Final answer:
The current value of one share of Combined Communications stock is approximately $2.14, which is calculated by determining the present value of the expected dividends considering the initial growth and then the perpetual growth at a reduced rate.
Step-by-step explanation:
To determine the current value of one share of Combined Communications stock, we must calculate the present value of its future dividends under a variable growth model. The initial dividend of $0.20 is expected to grow by 15% annually for the next 4 years before it stabilizes at a constant growth rate of 3.5%. Using the given required rate of return of 15.5%, we discount these expected dividends back to their present value.
Here is a breakdown of the calculations:
The dividends for the next 4 years will be:
Year 1: $0.20 * (1 + 0.15) = $0.23
Year 2: $0.23 * (1 + 0.15) = $0.2645
Year 3: $0.2645 * (1 + 0.15) = $0.3042
Year 4: $0.3042 * (1 + 0.15) = $0.3498
Then, we calculate the present value of these dividends:
The present value of the dividend at the end of year 1: $0.23 / (1 + 0.155) = $0.1991
The present value of the dividend at the end of year 2: $0.2645 / (1 + 0.155)^2 = $0.1983
The present value of the dividend at the end of year 3: $0.3042 / (1 + 0.155)^3 = $0.1974
The present value of the dividend at the end of year 4, including all subsequent dividends growing at 3.5% indefinitely (using the Gordon growth model), is calculated as follows: $0.3498 * (1 + 0.035) / (0.155 - 0.035) = $2.789
We divide this value by (1 + 0.155)^4 to account for the discounting back to the present value: $2.789 / (1 + 0.155)^4 = $1.5437
Adding these present values together: $0.1991 + $0.1983 + $0.1974 + $1.5437 = $2.1385
The current value of one share of Combined Communications stock is approximately $2.14