Compost Science, Inc. (CSI), is in the business of converting Boston’s sewage sl

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 10% book return on equity. At the end of the year CSI is expected to pay a $5.00 dividend. It has been reinvesting 30% of earnings and growing at 3% 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. Round your answer to 1 decimal place.)

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.)

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 70% 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.)

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.)

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 70% 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.)

Explanation / Answer

Here we can apply the standard growing perpetuity formula with

DIV 1 = 5, g = 0.03 and P 0 = $100:

r = DIV 1 / P 0 + g = (5/ 100) + 0.03 = 0.08 = 8%

The 5 dividend is 70 percent of earnings, implying that

EPS 1 = 5 / 0.7 = 7.14  

P 0 =( EPS 1 / r) + PVGO i.e., 100 = (7.14/ 0.08) + PVGO. Therefore PVGO = 10.75

b- DIV 1 will decrease to 0.20 × 7.14 = $1.428. However, by plowing back 80 percent of earnings, CSI will grow by 8 percent per year for 5 years. Thus

dividend+ dividend* growth rate dividend/dividend rate Year EPS 1 1.33 6.65 2 1.4364 7.182 3 1.551312 7.75656 4 1.67541696 8.377085 5 1.80945032 9.047252 6 7.81682537 9.771032 stock price after announcement dividend at year 6/ rate of return on equity- growth rate 195.4 Year dividend discount rate@8% dividend*discount factor 1 1.33 0.925926 1.231481 2 1.4364 0.857339 1.231481 3 1.551312 0.793832 1.231481 4 1.67541696 0.73503 1.231481 5 1.80945032 0.680583 1.231481 195.4 0.680583 132.986 CSI’s stock price will increase to present value 139.1434

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