Question

Compost Science Inc. (CSI) is in the business of converting Boston’s sewage sludge into fertilizer. The business is not in itself very profitable. However, to induce CSI to remain in business, the Metropolitan District Commission (MDC) has agreed to pay whatever amount is necessary to yield CSI a 12% book return on equity. At the end of the year, CSI is expected to pay a $4 dividend. It has been reinvesting 40% of earnings and growing at 4% a year.

a-1. Suppose CSI continues on this growth trend. What is the expected long-run rate of return from purchasing the stock at $100? (Do not round intermediate calculations. Enter your answer as a percent rounded to the nearest whole number.)

Rate of Return:
a-2. What part of the $100 price is attributable to the present value of growth opportunities? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

PVGO:
b. Now the MDC announces a plan for CSI to treat Cambridge sewage. CSI’s plant will, therefore, be expanded gradually over five years. This means that CSI will have to reinvest 80% of its earnings for five years. Starting in year 6, however, it will again be able to pay out 60% of earnings. What will be CSI’s stock price once this announcement is made and its consequences for CSI are known? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Stock price:

Answer 1

a-1). long-run rate of return (r) = (D1/P0) + g where D1 (expected dividend) = 4; P0 (current price) = 100; g (growth rate) = 4%

r = (4/100) + 4% = 8%

a-2). Since 40% of the earnings are being reinvested, the total earnings per share (EPS1) is D1/(1-40%) = 4/(1-40%) = 6.67

Current price P0 = (EPS1/r) + PVGO

100 = (6.67/8%) + PVGO

PVGO = 16.67

b). Price per share = 106.17