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# Stock valuation

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### Stock valuation

1. 1. Stock Valuation 9-1
2. 2. Key Concepts and Skills• Understand how stock prices depend on future dividends and dividend growth• Be able to compute stock prices using the dividend growth model• Understand how growth opportunities affect stock values• Understand the PE ratio• Understand how stock markets work 9-2
3. 3. 9.1 The PV of Common Stocks• The value of any asset is the present value of its expected future cash flows.• Stock ownership produces cash flows from: – Dividends – Capital Gains• Valuation of Different Types of Stocks – Zero Growth – Constant Growth – Differential Growth 9-3
4. 4. Case 1: Zero Growth• Assume that dividends will remain at the same level forever Div1 = Div 2 = Div 3 =  • Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity: Div1 Div 2 Div 3 P0 = + + + (1 + R) (1 + R) (1 + R ) 1 2 3 Div P0 = R 9-4
5. 5. Case 2: Constant GrowthAssume that dividends will grow at a constant rate, g,forever, i.e., Div1 = Div 0 (1 + g ) Div 2 = Div1 (1 + g ) = Div 0 (1 + g ) 2 Div 3 = Div 2 (1 + g ) = Div 0 (1 + g ) 3 . . .Since future cash flows grow at a constant rate forever,the value of a constant growth stock is the present valueof a growing perpetuity: Div1 P0 = R−g 9-5
6. 6. Constant Growth Example• Suppose Big D, Inc., just paid a dividend of \$.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk level, how much should the stock be selling for?• P0 = .50(1+.02) / (.15 - .02) = \$3.92 9-6
7. 7. Case 3: Differential Growth• Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter.• To value a Differential Growth Stock, we need to: – Estimate future dividends in the foreseeable future. – Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2). – Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate. 9-7
8. 8. A Differential Growth ExampleA common stock just paid a dividend of \$2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity.What is the stock worth? The discount rate is 12%. 9-8
9. 9. With the Formula  \$2(1.08) 3 (1.04)      \$2 × (1.08)  (1.08)   3 .12 − .04 P= 1− 3 + .12 − .08  (1.12)  (1.12) 3P = \$54 × [1 − .8966] + ( \$32.75) 3 (1.12)P = \$5.58 + \$23.31 P = \$28.89 9-9
10. 10. With Cash Flows 3 3 \$2(1.08) \$2(1.08) 2 \$2(1.08) \$2(1.08) (1.04) … 0 1 2 3 4 \$2.62 The constant \$2.16 \$2.33 \$2.52 + growth phase .12 − .04 beginning in year 4 can be valued as a0 1 2 3 growing perpetuity at time 3. \$2.16 \$2.33 \$2.52 + \$32.75P0 = + 2 + 3 = \$28.89 1.12 (1.12) (1.12) \$2.62 P3 = = \$32.75 .08 9-10