Kwame owns one share of stock of Fairfax Paint and one share of stock of Litchfi

Question

Kwame owns one share of stock of Fairfax Paint and one share of stock of Litchfield Design. The total value of his holdings is 179 dollars. Both stocks pay annual dividends that are expected to continue forever. The expected return on Fairfax Paint stock is 15.46 percent and its annual dividend is expected to remain at 12.54 dollars forever. The expected return on Litchfield Design stock is 18.56 percent. The next dividend paid by Litchfield Design is expected to be 6.91 dollars and all subsequent dividends are expected to grow at a constant rate. What growth rate is expected for Litchfield Design dividends? Assume the next dividend for both firms’ stocks will be paid in one year. Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Explanation / Answer

First we need to compute the value of Fairfax Paint stock. It is a stock with zero growth , so value of the stock would be:

Value of Fairfax paint = Div/ R

                                                = 12.54 / 0.1546

                                                = 81.1125

Now we can calculate the value of Litchfield design.

Value of Litchfield design = total investment – value of Fairfax paint

                                                   = 179 – 81.1125

                                                   = 97.8875

Litchfield design is a growing stock, therefore, the formula for the value of this stock would be:

V= D1 / (R-g)

97.8875 = 6.91 / (0.1856 – g)

18.16792-97.8875 g = 6.91

G = 11.25792/ 97.8875

G = 11.50%

Hence, growth rate would be 11.50%.

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