A fast-growing firm recently paid a dividend of $0.60 per share. The dividend is

Question

A fast-growing firm recently paid a dividend of $0.60 per share. The dividend is expected to increase at a 25 percent rate for the next four years. Afterwards, a more stable 10 percent growth rate can be assumed.

  

If an 11.5 percent discount rate is appropriate for this stock, what is its value? Need help Quickly pls

A fast-growing firm recently paid a dividend of $0.60 per share. The dividend is expected to increase at a 25 percent rate for the next four years. Afterwards, a more stable 10 percent growth rate can be assumed.

Explanation / Answer

Price = the sum of the discounted cash flows...
period 1: (0.60*1.25)/1.115
2: (0.60*1.25^2) / 1.115^2
3: (0.60*1.25^3) / 1.15^3
4: (0.60*1.25^4 / 1.15^4

4: [note: above are the discounted dividends, now you want to calculate the terminal price and discount it back 4 years. Price "known" IN year 4 is based on the future cash flows from THAT point.
Gordon growth model: Price in year 4 = D5 / (r - g)
P4 = (0.60*1.25^4)(1.10) / (0.115 - 0.10)
= 1.61133 / 0.015
= $107.42....now discount this 4 years...
107.42/1.115^4 = $69.50135 <this amount is added to the discounted dividends outlined above to arrive at a price today.

To summarize:
P0 = D1/(1+r)^1 + D2/(1+r)^2 +...+D4/(1+r)^4 + P4/(1+r)^4
where P4 = D5/(r-g)

1 0.6 1.25 1.115 0.672646 2 0.6 1.5625 1.243225 0.754087 3 0.6 1.953125 1.386196 0.845389 4 0.6 2.441406 1.545608 0.947746

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