i dont understand how to get the year 3 dividend value of 0.402344

Example - Phranque is a small but growing app writer, specializing in developing new iPhone apps. It does not expect to pay dividends for 2 years though its earnings are growing rapidly (25% per annum) with current earnings of $0.50 per share. - it expects competition to increase considerably by Year 3 during whid1 it expects earnings to grow at just 3% and this lower growth rate is expected to continue into the future. - The company is expected to start paying dividends at the end of the 3rd year. A dividends payout ratio of 0.50 is predicted. The appropriate discount rate for this rm is 12% per annum. - What is the price of a Phranque share given these details? Solution First write out the earnings over the next 3 years and then to calculate the dividends and calculate the value of the stock by discounting the present value of dividend perpetuity starting at year 3. now 1 2 3 earnings 0.5 0.625 0.78125 0.804688 payout ratio 0.5 0.5 0.5 0.5 dividends 0 0 0 0.402344 Divl 1 0.402344 1 Price = = $3.56 rs - g x (1 + rE)2 0.12 0.03 x (1.12)2