Question

Justin Owens is an analyst for an equity mutual fund that invests in British stocks. At the beginning of 2008, Owens is examining domestic stocks for possible inclusion in the fund. One of the stocks that he is analyzing is British Sky Broadcasting Group (London Stock Exchange: BSY). The stock has paid dividends per share of £9, £12.20, and £15.50 at the end of 2005, 2006, and 2007, respectively. The consensus forecast by analysts is that the stock will pay a dividend per share of £18.66 at the end of 2008 (based on 19 analysts) and £20.20 at the end of 2009 (based on 17 analysts). Owens has estimated that the required rate of return on the stock is 11 percent.

A. Compare the compound annual growth rate in dividends from 2005 to 2007 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 2009, inclusive.

B. Owens 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 2007 to 2009, inclusive, computed in Part A. Using the growth rate forecast of Owens as the constant growth rate from 2007 onwards, estimate the value of the stock as of the end of 2007 given an 11 percent required rate of return on equity.

C. State the relationship between estimated value and r and estimated value and g

Answer 1

Part A.  

The stock has paid dividends per share of £9, £12.20, and £15.50 at the end of 2005, 2006, and 2007.

Compound Annual Growth Rate formula : (Ending Value / Beginning Value)^{1 / N} - 1 (N = number of years)

Compound Annual Growth Rate in dividends from 2005 to 2007 inclusive = ( £15.50 / £9 )^{1 / 2} - 1

= 0.3123 or 31.23%

Consensus forecast by analysts is dividend per share of £20.20 at the end of 2009. (We don't need the 2008 forecast, it's not relevant here).

Consensus predicted Compound Annual Growth Rate in dividends from 2007 to 2009, inclusive = (£20.20 / £15.50)^{1 / 2} - 1

= 0.14158 = 0.1416 or 14.16%

The predicted Compound Annual Growth Rate of dividends from 2007 to 2009 is lower than the actual Compound Annual Growth Rate of dividends from 2005 to 2007.

Part B

Owens believes that the dividend growth rate will be constant going forward at half the consensus compound annual growth rate from 2007 to 2009, inclusive, which we calculated above as 14.16%,

Hence, constant growth rate forecast by Owens = 14.16% / 2 = 7.08%

Using the Constant growth model or dividend discount model : Value of the stock at the end of 2007, P₀ = D₁ / (r - g)

Here, D₁ is Dividend per share at the end of next year,i.e., 2008 = £18.66

r - required rate of return on equity (11%), g - growth rate (7.08%)

Hence, P₀ = £18.66 / (0.11 - 0.0708)

= £18.66 / 0.0392

= 476.02

Estimated value of the stock as of the end of 2007 = £ 476.02

Part C

Relationship between estimated value and r and estimated value and g :

• When the investor's required rate of return on equity (r) increases, the estimated value of the stock (P₀) decreases, and vice-versa.
• When the constant dividend growth rate g increases, the estimated value of the stock (P₀) also increases, and vice-versa.

Hence, estimated value and r have an inverse relationship with each other, while estimated value and g have a direct relationship with each other.