Question

Burke Tires just paid a dividend of $2.37. Analysts expect the company's dividend to grow by 30% this year, 20% next year (year 2), 10\% the following year (year 3), and then 5% in each subsequent year. If the required return to the stock is 7.1%, what is the best estimate of the stock's current market value (please enter the value to the penny)?

Answer 1

To estimate the current market value of Burke Tires' stock, we calculate the present value of future dividends under a varying growth rate for the first three years, and then apply the Gordon Growth Model to find the perpetuity value from the fourth year onward at a constant growth rate. This perpetuity value is then discounted back to the present to provide an estimated market value.

Step-by-step explanation:

To calculate the current market value of Burke Tires' stock given the dividend growth rates and the required return, we apply the dividend discount model (DDM). The dividends for the first three years, where the growth rates are different each year, can be found as follows:

• Year 1 Dividend: $2.37 × (1 + 0.30) = $3.08
• Year 2 Dividend: $3.08 × (1 + 0.20) = $3.70
• Year 3 Dividend: $3.70 × (1 + 0.10) = $4.07

To find the present value of these dividends, we discount them back at the required return rate (7.1%). In the fourth year and onward, the dividends grow by a steady rate of 5%. To accommodate this constant growth, we use the Gordon Growth Model to calculate the present value of all future dividends as of year 3:

PV of Perpetuity at year 3 = Year 4 Dividend / (Required Return - Constant Growth Rate) = $4.07 × (1 + 0.05) / (0.071 - 0.05)

Once we have the year 4 perpetuity value, we discount that back to the present as well. Adding the present value of the first three dividends and the present value of the perpetuity gives us the estimated current market value of the stock.