Question

Assuming that ROCE (return on common equity), g (the growth rate of the book value of common shareholders' equity) and rE (the cost of equity capital) are constant, that markets are efficient, and:

1. the company's dividend payout ratio d is 20%

2. g is 8%

3. the company's stock has an equity beta of 1.2

4. the risk free rate is 1% and the market risk premium is 6%

a) Explain the direction and magnitude of change when:

i) market risk premium increases to 7%

ii) market expectation of the dividend payout ratio changes to 50%

iii) market expectation of future ROCE changes to 9%

Answer 1

ROCE = Net income applicable to common stockholders/ Common shareholders equity

g(growth rate) = b (i.e. retention rate) * ROCE

=> 8% = 0.80 * ROCE

=> ROCE = 10%

D/P = 20%

b = 1-0.20 = 80%

g = 8%

beta = 1.20

Rf = 1%

(Rm - Rf) = 6%

Using CAPM, Re = Rf + Beta * (Rm-Rf) = 1% + 1.20*(6%) = 8.2%

Assuming ROCE, g and Re are constant

(I) If market risk premium increases to 7%

Re = 1% + 1.20 *(7%) = 9.4%

Re changes by (9.4% - 8.2%) = 1.2%

(ii) If market expectation of the dividend payout ratio changes to 50%

b = 1 - 0.50 = 50%

g = b * ROCE = 0.50 * 0.40 = 20%

The growth rate (g) changes (increases) by 12% i.e. (20% - 8%)

(iii) if market expectation of future ROCE changes to 9%

g = 0.80 * 9% = 7.2%

The growth rate (g) changes (decreases) by 0.80% i.e. (7.2% - 8%)