Final answer:
Using the Present Discounted Value method with a discount rate of 6% and a dividend growth rate of -3%, the adjusted discount rate becomes 9%. The present value of the perpetuity starting 9 years from now is calculated and then discounted back to the present, which yields a stock price of approximately $4.70, not matching the provided options.
Step-by-step explanation:
To estimate the current stock price of a company expected to pay its first $1 dividend in 9 years, growing at a rate of -3% per annum forever, we need to use the concept of Present Discounted Value (PDV). Given that the discount rate is 6% pa, we discount the perpetuity of dividends to the present value. Since the dividends decrease annually by 3%, we will adjust the discount rate to 6% (discount rate) - (-3%) (growth rate) = 9%. We use the formula for the present value of a growing perpetuity: PV = D / (r - g), where PV is the present value, D is the dividend, r is the discount rate, and g is the growth rate. However, the first payment is not immediate but starts in 9 years, so we must also discount the calculated perpetuity back 9 years.
To calculate the stock price, we plug in the values: PV = $1 / (0.09 - (-0.03)) = $1 / 0.12 = $8.3333. This result is the present value in year 9. To get the present value for today, we discount it back 9 years using the formula: PV = FV / (1 + r)^n, where FV is future value, r is the discount rate, and n is the number of periods. Therefore, PV = $8.3333 / (1 + 0.06)^9.
After computing the above, we find that the present value today is approximately $4.70. This does not match any of the options provided, indicating a possible miscalculation or misunderstanding in the question. In such cases, it is advisable to revisit the question or seek clarification.