: Assume today is December 31, 2013. Imagine Works Inc. just paid a dividend of

Question

: Assume today is December 31, 2013. Imagine Works Inc. just paid a dividend of $1.15 per share at the end of 2013. The dividend is expected to grow at 18% per year for 3 years, after which time it is expected to grow at a constant rate of 5.5% annually. The company's cost of equity (rs) is 10%. Using the dividend growth model (allowing for nonconstant growth), what should be the price of the company's stock today (December 31, 2013)? Round your answer to the nearest cent. Do not round intermediate calculations.

Explanation / Answer

first let us calculate the price of stock at the end of year 3.

P3 = D3 *(1+g) / k -g

here,

D0 = $1.15.

D1 = $1.15 +18% =>$1.357..

D2 = $1.357 +18% =>$1.60126.

D3= $1.60126 + 18% =.$1.8894868.

g= 5.5% =>0.055.

k = 10% =>0.10.

now,

P3 = $1.8894868*(1.055) / (0.10 -0.055)

=>$44.30.

now,

price of company's stock today:

price of company's stock today =$37.26.

Year Discounting factor @10% Cash flow Discounted cash flow 1 1/(1.10) =>0.90909 $1.357 $1.23363513 2 1/(1.10)^2=>0.82645 $1.60126 $1.323361327 3 1/(1.10)^3=>0.75131 $1.8894868 $1.4195903277 3 1/(1.10)^3=>0.75131 $44.30 (price at end of year 3) $33.283033 Value of stock $37.26

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