Two investors are evaluating General Electrics stock for possible purchase. They agree on the expected value of D1 and also on the expected future dividend growth rate. Further, they agree on the risk of the stock. However, one investor normally holds stocks for 2 years and the other normally holds stocks for 12 years.

Should both be willing to pay the same price for General Electric?s stock? True or false? Explain.

Investors do not always agree on the required return on a stock. Every investor may have a different opinion of the stocks risk and require a different rate of return. The cost of equity for the firm is determined by the aggregate opinion of the market.

Both investors should be willing to pay the same price because the present value of all stock payments to the two investors are the same.

For one of the investors, the stock price today is worth the expected value of the first 12 dividends plus the stock price in 12 years:

eqP_0=\fracD_11+r+\fracD_2(1+r)^2+\fracD_3(1+r)^3+\fracD_4(1+r)^4+\fracD_5(1+r)^5+\fracD_6(1+r)^6+\fracD_7(1+r)^7+\fracD_8(1+r)^8+\fracD_9(1+r)^9+\fracD_10(1+r)^10+\fracD_11(1+r)^11+\fracD_12(1+r)^12+\frac1(1+r)^12*P_12\\ P_0=\fracD_11+r+\fracD_2(1+r)^2+\fracD_3(1+r)^3+\fracD_4(1+r)^4+\fracD_5(1+r)^5+\fracD_6(1+r)^6+\fracD_7(1+r)^7+\fracD_8(1+r)^8+\fracD_9(1+r)^9+\fracD_10(1+r)^10+\fracD_11(1+r)^11+\fracD_12(1+r)^12+\frac1(1+r)^12*\fracD_13r-g\\ /eq

For the second investor the stock price today is the value of the first 2 dividends plus the stock price in 2 years:

eqP_0=\fracD_11+r+\fracD_2(1+r)^2+\frac1(1+r)^2*P_2\\ P_0=\fracD_11+r+\fracD_2(1+r)^2+\frac1(1+r)^2*(\fracD_31+r+\fracD_4(1+r)^2+\fracD_5(1+r)^3+\fracD_6(1+r)^4+\fracD_7(1+r)^5+\fracD_8(1+r)^6+\fracD_9(1+r)^7+\fracD_10(1+r)^8+\fracD_11(1+r)^9+\fracD_12(1+r)^10+\frac1(1+r)^10*\fracD_13r-g)\\ P_0=\fracD_11+r+\fracD_2(1+r)^2+\fracD_3(1+r)^3+\fracD_4(1+r)^4+\fracD_5(1+r)^5+\fracD_6(1+r)^6+\fracD_7(1+r)^7+\fracD_8(1+r)^8+\fracD_9(1+r)^9+\fracD_10(1+r)^10+\fracD_11(1+r)^11+\fracD_12(1+r)^12+\frac1(1+r)^12*\fracD_13r-g\\ /eq

As the expressions above, show, the stock is worth the same amount of money to both investors. It does not matter when the stock is sold. Its price today is the present value of all payments from now to infinity.

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