Question

Synovec Corporation is expected to pay the following dividends over the next four years: $5.20, $16.20, $21.20, and $3.00. Afterward, the company pledges to maintain a constant 5.5 percent growth rate in dividends forever. If the required return on the stock is 9 percent, what is the current share price?

Answer 1

The current share price of Synovec Corporation is $126.95.

The Breakdown

We need to determine the present value of the expected future dividends and the perpetuity of dividends.

Given:

Dividends: $5.20, $16.20, $21.20, and $3.00

Growth rate: 5.5%

Required return: 9%

Step 1: Calculate the present value of the expected future dividends.

PV = D1 / (1 + r) + D2 / (1 + r)² + D3 / (1 + r)³ + D4 / (1 + r)⁴

Where:

PV = Present value

D1, D2, D3, D4 = Expected dividends for each year

r = Required return

PV = $5.20 / (1 + 0.09) + $16.20 / (1 + 0.09)² + $21.20 / (1 + 0.09)³ + $3.00 / (1 + 0.09)⁴

PV = $4.77 + $13.47 + $16.24 + $2.18

PV = $36.66

Step 2: Calculate the perpetuity of dividends.

Perpetuity = D5 / (r - g)

Where:

D5 = Dividend in year 5

g = Growth rate

D5 = $3.00 × (1 + 0.055) = $3.16

Perpetuity = $3.16 / (0.09 - 0.055)

Perpetuity = $3.16 / 0.035

Perpetuity = $90.29

Step 3: Calculate the current share price.

Current share price = PV + Perpetuity

Current share price = $36.66 + $90.29

Current share price = $126.95

Therefore, the current share price of Synovec Corporation is $126.95.

Answer 2

Present value = $92.6899 rounded off to $92.69

Step-by-step explanation:

Using the dividend discount model, we calculate the price of the stock today. It values the stock based on the present value of the expected future dividends from the stock. To calculate the present value of the next four dividends, we will use the following formula,

Present value = D1 / (1+r) + D2 / (1+r)^2 + D3 / (1+r)^3 + D4 / (1+r)^4 +

[(D4 * (1+g) / (r - g)) / (1+r)^4]

Where,

• r is the required rate of return
• g is the constant growth rate in dividends

Present value = 5.2 / (1+0.09) + 16.2 / (1+0.09)^2 + 21.2 / (1+0.09)^3 +

3 / (1+0.09)^4 + [(3 * (1+0.055) / (0.09 - 0.055)) / (1+0.09)^4]

Present value = $92.6899 rounded off to $92.69