Eastern Auto Parts' last dividend was D₀ = $0.50,and the company expects to experience no growth for the next 2 years.However,Eastern will grow at an annual rate of 5 percent in the third and fourth years,and,beginning with the fifth year,it should attain a 10 percent growth rate which it should sustain thereafter.Eastern has a required rate of return of 12 percent.What should be the present price per share of Eastern common stock? A) $19.26 B) $31.87 C) $30.30 D) $20.83 E) $19.95

Question

Quizplus · Accepted Answer

To calculate the present price per share of Eastern common stock, we need to consider the dividends for the first four years and the terminal value starting from the fifth year. The dividends for the first two years are $0.50 each (no growth), for the third and fourth years, the dividends grow by 5% annually, and from the fifth year onwards, the growth rate is 10%.1. Calculate dividends for each of the first four years:   - Year 1: $0.50   - Year 2: $0.50   - Year 3: $0.50 * (1 + 0.05) = $0.525   - Year 4: $0.525 * (1 + 0.05) = $0.551252. Calculate the terminal value at the end of year 4, which is the present value of all future dividends from year 5 onwards. The dividend in year 5 can be calculated as the year 4 dividend grown by 10%:   - Year 5 dividend: $0.55125 * (1 + 0.10) = $0.606375   - The terminal value at the end of year 4 is the year 5 dividend divided by the difference between the required rate of return and the growth rate: $0.606375 / (0.12 - 0.10) = $30.318753. Discount all future cash flows (dividends and terminal value) back to the present value using the required rate of return of 12%:   - PV of dividends: $0.50 / (1 + 0.12)^1 + $0.50 / (1 + 0.12)^2 + $0.525 / (1 + 0.12)^3 + $0.55125 / (1 + 0.12)^4   - PV of terminal value: $30.31875 / (1 + 0.12)^44. Summing these present values gives the current price per share. When calculated correctly, this sum equals approximately $20.83, which matches option D.

Eastern Auto Parts' Last Dividend Was D0 = $0

Eastern Auto Parts' Last Dividend Was D₀ = $0