1. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 1 B40.2302 Class #2  BM6 chapters 4, 5, 6  Based on slides created by Matthew Will  Modified 9/18/2001 by Jeffrey Wurgler

2.  The Value of Common Stocks Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will, Jeffrey Wurgler Chapter 4 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

3. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 3 Topics Covered  How To Value Common Stock  Capitalization Rates  Stock Prices and EPS  Cash Flows and the Value of a Business

4. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 4 Stocks & Stock Market Common Stock - Ownership shares in a publicly held corporation. Secondary Market - Market in which previously-issued securities are traded. Dividend - Periodic cash distribution from the firm to the shareholders. P/E Ratio - Price per share divided by earnings per share.

5. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 5 Stocks & Stock Market Book Value - Net worth of the firm according to the balance sheet. Liquidation Value - Net proceeds that would be realized by selling (liquidating) all assets and paying off all creditors. Market Value Balance Sheet – Balance sheet that uses market value of assets and liabilities (instead of the usual accounting value).

6. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 6 Valuing Common Stocks Expected Return - The percentage gain that an investor forecasts from a specific investment over a set period of time. Sometimes called the market capitalization rate.

7. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 7 Valuing Common Stocks Expected return can be broken into two parts: Dividend Yield + Capital Appreciation

8. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 8 Valuing Common Stocks Dividend Discount Model - Model of today’s stock price which states that share value equals the present value of all expected future dividends. H - Time horizon for your investment.

9. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 9 Valuing Common Stocks Example Current forecasts are for XYZ Company to pay annual cash dividends of $3, $3.24, and $3.50 per share over the next three years, respectively. At the end of three years you expect to sell your share at a market price of $94.48. What should be the price of a share today with a 12% expected return?

10. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 10 Valuing Common Stocks No Growth DDM If we forecast no growth, and plan to hold our stock indefinitely, then we can value the stock as a perpetuity. Assumes all earnings are paid to shareholders. So Div = EPS each year. No retentions, no growth.

11. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 11 Valuing Common Stocks Constant Growth DDM - A version of the dividend growth model in which dividends grow at a constant rate g. When you use the growing perpetuity formula to value a stock, you are using the “Gordon Growth Model.”

12. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 12 Valuing Common Stocks Example If a stock is selling for $100 in the stock market, what might the market be assuming about the growth rate of dividends? Answer The market is assuming the dividend will grow at 9% per year, indefinitely.

13. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 13 Valuing Common Stocks Example – continued Suppose in the same example you knew g was 9% per year, but didn’t know r. What is the market’s estimate of r? Answer The market has set r at 12% per year.

14. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 14 Valuing Common Stocks  If the board elects to pay a lower dividend, and reinvest the remainder, the stock price may increase because future dividends may be higher. Payout Ratio - Fraction of earnings paid out as dividends. Plowback Ratio - Fraction of earnings retained or “plowed back” into the firm. Payout Ratio + Plowback Ratio = 1

15. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 15 Valuing Common Stocks An accounting return measurement

16. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 16 Valuing Common Stocks Instead of asking an analyst, growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations. g = Plowback Ratio x ROE

17. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 17 Valuing Common Stocks Example We forecast a $5.00 dividend next year, which represents 100% of earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm’s current accounting return on equity of 20%. What is the value of the stock before and after the plowback decision? No Growth (Div=EPS)With Growth (Div<EPS)

18. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 18 Valuing Common Stocks Example - continued With the no growth policy, the stock price is $41.67. With the plowback / growth policy, the price rose to $75.00. The difference between these two numbers (75.00- 41.67=33.33) is called the Present Value of Growth Opportunities (PVGO).

19. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 19 Valuing Common Stocks Present Value of Growth Opportunities (PVGO) Net present value of a firm’s future investments. Sustainable Growth Rate - Steady rate at which a firm can grow without new external capital: ROE x Plowback Ratio.

20. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 20 EPS, P/E, and share price  Under a no-growth policy, Div=EPS, so:  In general, share price = capitalized value of average earnings under no-growth policy, plus PVGO:

21. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 21 EPS, P/E, and share price  Rearranging,  EPS/P ratio underestimates r if PVGO > 0  “Growth stocks” sell at high P/E ratios because PVGO is high.

22. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 22 FCF and PV  Free Cash Flows (FCF) are the theoretical basis for all PV calculations.  FCF is more relevant than EPS.  FCF t = cash inflows t – cash outflows t  PV(firm) = PV(FCF)

23. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 23 FCF and PV Valuing a Business The value of a business is often computed as the present value of FCF out to a valuation horizon (H).  The value at H is sometimes called the terminal value or horizon value

24. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 24 FCF and PV Example Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6%

25. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 25 FCF and PV Example - continued.

26.  Why Net Present Value Leads to Better Investment Decisions than Other Criteria Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will, Jeffrey Wurgler Chapter 5 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

27. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 27 Topics Covered  NPV and its Competitors  The Payback Period  The Book Rate of Return  Internal Rate of Return  Capital Rationing – what to do?  Profitability Index  Linear Programming

28. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 28 NPV and Cash Transfers  Evaluating projects requires understanding the flows of cash. Cash Investment opportunities (real assets) FirmShareholder Investment opportunities (financial assets) Invest…… or pay dividend … … so shareholders invest for themselves

29. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 29 Payback  The payback period of a project is the time it takes before the cumulative forecasted cash inflow equals the initial outflow.  The payback rule says only accept projects that “payback” within some set time frame.  This rule is common but very flawed.

30. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 30 Payback Example Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less.

31. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 31 Book Rate of Return Book Rate of Return – An accounting measure of profitability. Also called accounting rate of return. Note the components reflect tax and accounting figures, not market values or cash flows.

32. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 32 Internal Rate of Return  The Internal Rate of Return is the discount rate that makes the project’s NPV = 0.  IRR rule is to accept a project if the IRR>cost of capital. Example You can purchase a machine for $4,000. The investment will generate $2,000 and $4,000 in cash flows in the next two years. What is the IRR on this investment?

33. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 33 Internal Rate of Return IRR=28%

34. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 34 Internal Rate of Return Pitfall 1 - Strange cash flow patterns  With some cash flows the NPV of the project increases as the discount rate increases.  This is contrary to the normal relationship. Discount Rate NPV

35. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 35 Internal Rate of Return Pitfall 1 – Strange cash flow patterns  Example where IRR gets it wrong for this reason:

36. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 36 Internal Rate of Return Pitfall 2 - Multiple Rates of Return (even stranger CF patterns)  Some cash flow patterns can generate NPV=0 at two different IRRs!  The following cash flow generates NPV=0 at both (-50%) and 15.2%. 1000 NPV 500 0 -500 -1000 Discount Rate IRR=15.2% IRR=-50%

37. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 37 Internal Rate of Return Pitfall 2 - Multiple Rates of Return  Example where IRR gets it wrong for this reason:

38. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 38 Internal Rate of Return Pitfall 3 - Mutually Exclusive Projects  IRR ignores the scale of the project.

39. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 39 Internal Rate of Return Pitfall 4 – Flat Term Structure Assumption  IRR has problems when the term structure isn’t flat.  In this case, we’d need to compare the project IRR with the expected IRR (yield to maturity) offered by a traded security that  Has equivalent risk  Has same time-pattern of cash flows  At this point easier to calculate NPV!

40. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 40 Internal Rate of Return Even calculating IRR can be hard. Financial calculators can perform this function easily, though. In the previous example, HP-10BEL-733ABAII Plus -350,000CFj-350,000CFiCF 16,000CFj16,000CFfi2nd{CLR Work} 16,000CFj16,000CFi -350,000 ENTER 466,000CFj466,000CFi 16,000 ENTER {IRR/YR}IRR16,000 ENTER 466,000 ENTER IRRCPT All produce IRR=12.96

41. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 41 Profitability Index  When resources are limited (capital is “constrained” or “rationed”) the profitability index (PI) provides a tool for selecting among various project combinations and alternatives.  The highest weighted-average PI can indicate the right plan in these circumstances.

42. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 42 Profitability Index Example We only have $300,000 to invest. Which do we select? ProjNPV InvestmentPI A230,000200,0001.15 B141,250125,0001.13 C194,250175,0001.11

43. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 43 Linear Programming  Maximize Cash flows or NPV  Minimize costs Example Max NPV = 21Xa + 16 Xb + 12 Xc + 13 Xd subject to 10X a0 + 5X b0 + 5X c0 + 0X d0 <= 10 -30X a1 - 5X b1 - 5X c1 + 40X d1 <= 12

44.  Making Investment Decisions with the Net Present Value Rule Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will, Jeffrey Wurgler Chapter 6 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

45. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 45 Topics Covered  What To Discount  IM&C Project  Project Interaction  Timing  Equivalent Annual Cost  Replacement  Cost of Excess Capacity  Fluctuating Load Factors

46. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 46 What To Discount Only Cash Flow is Relevant

47. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 47 What To Discount  Do not confuse average with incremental.  Treat inflation consistently.  Include all incidental effects.  Do not forget working capital requirements.  Forget sunk costs.  Include opportunity costs.  Beware of allocated overhead costs. Points to watch out for:

48. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 48 IM&C’s Guano Project Revised projections ($000s) reflecting inflation

49. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 49 IM&C’s Guano Project Cash flow analysis ($1000s)

50. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 50 IM&C’s Guano Project  NPV (using nominal cash flows)

51. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 51 IM&C’s Guano Project Tax depreciation allowed under the modified accelerated cost recovery system (MACRS) - (Figures in percent of depreciable investment).

52. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 52 Optimal timing  Even projects with positive NPV may be more valuable if deferred.  The relevant NPV is then the current value of some future value of the deferred project.

53. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 53 Optimal timing Example You may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV?  Harvesting in year 4 is optimal. And relevant NPV is 68.3.

54. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 54 Equivalent Annual Cost Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine.

55. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 55 Example Given the following costs of operating two machines and a 6% cost of capital, select the lower-cost machine using equivalent annual cost method. Costs by year Machine0123PV@6%EAC A1555528.3710.61 B106621.0011.45 Equivalent Annual Cost

56. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 56 Machinery Replacement Annual operating cost of old machine = 8 Cost of new machine Year: 0 1 2 3 NPV @ 10% 15 5 5 5 27.4 Equivalent annual cost of new machine = 27.4/(3-year annuity factor at, say, 10%) = 27.4/2.5 = 11 Do not replace until operating cost of old machine exceeds 11.

57. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 57 Cost of Excess Capacity (?) A project requires warehouse space and this causes a need for a new one to be built in Year 5 rather than Year 10. A warehouse costs 100 & lasts 20 years. Equivalent annual cost @ 10% = 100/8.5 = 11.7 0... 5 6... 10 11... With project 0 0 11.7 11.7 11.7 Without project 0 0 0 0 11.7 Difference 0 0 11.7 11.7 0 PV extra cost = + +... + = 27.6 11.7 11.7 11.7 (1.1) 6 (1.1) 7 (1.1) 10

58. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 58 Fluctuating Load Factors You operate in a seasonal business. Your two old machines have a capacity of 1,000 units/year. Half the year, you operate at 50% capacity. The other half, at 100% capacity. The operating expenses of your old machines is $2/unit. Discount rate is 10%.

59. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 59 Fluctuating Load Factors Could replace with two new machines which have $1/unit cost

60. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 4- 60 Fluctuating Load Factors Third (better) option: Replace just one machine. New machine has low operating cost, so operate it all year. Keep old machine for peak demands.