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Pine Grove, Inc., is a thriving young company and it expects no dividends over the next 3 years because the company needs to reinvest its earnings to fund its various projects. The company will pay a $3.4 per share dividend in 4 years and will increase the dividend by 8 percent per year thereafter. If the required return on this stock is 13.3 percent, the current share price should be $_______. (Do not include the dollar sign ($). Round your answer to 2 decimal places. (e.g., 32.16))

Respuesta :

Shahzaibfaraz

Answer:

P0 = 42.0443036 rounded off to 42.04

Explanation:

Using the constant growth model of dividend discount model, we can calculate the price of the stock today. The DDM values a stock based on the present value of the expected future dividends from the stock. The formula for price today under this model is,

P0 = D0 * (1+g) / (r - g)

Where,

  • Do is the last dividend paid
  • D0 * (1+g) is dividend expected for the next period
  • g is the growth rate
  • r is the required rate of return  

We use D1 to  calculate the price of the stock today (P0). Thus, we will use D5 to calculate the price of the stock in year 4 and will discount it back for 4 years to calculate the price of the stock today.

P4 = 3.4 * (1+0.08)  /  (0.133 - 0.08)

P4 = 69.28301887

Now we will discount back the P4 to P0.

P0 = 69.28301887  / (1+0.133)^4

P0 = 42.0443036 rounded off to 42.04

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