Question

(10 points) ABC research projects a return on equity of 30%. Management plans to plow back 30% of all earnings into the firm. Earnings this year will be $5 per share, and investors expect a 15% rate of return on the stock (r=15%). What is the present value of growth opportunities?

Answer 1

Plowback Ratio = 0.30

Payout Ratio = 1 - Plowback Ratio
Payout Ratio = 1 - 0.30
Payout Ratio = 0.70

Growth Rate = Return on Equity * Plowback Ratio
Growth Rate = 30.00% * 0.30
Growth Rate = 9.00%

Current Dividend = Current Earnings * Payout Ratio
Current Dividend = $5.00 * 0.70
Current Dividend = $3.50

Expected Dividend = Current Dividend * (1 + Growth Rate)
Expected Dividend = $3.50 * 1.09
Expected Dividend = $3.815

Current Price with Growth = Expected Dividend / (Required Return - Growth Rate)
Current Price with Growth = $3.815 / (0.15 - 0.09)
Current Price with Growth = $63.58

Current Price without Growth = Current Earnings / Required Return
Current Price without Growth = $5.00 / 0.15
Current Price without Growth = $33.33

Present Value of Growth Opportunities = Current Price with Growth - Current Price without Growth
Present Value of Growth Opportunities = $63.58 - $33.33
Present Value of Growth Opportunities = $30.25