Question

24. CSI converts Boston’s sewage sludge to fertilizer. MDC (Metropolitan District Commission) has agreed to pay whatever amount is necessary to yield CSI a 10% book ROE. At the end of the year, CSI is expected to pay a $4 dividend. It has been reinvesting 40% of its earnings and growing at 4% per year. a. Suppose CSI continues this growth trend. What is the expected long-run rate of return from purchasing the stock at $100. What part of the $100 is attributable to the present value of growth opportunities? b. Now MDC announces a plan for CSI to treat Cambridge sewage. CSI’s plant will be expected gradually over 5 years. This means that CSI will have to reinvest 80% for 5 years. Starting in year 6, CSI will again be able to pay out 60% if its earnings. What will be CSI’s stock price once this announcement is made and its consequences for CSI are known?

Answer 1

Answer :

(a.) Calculation of Expected Return

Expected Return = (Expected Dividend / Share Price) + Growth rate

= (4 / 100) + 0.04

= 0.08 or 8%

Calculation of the part Attrubutable to the present value of growth opportunities :

Present Value of Growth Opprotunities = [Current Price - (Expected EPS / Expected Return)]

Since $4 dividend which is 60% of its earnings (as reinvestment rate is 40%)

Therefore Expected Earning per share = 4 / 0.60 = 6.66667

Present Value of Growth Opprotunities = [100 - (6.66667 / 0.08)] or [100 - (6.67 / 0.08)]

= 16.67 or 16.63

Note : You can also do rounding upto two Decimal places.

(b.) Calculation of Stock Price :

Stock Price is the sum of Present Value of Dividend and Terminal Value

Dividend in year 1 = Expected Earning * (1 - Reinvestment Rate)

= 6.66667 * (1 - 0.80)

= 1.333

New Growth Rate = Reinvestment Rate * Return on Equity

= 0.80 * 0.10

= 0.08 or 8%

Dividend will grow rate of 8% for 5 years .

Below is the table showing calculation of Stock Price :

Year	ROE	Retention Ratio	Growth Rate	Dividend Payout Ratio	EPS	Dividend/Price	PVF @8%	Present Value of Cash Flows
			(ROE*Retention Ratio)	(100 - Retention Ratio)	=EPS * (1 + Growth rate)	Dividend = EPS * Dividend Payot Ratio)
1	10.0%	80%	8.00%	20%	6.666666667	1.33	0.925925926	1.231481481
2	10.0%	80%	8.00%	20%	7.2	1.44	0.85733882	1.234567901
3	10.0%	80%	8.00%	20%	7.776	1.56	0.793832241	1.238378296
4	10.0%	80%	8.00%	20%	8.39808	1.68	0.735029853	1.234850153
5	10.0%	80%	8.00%	20%	9.0699264	1.81	0.680583197	1.231855587
6	10.0%	40%	8.00%	60%	9.795520512	147	0.680583197	100.04573
							Share Price	106.2168634 or 106.21

Note : You can also do rounding upto two Decimal places.Above Problem has been solved by rounding the dividend figures to 2 deciamal places for ease.