Polycorp has a current dividend of $5.00 due tomorrow and is expected to pay a dividend $5.50 at the end of the first year. Its dividend is expected to grow at 8% pa for the following year. Dividends are then expected to grow at 4% pa for another two years. Then they are expected to grow at 3.5%pa forever after that. Shareholders required return on equity is 11.85% pa. What is the current price (-dividend) of Polycorp shares?

Question

Polycorp has a current dividend of $5.00 due tomorrow and is expected to pay a dividend $5.50 at the end of the first year. Its dividend is expected to grow at 8% pa for the following year. Dividends are then expected to grow at 4% pa for another two years. Then they are expected to grow at 3.5%pa forever after that. Shareholders required return on equity is 11.85% pa. What is the current price (-dividend) of Polycorp shares?

Answer 1

To calculate the current price of Polycorp shares, we need to use the dividend discount model (DDM) formula. DDM calculates the present value of all the future dividends expected to be paid by the company. Here are the steps to solve the question:

Step 1: Calculate the present value of dividends for the first three years.
- Dividend at the end of the first year: $5.50
- Dividend growth rate in the first year: 8%
- Shareholders required return on equity: 11.85%

We can use the formula for the present value of a growing perpetuity to calculate the present value of dividends for the first three years:
PV = D1 / (1 + r)^1 + D2 / (1 + r)^2 + D3 / (1 + r)^3, where PV is the present value, D1 is the dividend at year 1, D2 is the dividend at year 2, D3 is the dividend at year 3, and r is the required return on equity.

Applying the formula:
PV = $5.50 / (1 + 0.1185)^1 + $5.50 * (1 + 0.08) / (1 + 0.1185)^2 + $5.50 * (1 + 0.08)^2 / (1 + 0.1185)^3

Step 2: Calculate the present value of the perpetual dividend.
- Dividend growth rate from year 4 onwards: 3.5%
- Using the formula for the present value of a perpetuity:
PV_perpetual = D4 / (r - g), where D4 is the dividend at year 4 onwards and g is the growth rate.
Since the dividend is expected to grow at a constant rate, we can calculate D4 as follows:
D4 = $5.50 * (1 + 0.08)^3 * (1 + 0.04), where (1 + 0.08)^3 accounts for the growth from year 1 to year 4 and (1 + 0.04) accounts for the growth rate from year 4 onwards.

PV_perpetual = D4 / (r - g) = $5.50 * (1 + 0.08)^3 * (1 + 0.04) / (0.1185 - 0.035)

Step 3: Calculate the current price of Polycorp shares.
Current price = PV + PV_perpetual

Plugging in the values calculated in Step 1 and Step 2:
Current price = PV + PV_perpetual = PV + $5.50 * (1 + 0.08)^3 * (1 + 0.04) / (0.1185 - 0.035)

Now, you just need to calculate this expression to find the current price of Polycorp shares.