 r PV 909 $ 100 , + 1 1 . 1

  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: 900 000 , = = PV 818 $ 000 , 1 . 1

  19. Risk, DCF and CEQ Risk, Discounted Cash Flow (DCF), and Certainty Equivalents (CEQ) CEQ + C + = = PV t r t ) t t 1 ( ) 1 ( r f

  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? = + ( ) r r B r r f m f = + 6 75 . ) 8 ( = 12 %

  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? Project A Year Cash Flow 12% @ PV 1 100 89.3 2 100 79.7 = + ( ) r r B r r f m f 3 100 71.2 = + 6 . 75 ) 8 ( Total PV 240.2 = 12 %

  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? Project A Year Cash Flow 12% @ PV Now assume that the cash flows change, but are RISK FREE. What is the new PV? 1 100 89.3 2 100 79.7 3 100 71.2 Total PV 240.2 = + ( ) r r B r r f m f = + 6 . 75 ) 8 ( = 12 %

  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? Project B Project A Year Cash Flow PV @ 6% Year Cash Flow 12% @ PV 1 94.6 89.3 1 100 89.3 2 89.6 79.7 2 100 79.7 3 84.8 71.2 3 100 71.2 Total PV 240.2 Total PV 240.2

  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? Project B Project A Year Cash Flow PV @ 6% Year Cash Flow 12% @ PV 1 94.6 89.3 1 100 89.3 2 89.6 79.7 2 100 79.7 3 84.8 71.2 3 100 71.2 Total PV 240.2 Total PV 240.2 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 Deduction Year Cash Flow CEQ for risk 1 100 94.6 5.4 2 100 89.6 10.4 3 100 84.8 15.2

  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 Risky cash flow = certainty equivalent cash flow . 1 054

  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? 100 = = Year 1 94 6 . . 1 054 100 = = Year 2 89 6 . 2 . 1 054 100 = = Year 3 84 8 . 3 . 1 054

  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 Range Variable Pessimisti c Expected Optimistic Market Size mil .9 1.0 mil 1.1 mil Market Share .04 .1 .16 Unit price 350,000 375,000 380,000 Unit Var Cost 360,000 300,000 275,000 Fixed Cost 4 bil 3 bil 2 bil

  33. Sensitivity Analysis Example - continued NPV Possibilities (Billions Yen) Range Variable Pessimisti c Expected Optimistic Market Size 1.1 3.4 5.7 Market Share - 10.4 3.4 17.3 Unit price - 4.2 3.4 5.0 Unit Var Cost - 15.0 3.4 11.1 Fixed Cost 0.4 3.4 6.5

  34. Sensitivity Analysis Year 0 Years 1 - 10 Investment - 15 Sales 37.5 Variable Costs 30 Fixed Costs 3 Depreciati on 1.5 Pretax profit 3 .Taxes 50% @ 1.5 Profit after tax 1.5 Operating cash flow 3.0 Net Cash Flow - 15 3 NPV= 3.43 billion Yen

  35. Sensitivity Analysis Example - continued Possible Outcomes Range Variable Pessimisti c Expected Optimistic Market Size mil .9 1.0 mil 1.1 mil Market Share .04 .1 .16 Unit price 350,000 375,000 380,000 Unit Var Cost 360,000 300,000 275,000 Fixed Cost 4 bil 3 bil 2 bil

  36. Sensitivity Analysis NPV Calculations for Optimistic Market Size Scenario Year 0 Years 1 - 10 Investment - 15 Sales 41.25 Variable Costs 33 Fixed Costs 3 Depreciati on 1.5 Pretax profit 3.75 .Taxes 50% @ 1.88 Profit after tax 1.88 NPV= +5.77 bil yen Operating cash flow 3.38 + Net Cash Flow - 15 3.38

  37. Sensitivity Analysis Example - continued NPV Possibilities (Billions Yen) Range Variable Pessimisti c Expected Optimistic Market Size 1.1 3.4 5.7 Market Share - 10.4 3.4 17.3 Unit price - 4.2 3.4 5.0 Unit Var Cost - 15.0 3.4 11.1 Fixed Cost 0.4 3.4 6.5

  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 Revenues 60 Break -even Profit =0 Accounting revenue and costs (Yen) 40 Billions Costs 20 Sales, thousands 60 200

  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 PV inflows PV (Yen) Billions Break-even NPV = 0 400 PV Outflows 200 19.6 Sales, thousands 85 200

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

  41. Monte Carlo Simulation

  42. Decision Trees Success Test (Invest $200,000) Pursue project NPV=$2million Failure Stop project NPV=0 Don t test NPV=0

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

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

  45. Decision Trees 960 (.8) 812 +150(.6) Turboprop 220(.2) -550 930(.4) 456 +30(.4) NPV= ? 140(.6) 800(.8) 660 -150 100(.2) +100(.6) or 410(.8) 364 0 Piston 180(.2) -250 220(.4) 812 ( +50(.4) ) ( + ) = 960 80 . 220 20 . 148 NPV= ? 100(.6)

  46. Decision Trees 960 (.8) NPV=888.18 812 +150(.6) 220(.2) Turboprop -550 930(.4) 456 +30(.4) NPV= ? 140(.6) NPV=444.55 800(.8) *450 660 812 -150 100(.2) + NPV=550.00 150 = +100(.6) 18 . 888 or . 1 10 410(.8) 364 0 Piston 180(.2) 331 -250 220(.4) +50(.4) 148 NPV= ? 100(.6) NPV=184.55

  47. Decision Trees 960 (.8) NPV=888.18 812 +150(.6) Turboprop 220(.2) 710.73 -550 930(.4) 456 +30(.4) NPV= ? 140(.6) NPV=444.55 800(.8) *450 660 -150 100(.2) NPV=550.00 ( = +100(.6) 18 . or 60 . 410(.8) . ) ( + ) 364 . 0 Piston 888 444 55 40 180(.2) 331 403.82 -250 220(.4) +50(.4) 148 NPV= ? 100(.6) NPV=184.55

  48. Decision Trees 960 (.8) NPV=888.18 812 +150(.6) Turboprop 220(.2) 710.73 -550 930(.4) 456 +30(.4) NPV=96.12 140(.6) NPV=444.55 800(.8) *450 660 -150 100(.2) NPV=550.00 +100(.6) 73 . or 410(.8) 364 710 0 Piston 180(.2) 12 . 96 = 550 331 403.82 10 . 1 -250 220(.4) +50(.4) 148 NPV=117.00 100(.6) NPV=184.55

  49. Decision Trees 960 (.8) 660 812 = +150(.6) 150 450 Turboprop 220(.2) . 1 10 -550 930(.4) 456 +30(.4) NPV= ? 140(.6) 800(.8) *450 660 -150 100(.2) +100(.6) or 410(.8) 364 0 Piston 180(.2) 331 -250 220(.4) 148 +50(.4) NPV= ? 100(.6)

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

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