Question

Share X has Earnings Per Share of 12 and its Present Value of Growth Opportunities is $101.34. Given a market capitalization rate of 18.85%, and a plowback ratio of 45%

calculate the Return on Equity for Share X.

Answer 1

'g' is the growth rate = ROE*Plowback ratio

Value with no growth = Next year's EPS/Market cap rate = 12*(1+g)/0.1885

Value with growth = Next year's EPS*(1-Plowback ratio)/(Market cap rate - g)

Value with growth = 12*(1+g)*(1-0.45)/(0.1885-g)

Present value of growth opportunities = Value with growth - Value with no growth

Substituting,

101.34 = 12*(1+g)*(1-0.45)/(0.1885-g) - 12*(1+g)/0.1885

101.34 = 6.6*(1+g)/(0.1885-g) - 63.66*(1+g)

Solving for g, we get g = 0.1451

g = ROE*Plowback ratio

0.1451 = ROE*0.45

Return on equity (ROE) = 0.3224 = 32.24%