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 6% annually. The company's cost of equity (rs) is 9.5%. 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. $ per share

Answer 1

Intrinsic Value $43.69

Step-by-step explanation:

`\left[\begin{array}{ccc}Year&Dividends&Present Value\\1&1.357&1.23926940639269\\2&1.60126&1.33546840140948\\3&53.9853371428571&41.1181399520726\\Intrinsic&Value&43.6928777598748\\\end{array}\right]`

The first Step is calculate the dividends:

`dividends * growth \: rate = next\: perdiod \: dividends`

We multiply 1.15 today dividends by the growth rate of 18% to get year 1

then year 1 by this growth rate to get year 2 and finally

year 2 times growth rate to get year 3 Dividends

Then on year 3 we apply the Dividends growth model

`(divends)/(return-growth) = Intrinsic \: Value`

`(Year3 )/(0.095-0.06) = Intrinsic \: Value`

Third, we need to bring this values to present

`(Nominal)/((1+rate)^(time) ) = PV`

Year 1 /1.095

Year 2 /1.095^2

Year 2 /1.095^3

Final step, we add them to get the intrinsic value of the bond today.