Final answer:
The present value of an annual dividend expected in 4 years is calculated by discounting the dividend using the formula PV = D / (1 + r)^n, where D is the dividend, r is the discount rate, and n is the number of years. In this case, the dividend is derived from the share price and expected return, and then discounted back to its present value using the expected annual return rate.
Step-by-step explanation:
To calculate the present value of the annual dividend that is expected in 4 years from today, we need to discount the future dividend back to the present using the expected annual return of 9.42 percent as the discount rate. Here, we are assuming a constant dividend growth model, which means the dividend is expected to stay the same indefinitely.
The formula for the present value of a perpetuity is Dividend / Discount Rate. In this scenario, since we know the stock's price of $52.00 and its expected annual return of 9.42%, we can assume that the annual dividend is the share price multiplied by the return, so $52.00 * 9.42% = $4.8984 per year. To find the present value of that dividend in 4 years, we use the formula: PV = D / (1 + r)^n, where D is the dividend, r is the discount rate, and n is the number of years until the payment.
Therefore, the present value of the fourth year dividend is PV = $4.8984 / (1 + 0.0942)^4, which we would calculate and then round to the nearest hundredth.