Question

-Rashpal Sohan is an analyst for an equity mutual fund that invests in British stocks. At the beginning of 1997, Rashpal is examining domestic stocks for possible inclusion in the fund. One of the stocks that he is analyzing is British Sky Broadcasting Group (BSY). The stock has paid dividends per share of £9, £12.20, and £15.50 at the end of 1994, 1995, and 1996, respectively. The consensus forecast by analysts is that BSY will pay a dividend per share of £18.66 at the end of 1997 (based on 19 analysts) and £20.20 at the end of 1998 (based on 17 analysts). Rashpal has estimated that the required rate of return on BSY is 11%. A. Compare the compound annual growth rate in dividends from 1994 to 1996 inclusive (i.e., from a beginning level of £9 to an ending level of £15.50) with the consensus predicted compound annual growth rate in dividends from 2007 to 1998, inclusive. B. Rashpal believes that BSY has matured such that the dividend growth rate will be constant going forward at half the consensus compound annual growth rate from 1996 to 1998, inclusive, computed in Part A. Using the growth rate forecast of Rashpal as the constant growth rate from 1996 onwards, compute the estimated value of the stock, Vo, as of the end of 1996 given an 11% required rate of return on equity. C. State the relationship between Vo and r, and V, and g.

Answer 1

At the outset, I want to bring to your notice that the mention of the year 2007 in part A of the question is erroneous. There is mention of the year 2007 in the data given in the question, hence the reference to the year 2007 is not valid.

Since part B of the question refers to the same rate calculated from the year 1996 to 1998, I am assuming that 2007 mentioned in part A should have been 1996.

A) CAGR_{1994 - 1996} = (D₁₉₉₆ / D₁₉₉₄)^{1 / (1996 - 1994)} - 1 = (15.50 / 9.00)^1/2 - 1 = 31.23%

CAGR_{1996 - 1998} = (D₁₉₉₈ / D₁₉₉₆)^{1 / (1998 - 1996)} - 1 = (20.20 / 15.50)^1/2 - 1 = 14.16%

B) g = 14.16% / 2 = 7.08%

D₁₉₉₇ = D₁ = D₀ x (1 + g) = D₁₉₉₆ x (1 + g) = 15.50 x (1 + 7.08%) = 16.60

r = 11%

Hence, Price at the end of 1996 = V₀ = D₁₉₉₇ / (r - g) = 16.60 / (11% - 7.08%) = 423.34

C) V₀ = D₁ / (r - g) = D₀ x (1 + g) / (r - g)

V₀ bears an inverse relationship with r. If r increases, V₀ and vice versa.

V₀ bears a direct relationship with g. As g increases, (1 + g) increases in the numerator and (r - g) decreases in the numerator, leading to an increase in V₀. Hence, when g increases V₀ increases and vice versa.