Question

You have decided to expand your business and will now value shares. Given the following information, what is the value of a share in AMS today using the following information. AMS Ltd will not pay any dividends for the next 7 years; In exactly 7 years from today, AMS Ltd will pay a dividend of $1.28; The following four dividends (years 8, 9, 10 and 11) will grow at a rate of 40% per year; The dividends from year 12 onwards will grow at a more sustainable rate of 3% per year in perpetuity (note: the year 12 dividend will be 3% higher than the year 11 dividend); and, Dividends are paid annually, and the required rate of return on equity is 6% p.a compounded annually.​

Answer 1

To value the share of AMS Ltd, we need to calculate the present value of all future dividends and the future sale price of the share. Here are the steps to calculate the value of a share in AMS:

1. Calculate the present value of the 7th-year dividend:

PV(dividend in year 7) = $1.28 / (1 + 6%)^7 = $0.84

2. Calculate the present value of the dividends from years 8 to 11:

PV(dividends in years 8-11) = $1.28 * (1 + 40%) / (1 + 6%)^8 + $1.28 * (1 + 40%)^2 / (1 + 6%)^9 + $1.28 * (1 + 40%)^3 / (1 + 6%)^10 + $1.28 * (1 + 40%)^4 / (1 + 6%)^11

PV(dividends in years 8-11) = $4.98

3. Calculate the present value of the future dividends beyond year 11:

PV(future dividends) = $1.28 * (1 + 40%)^5 * (1 + 3%) / (6% - 3%) / (1 + 6%)^11

PV(future dividends) = $17.29

4. Calculate the present value of the future sale price of the share:

PV(future sale price) = $1.28 * (1 + 40%)^5 / (6% - 3%) / (1 + 6%)^11

PV(future sale price) = $44.79

5. Add up the present values of all future cash flows to get the total value of the share:

Value of a share in AMS = $0.84 + $4.98 + $17.29 + $44.79

Value of a share in AMS = $67.90

Therefore, the value of a share in AMS today is $67.90.