Final answer:
The present value of the stock is $52.88.option a.
Step-by-step explanation:
The present value of the stock can be calculated using the present discounted value (PDV) method.
First, we need to calculate the present value of the dividends. The dividends are paid annually starting one year from today, so we use a time period of one year. The PDV formula is:
PDV = Dividend / (1 + r)^n
Where Dividend is the annual dividend, r is the discount rate, and n is the number of years.
In this case, the annual dividend is $55, the discount rate is the sum of the risk-free return (3%) and the equity risk premium (1%), which is 4%, and the number of years is 1. Substituting these values into the formula:
PDV = 55 / (1 + 0.04)^1 = 55 / 1.04 = 52.88
So, the present value of the dividends is $52.88.
Next, we need to calculate the present value of the stock price at the end of the holding period. The stock price at the end of the holding period can be calculated using the formula:
PDV = Stock Price / (1 + r)^n
Where Stock Price is the expected stock price at the end of the holding period, r is the discount rate, and n is the number of years. In this case, the expected stock price at the end of the holding period is $0, since the stock will no longer exist. Substituting these values into the formula:
PDV = 0 / (1 + 0.04)^1 = 0
So, the present value of the stock price at the end of the holding period is $0.
Finally, we calculate the present value of the stock by summing the present values of the dividends and the present value of the stock price at the end of the holding period:
Present Value of Stock = Present Value of Dividends + Present Value of Stock Price at End
Present Value of Stock = $52.88 + $0 = $52.88
Therefore, the present value of the stock is $52.88.