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

a1) Stock price today (P0) = Next year Dividend (D1)/ (required rate of return (r)- growth rate (g))

=> $100 = $4/(r-0.04)

=> r = 0.04+0.04 = 0.08 =8%

Stock price after one year = Dividend paid after 2 years/(r-g) = $4*1.04/(0.08-0.04)

P1 = $104

So, return from the stock in 1 year = ( (P1-P0)+ D1) /P0

=((104-100)+4)/100 = 0.08 = 8%

So, the long run rate of return from holding the stock is 8%

a2) Present value of growth opportunities is given by

PVGO = P0 - E1/r

Now, Dividend payout ratio = 1-reinvestment ratio = 1-0.3 = 0.7

D1= E1*Dividend payout ratio

=> E1 = $4/0.7 = $5.714286

So, PVGO = $100- $5.714286/0.08 = $28.57143   

(rounding E1 to two decimals result in PVGO =$28.63)

b)

Growth rate in Years 1-6 = ROE* reinvestment rate = 15%*0.6= 9% and after year 6 , it will again become 4%

So

E1 = $5.71428, D1= $5.71428*0.4 = $2.285714

E2= $5.71428 * 1.09 = $6.228571, D2= E2*0.4 =$2.491429

E3=  $6.228571*1.09= $6.789143, D3 =E3*0.4 =$2.725657

E4 = $6.789143*1.09= $7.400166, D4= E4*0.4 =$2.960066

E5= $7.400166*1.09 = $8.066181 , D5 = E5*0.4 =$3.226472

E6 =$8.066181*1.09 =$8.792137, D6 = E6*0.7 = $6.154496

Horizon value at end of year 6 = D7/(r-g) = D6*1.04/(0.08-0.04) = $160.0169

So, Price of share after announcement = D1/(1+r) + D2/(1+r)^2+ ... +D6/(1+r)^6+H6/(1+r)^6  

=$115.50