Consider the n-period version of the Gordon Growth model studied in class. In the n-period version of the Gordon Growth model, the price of a stock is determined as the present discounted value of the stream of dividends, plus any expected future capital gains, i.e. Pt = Xn j=1 De t+j (1 + ke) j + P e t+n (1 + ke) n (1)

a. Assume that under rational expectations, dividends are expected to grow at a constant rate g from period t. Under the assumption of no bubbles in the asset market, and using the fact that the return from holding the stock should equal the risk-free rate, Rt plus a risk premium, , use equation (1) above to derive the following expression: Dt Pt + g = Rt + (2) where Dt Pt represents the dividend-price ratio, or the dividend yield. [Hint: You may want to take the limit of the expression in equation (1) as it tends to .]

b. Suppose that the economy is expected to grow at 2% over the next year, and that the current risk-free rate is 1%. Now suppose that we are looking at microsoft stock. The current share price for Microsoft is $184 per share and the annual dividend this past year was $7.36 per share. Based on this information, use equation (2) to obtain an estimate of the risk-premium for Microsoft stock.

Equation 1 is Pt = Xn j=1 De t+j (1 + ke) j + P e t+n (1 + ke) n

Equation 2 is Dt Pt + g = Rt +