Question

Next year's earnings are estimated to be $4. The company plans to reinvest 25% of its earnings at 20%. If the cost of equity is 13%, what is the present value of growth opportunities?

Answer 1

Expected Earnings per share, EPS1 = $4.00
Retention Ratio, b = 25%
Return on Equity, ROE = 20%
Cost of Equity, k = 13%

Expected Dividend, D1 = EPS1 * (1 - b)
Expected Dividend, D1 = $4.00 * (1 - 0.25)
Expected Dividend, D1 = $3.00

Growth Rate, g = ROE * b
Growth Rate, g = 20% * 25%
Growth Rate, g = 5%

Value with Growth = D1 / (k - g)
Value with Growth = $3.00 / (0.13 - 0.05)
Value with Growth = $37.50

Value without Growth = EPS1 / k
Value without Growth = $4.00 / 0.13
Value without Growth = $30.77

Present Value of Growth Opportunity, PVGO = Value with Growth - Value without Growth
Present Value of Growth Opportunity, PVGO = $37.50 - $30.77
Present Value of Growth Opportunity, PVGO = $6.73