Question

If the expected return for Belmont Bagels stock is 9.47 percent; the dividend is expected to be $0.00 in one year, $5.59 in two years, $0.00 in three years, $4.69 in four years, and $2.21 in five years; and after the dividend is paid in five years, the dividend is expected to begin growing by 4.55 percent a year forever, then what is the current price of one share of the stock?

Answer 1

The current price of one share of Belmont Bagels stock is determined by calculating the present value of expected dividends and using the Gordon Growth Model for the perpetuity growth of dividends after five years, discounted by the expected rate of return of 9.47%.

Step-by-step explanation:

To calculate the current price of one share of Belmont Bagels stock, we need to use the present value of the expected dividends as well as the present value of the stock after the last dividend assuming a perpetuity growth. In this scenario, it involves finding the present value of the cash flows at year 2 and 4, and applying the Gordon Growth Model (also known as Dividend Discount Model) for the perpetuity calculation starting at year 5. The present value of the dividends is calculated by discounting them with the expected rate of return which acts as the discount rate (9.47% in this case). Crucially, we also need to calculate the present value of the stock price at year 5, obtained by dividing the year 6 dividend ($2.21 growing at 4.55%) by the difference between the discount rate and the growth rate (9.47% - 4.55%).

Then, we add the present values of the dividends and the stock price to determine the current share price. The calculations are done as follows (1) PV of $5.59 at Year 2, (2) PV of $4.69 at Year 4, and (3) PV of the stock price at Year 5 after dividends begin growing indefinitely. The summation of the present values will provide an investor with an estimate of what they should pay for the stock today, which is the stock's theoretical intrinsic value.