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 2005, CSI is expected to pay a $4 dividend per share. It has been reinvesting 40%
of earnings and growing at 4% a year.

(a) Suppose CSI continues on this growth trend. What is the expected long-run rateof return from purchasing the stock at $100 per share at the beginning of 2005?What part of the $100 price is attributable to the present value of the growthopportunities?

(b) Now, at the beginning of 2005, the MDC announces a plan for CSI to treatCambridge sewage. CSI’s plant will, therefore, be expanded gradually over 5years. This means that CSI will have to reinvest 80% of its earnings for five years.Starting in 2010, however, it will again be able to pay out 60% of earnings. Whatwill be CSI’s stock price once this announcement is made and its consequencesfor CSI are known?

Explanation / Answer

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 2005, CSI is expected to pay a $4 dividend per share. It has been reinvesting 40%
of earnings and growing at 4% a year.

(a) Suppose CSI continues on this growth trend. What is the expected long-run rateof return from purchasing the stock at $100 per share at the beginning of 2005?What part of the $100 price is attributable to the present value of the growthopportunities?

Div 1= $4

g--------0.04

P0----$100

P0= Div 1 /(r-g)

r= Div 1 / P0      + g= 4 /100 + 0.04 = 0.08 =8%

EPS =div/payout ratio =4/0.6= $ 6.67

P0= EPS1/r + PVGO

100= $ 6.67 /0.08 + PVGO

PVGO =$ 16.63

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