Given the following data at t =0:

Dividend at t=1 (Div_1) 5

Expected return (r) 0.08

Earnings per share (EPS) 7

Book equity per share 100

Payout ratio 0.3

Question1. Obtain the price of the stock at t= 0 as the present value of all expected future dividends.

Question2. Obtain the expected price of the stock at times t=1, t=5 and t=10 if both r and the pay-out ratio remain unaffected all the future periods.

Question3. Sensitivity analysis:

Question3.1.Obtain the differences in the price of the stock at t = 0 if the Dividend in t=1 changes by 1 monetary unit (i.e. consider the following two scenarios, a) Div_1 =6 and b) Div_1=4). Are those changes in price symmetrical?

Question 3.2.Consider also two more scenarios: c) Div_1=7 and d) Div_1 = 8 and obtain the new price for the stock at t= 0. What conclusions can you infer from the results (i.e., how does a given change in the dividend at t=1 affect the price of the stock given the remaining variables unaffected? Prove them mathematically.

Question4. Obtain the differences in price at t=0 if the pay-out ratio changes by 10 percentage points (i.e. consider two scenarios a) pay-out ratio =0.2 and b) pay-out ratio = 0.4). Are changes in price symmetrical?

Question5. How does affect any change in earnings per share to the price if the pay-out ratio is assumed to be 100%, i.e. all the earnings are given out as dividends in the future?