4 1 B 40 2302 Class 2 w

4 - 1 B 40. 2302 Class #2 w BM 6 chapters 4, 5, 6 w Based on slides created by Matthew Will w Modified 9/18/2001 by Jeffrey Wurgler Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

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

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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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). Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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? Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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. ” Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

4 - 14 Valuing Common Stocks w 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 Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

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 Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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) Irwin/Mc. Graw Hill With Growth (Div<EPS) ©The Mc. Graw-Hill Companies, Inc. , 2000

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. 0041. 67=33. 33) is called the Present Value of Growth Opportunities (PVGO). Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

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

4 - 22 FCF and PV w Free Cash Flows (FCF) are theoretical basis for all PV calculations. w FCF is more relevant than EPS. w FCFt = cash inflowst – cash outflowst w PV(firm) = PV(FCF) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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). w The value at H is sometimes called the terminal value or horizon value Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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% Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

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

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

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

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

4 - 30 Payback Example Examine 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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

4 - 31 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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

4 - 32 Internal Rate of Return w The Internal Rate of Return is the discount rate that makes the project’s NPV = 0. w 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? Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

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

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

4 - 36 Internal Rate of Return Pitfall 2 - Multiple Rates of Return (even stranger CF patterns) w Some cash flow patterns can generate NPV=0 at two different IRRs! w The following cash flow generates NPV=0 at both (-50%) and 15. 2%. NPV 1000 IRR=15. 2% 500 Discount Rate 0 -500 IRR=-50% -1000 Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

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

4 - 39 Internal Rate of Return Pitfall 4 – Flat Term Structure Assumption w IRR has problems when the term structure isn’t flat. w 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 w At this point easier to calculate NPV! Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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-10 B EL-733 A BAII Plus -350, 000 CFj -350, 000 CFi CF 16, 000 CFj 16, 000 CFfi 2 nd 16, 000 CFj 16, 000 CFi -350, 000 ENTER 466, 000 CFj 466, 000 CFi 16, 000 ENTER {IRR/YR} IRR {CLR Work} 466, 000 ENTER All produce IRR=12. 96 Irwin/Mc. Graw Hill IRR CPT ©The Mc. Graw-Hill Companies, Inc. , 2000

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

4 - 42 Profitability Index Example We only have $300, 000 to invest. Which do we select? Proj A B C Irwin/Mc. Graw Hill NPV 230, 000 141, 250 194, 250 Investment 200, 000 125, 000 175, 000 PI 1. 15 1. 13 1. 11 ©The Mc. Graw-Hill Companies, Inc. , 2000

4 - 43 Linear Programming w Maximize Cash flows or NPV w Minimize costs Example Max NPV = 21 Xa + 16 Xb + 12 Xc + 13 Xd subject to 10 Xa 0 + 5 Xb 0 + 5 Xc 0 + 0 Xd 0 <= 10 -30 Xa 1 - 5 Xb 1 - 5 Xc 1 + 40 Xd 1 <= 12 Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

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

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

4 - 47 What To Discount Points to watch out for: ÜDo not confuse average with incremental. ÜTreat inflation consistently. ÜInclude all incidental effects. ÜDo not forget working capital requirements. ÜForget sunk costs. ÜInclude opportunity costs. ÜBeware of allocated overhead costs. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

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

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

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

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

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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

4 - 55 Equivalent Annual Cost 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 Machine A B Irwin/Mc. Graw Hill 0 15 10 1 5 6 2 5 6 3 5 PV@6% 28. 37 21. 00 EAC 10. 61 11. 45 ©The Mc. Graw-Hill Companies, Inc. , 2000

4 - 56 Machinery Replacement Annual operating cost of old machine = 8 Cost of new machine Year: 0 15 1 5 2 5 3 5 NPV @ 10% 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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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 Without project 0 0 11. 7 Difference 0 0 11. 7 0 PV extra cost = 11. 7 6 + 11. 77 +. . . + 11. 7 10 = 27. 6 (1. 1) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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%. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000

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

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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000