Question

Growth Opportunities Lewin Skis, Inc., today expects to earn $8.50 per share for each of the future operating periods (beginning at Time 1), today if the firm makes no new investments and returns the earnings as dividends to the shareholders. However, Clint Williams, president and CEO, has discovered an opportunity to retain and invest 20 percent of the earnings beginning three years from today. This opportunity to invest will continue for each period indefinitely. He expects to earn 10 percent on this new equity investment, the return beginning one year after each investment is made. The firm’s equity discount rate is 12 percent.

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

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

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

Answer 1

a. If the company does not make any new investments, the stock price will be the present value of the constant perpetual dividends. In this case, all earnings are paid as dividends, so, applying the perpetuity equation, we get:

 P = Dividend / R

 P = $8.50 / .12

 P = $70.83

b. 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 × Return on Retained Earnings

g = 0.20 × 0.10

g = 0.02, or 2.00%

Next, we need to calculate the NPV of the investment. During Year 3, 20 percent of the earnings will be reinvested. Therefore, $1.70 is invested ($8.50 × .20). One year later, the shareholders receive a return of 10 percent on the investment, or $0.17 ($1.70 × .10), in perpetuity. The perpetuity formula values that stream as of Year 3. Since the investment opportunity will continue indefinitely and grows at 2 percent, 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 = [(–$1.70 + $0.17 / .12) / (0.12 – 0.02)] / (1.12)2

NPVGO = –$2.26

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 = $70.83 – 2.26

P = $68.57

c. Zero percent! There is no retention ratio which would make the project profitable for the company. If the company retains more earnings, the growth rate of the earnings on the investment will increase, but the project will still not be profitable. Since the return of the project is less than the required return on the company stock, the project is never worthwhile. In fact, the more the company retains and invests in the project, the less valuable the stock becomes.