Final answer:
To calculate the price of a stock at the end of one year using the present discounted value method, we need to determine the present value of the future dividend and the future stock price. Using the given information, the price of the stock at the end of one year (P1) would be $22.73.
Step-by-step explanation:
To calculate the price of a stock at the end of one year (P1) using the present discounted value method, we need to determine the present value of the future dividend (D2) and the future stock price (P2). The present value is calculated by discounting the future cash flows using the discount rate. In this case, the dividend for year 2 (D2) is $5, the price for year 2 (P2) is $20, and the discount rate is 10%.
We can calculate the present value of the dividend (PD2) using the formula PD2 = D2 / (1 + r), where r is the discount rate. Substituting the values, PD2 = 5 / (1 + 0.1) = 4.55.
We can calculate the present value of the stock price (PP2) using the formula PP2 = P2 / (1 + r), where r is the discount rate. Substituting the values, PP2 = 20 / (1 + 0.1) = 18.18.
Finally, we can calculate the price of the stock at the end of one year (P1) using the formula P1 = PD2 + PP2 = 4.55 + 18.18 = $22.73.