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 15% book return on equity. At the end of the year, CSI is expected to pay a $4 dividend. It has been reinvesting 30% of earnings and growing at 4% a year.

a1) Suppose CSI continues on this growth trend. What is the expected long-run rate of return from purchasing the stock at $100

a2) What part of the $100 price is attributable to the present value of growth opportunities?

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 60% 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?

Answer 1

a1)

As given that CSI continues this growth trend, we apply the standard growing perpetuity formula to calculate the expected long run rate of return

To calculate the expected long run rate of return we can apply the standard growing perpetuity formula with

DIV1 = $ 4 , g = 4% = 0.04 and P0 = $100

P0 = DIV1 / ( r - g )

r = DIV1 / P0 + g

= $4/ $100 + 0.04 = 0.08 or 8%

a2)

As 30% reinvestment is done which implies that the dividends ( $4 ) are 70% of earning. So we can calculate the earning per share as :

Payout Ratio = DIV / EPS

EPS = DIV / Payout Ratio = 4 / 0.7 = $5.71

Also, from here it is now easy to proceed with the estimation of the present value of growth opportunities (PVGO):

P0 = EPS1 / r + PVGO

100 = 5.71 / 0.08 + PVGO

PVGO = 100 – (5.71 / 0.08) = $28.625

Therefore the present value of growth opportunities (PVGO) = $28.63

b)

reinvest 60% of earnings for five years implies 40% payout rate

EPS = DIV / Payout Ratio

DIV = EPS * Payout Ratio = 5.71 * 0.4 = $2.284