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# Chapter 5

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• Basic formula for valuing a share of stock easy to state; P0 is equal to the present value of the expected stock price at end of period 1, plus dividends received, as in Eq 4.4: But how to determine P1? This is the PV of expected stock price P2, plus dividends. P2 in turn, the PV of P3 plus dividends, and so on. Repeating this logic over and over, find that today’s price equals PV of the entire dividend stream the stock will pay in the future, as in Eq 4.5:
• Basic formula for valuing a share of stock easy to state; P0 is equal to the present value of the expected stock price at end of period 1, plus dividends received, as in Eq 4.4: But how to determine P1? This is the PV of expected stock price P2, plus dividends. P2 in turn, the PV of P3 plus dividends, and so on. Repeating this logic over and over, find that today’s price equals PV of the entire dividend stream the stock will pay in the future, as in Eq 4.5:
• Assume the dividend of Disco Company is expected to remain at \$1.75/share indefinitely, and the required return on Disco’s stock is 15%. P0 is determined to be \$11.67
• The Gordon Company’s dividends have grown by 7% per year, reaching \$1.40 per share. This growth is expected to continue, so D1=\$1.40 x 1.07=\$1.50. If required return is 15%: P(0) = \$18.75
• The Gordon Company’s dividends have grown by 7% per year, reaching \$1.40 per share. This growth is expected to continue, so D1=\$1.40 x 1.07=\$1.50. If required return is 15%: P(0) = \$18.75
• Find the value of the dividends at the end of each year, D t , during the initial high-growth phase. Find the PV of the dividends during this high-growth phase, and sum the discounted cash flows. Using the Gordon growth model, find the value of the stock at the end of the high-growth phase using the next period’s dividend (after one year’s growth at g 2 ). Then compute PV of this price by discounting back to time 0. Determine the value of the stock today (P 0 ) by adding the PV of the stock price computed in step 3 to the sum of the discounted dividend payments from step 2. Allows for a change in the dividend growth rate as future growth rates might change Let g 1 = the initial, higher growth rate and g 2 = the lower, subsequent growth rate, and assume a single shift in growth rates from g 1 to g 2 . Model can be generalized for two or more changes in growth rates, but keep simple now.
• -Yield to Maturity (YTM) is the rate of return investors earn if they buy the bond at P 0 and hold it until maturity. The YTM on a bond selling at par ( P 0 = Par ) will always equal the coupon interest rate. When P 0  Par , the YTM will differ from the coupon rate. YTM is the discount rate that equates the PV of a bond’s cash flows with its price. If P 0 , CFs, n known, can find YTM Use T-Bond with n=2 years, 2n=4, C/2=\$20, P 0 =\$992.43
• Formula can be rearranged to compute required return, if price and dividend known: Equity Valuation As will be discussed in chapter 5, the required return on common stock is based on its beta, derived from the CAPM Valuing CS is the most difficult, both practically &amp; theoretically Preferred stock valuation is much easier (the easiest of all) Whenever investors feel the expected return, rˆ , is not equal to the required return, r , prices will react: If exp return declines or reqd return rises, stock price will fall If exp return rises or reqd return declines, stock price will rise Asset prices can change for reasons besides their own risk Changes in asset’s liquidity, tax status can change price Changes in market risk premium can change all asset values Most dramatic change in market risk: Russian default Fall 98 Caused required return on all risky assets to rise, price to fall