Growth Opportunities 2

Growth Opportunities – Lewin Skis, Inc (today) expects to earn $6.25 per share for each of the future operating periods (beginning at time I) if the firm makes no new investments and returns the earnings as dividend as dividends to the shareholders. However, Clint Williams, president and CEO, has discovered an opportunity to retain and invest 20% of the earnings beginning three years from today. This opportunity to invest will continue for each period indefinitely. He expects to earn 11% on made. The firm’s equity discount rate is 13% throughout.

What is the price per share of Lewin Skies, Inc., stock without making the new investment?

P = Dividend/R

P = $6.25/0.13

P = $48.08

If the new investment is expected to be made, per the preceding information, what would the price of the stock be now?

The investment occurs every year in the growth opportunity, so the opportunity is a growing perpetuity. So we first need to find the growth rate. The growth rate is:

g = retention ratio x return on retain earnings

g = 0.20 x 0.11

g = 0.022 or 2.20%

next we need to calculate the NPV of the investment. During year 3, 20% of the earnings will be reinvested. Therefore, $1.25 is invested ($6.25 x 0.20). one year later, the shareholders receive an 11 percent return on the investment, or $0.138 ($1.25 x 0.11), in perpetuity.

The perpetuity formula values that streams as of year 3. Since the investment opportunity will continue indefinitely and growth at 2.2 %, apply the growing perpetuity formula to calculate the NPV of the investment as of year 2. Discount that value back two years to today.

NPVGO = ((investment + return) / R ) / (R – g) / (1+R)²

NPVGO = (-$1.25 + $0.138) / 0.13) / (0.13 – 0.022) / (1.13)²

NPVGO = -$1.39  

The value of the stock is the PV of the firm without making the investment plus the NPV of the investment, or:

P = PV (EPS) + NPVGO

P = $48.08 – 1.39

P = $46.68

Suppose the company could increase the investment in the project by whatever amount it chose. What would the retention ration need to be to make this project attractive?

Zero percent

Reference:  Chapter 9, Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.