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.

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= 8%(Correct answer)

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.)
Present value of growth opportunities= 28.63(Corect answer)

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? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answers of a-1 and a-2 are correct I need the answer of part b. Thank you.

Answer 1

b.

growth rate (g) = ROE *  retention rate (b)

g1 = 15% * 60% = 9% , this growth rate will continue till year 5

g6 = 15% * 30% = 4.5%

D1 = $ 4

D2 = $ 4 * (1+g1) = $ 4.36

D3 = $ 4 * (1+g1)^2 = $ 4.7524

Similarly, D4 = $ 5.180116 and D5 = $ 5.646326

Data is not given regarding the cost of equity, hence assuming cost of equity (k) = ROE, we can calculate the sum of present values of D1 to D5

PV (D1 to D5) = $ 15.6688

D6 = D5 * (1+g6) = $ 5.900411

PV (D6 to D-infinity) = D6 / [(k-g6)(1+k)^5] = $ 25.50911

Hence, using multistage dividend discount model,

CSI’s stock price = PV (D1 to D5) + PV (D6 to D-infinity) = $ 41.18