Question

Apocalyptica Corporation is expected to pay the following dividends over the next four years: $5.60, $16.60, $21.60, and $3.40. Afterwards, the company pledges to maintain a constant 5.25 percent growth rate in dividends, forever.

Required:
If the required return on the stock is 9 percent, what is the current share price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current share price $

Answer 1

To determine the current share price, the present value of the expected dividends and the perpetual growth rate is calculated. Using the present value formula, the present value of each dividend is computed separately. The present values are then summed up to find the current share price.

Step-by-step explanation:

To determine the current share price of Apocalyptica Corporation, we need to calculate the present value of the expected dividends and the growth rate forever. Since the dividends are paid at different time periods, we need to calculate the present value of each dividend separately. The present value (PV) of each dividend is calculated using the formula PV = D / (1+r)^n, where D is the dividend amount, r is the required return, and n is the number of periods. The PV of the dividends over the next four years are:

1. PV1 = $5.60 / (1+0.09)^1 = $5.13
2. PV2 = $16.60 / (1+0.09)^2 = $13.25
3. PV3 = $21.60 / (1+0.09)^3 = $15.93
4. PV4 = $3.40 / (1+0.09)^4 = $2.33

Next, we calculate the present value of the perpetual growth using the formula PV = D / (r - g), where D is the last dividend, r is the required return, and g is the growth rate. The PV of the perpetual growth is:

PV5 = $3.40 / (0.09 - 0.0525) = $78.29

Finally, we sum up all the present values to get the current share price:

Current share price = PV1 + PV2 + PV3 + PV4 + PV5 = $5.13 + $13.25 + $15.93 + $2.33 + $78.29 = $115.93

Therefore, the current share price of Apocalyptica Corporation is $115.93.