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Pasha Entertainment, Inc. is expected to pay the following dividends over the next four years: $6, $12, $17, and $3.25. Afterward, the company pledges to maintain constant 5% growth rate in dividends, forever. If the required return on the stock is 11%, what is the current share price?

Question

Pasha Entertainment, Inc. is expected to pay the following dividends over the next four years: 6,6, 12, 17,and17, and 3.25. Afterward, the company pledges to maintain constant 5% growth rate in dividends, forever. If the required return on the stock is 11%, what is the current share price?

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Solution

To calculate the current share price, we need to calculate the present value of the dividends for the first four years and the present value of the dividends from the fifth year onward (which grow at a constant rate).

Step 1: Calculate the present value of the dividends for the first four years.

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

Where: D1, D2, D3, D4 are the dividends for the first, second, third, and fourth years respectively. r is the required return on the stock.

PV = 6/(1+0.11)1+6/(1+0.11)^1 + 12/(1+0.11)^2 + 17/(1+0.11)3+17/(1+0.11)^3 + 3.25/(1+0.11)^4 PV = 5.41+5.41 + 9.73 + 12.03+12.03 + 2.09 PV = $29.26

Step 2: Calculate the present value of the dividends from the fifth year onward.

The price at the end of year 4 (P4) can be calculated using the Gordon growth model:

P4 = D5 / (r - g)

Where: D5 is the dividend in the fifth year, which is the dividend in the fourth year grown by the constant growth rate (g). r is the required return on the stock. g is the constant growth rate in dividends.

D5 = D4 * (1+g) D5 = 3.25(1+0.05)D5=3.25 * (1+0.05) D5 = 3.41

P4 = 3.41/(0.110.05)P4=3.41 / (0.11 - 0.05) P4 = 56.83

The present value of P4 is then calculated as:

PV_P4 = P4 / (1+r)^4 PV_P4 = 56.83/(1+0.11)4PVP4=56.83 / (1+0.11)^4 PV_P4 = 36.57

Step 3: The current share price is the sum of the present values calculated in steps 1 and 2.

P0 = PV + PV_P4 P0 = 29.26+29.26 + 36.57 P0 = $65.83

So, the current share price is $65.83.

This problem has been solved

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