Question

Problem 4-20 Two-stage DCF model 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 14% book return on equity. At the end of the year, CSI is expected to pay a $5 dividend. It has been reinvesting 40% of earnings and growing at 5% 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.) Answer is complete and correct. Rate of return 100% 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.) Answer is complete and correct. $ 16.67 PVGO 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 80% of its earnings for five years. Starting in year 6, however, it will again be able to pay out 60% 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.) Answer is complete but not entirely correct. Stock price $ 106.17

Answer 1

PLEASE DO PROVIDE YOUR VALUABLE COMMENTS AND RATINGS

PROBLEM 4-20

a-1) Based on growing perpetuity formula with DIV1 = $5, g = 0.05 and P0 = $100:

r = DIV1/P0 + g

r = $5/$100 + 0.05

r = 10%

a-2) The formula to evaluate present of growth opportunities (PVGO)

The $5 dividend is (100-40)60% of earnings. Thus:

EPS1 = 5/0.6 = $8.33

and

P0 = EPS/r + PVGO

$100 = $8.33/0.10 + PVGO

PVGO = $16.67

b) Now the earnings are paid at 80%, that implies Dividend are reduced to 20%(8.33 * 20%) = 1.67

However, by plowing/availing back 80% of earnings, CSI will grow by 10% per year for five years. Thus:

year1	1	2	3	4	5	6	7..8..
Dividendt	1.67	1.83	2.02	2.22	2.44	8.05	Continues at 5% growth rate
EPSt	8.33	9.16	10.08	11.09	12.20	13.42	Continues at 5% growth rate

***Note that DIV6 increases sharply as the firm switches back to a 60% payout policy.

Forecasted stock price in year 5 is:

P5 = DIV6/ (r - g)

P5 = 8.05/ (0.10 - 0.05) = $161

Therefore, CSI’s stock price will increase to:

P0 = $1.67/1.10 + $1.83/1.10^2 + 2.02/1.10^3 + 2.22/1.10^4 + (2.44 + 161)/1.10^5 = $107.55

STOCK PRICE = $107.55

PROBLEM 4-28

? * C1 - Excel DEVELOPER - - Sign in FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW A PRODUCT NOTICE Excel hasn't been activated. To keep using Excel without interruption, activate before Sunday, March 1, 2020. Activate c27 A The present value of dividends to be paid in 2022 and FURTHER years can be computed by CONSIDERING both revenues and expenses can be treated as growing perpetuities. Since production will decrease 7% per year while costs per barrel remain constant, the growth rate of expenses is: -7.0% AB 1000000 2018 1900000 2021 1528278. 3 7% YEARS PRODUCTION(MILLION BARRELS) PRICE/BARREL COST/BARREL 2019 1767000 61 26 2020 1643310 56 26 2022 1421298.819 53.55 26 66 5% 26 26 125400000 49400000 REVENUE EXPENSES NET INCOME NET INCOME IN VALUES(IN MILLIONS) 107787000 45942000 35 61845000 92025360 42726060 30 77942193. 3 39735235.8 25 38206957.5 76110551.76 36953769.29 27.55 39156782.46 40 76000000 PRESENT VALUE OF DIVIDENDS CALCULATIONS TO PAID IN 2019,2020,2021 YEARS 2019 2020 2021 DIVIDENDS 61845000 49299300 38206957.5 PVFACTOR 9% 0.9174 0.8417 0.7722 PV OF DIVID 56736603 41495220.81 29503412.58 TOTAL 127735236.4 The present value of dividends to be paid in 2022 and FURTHER years can be computed by CONSIDERING both revenues and expenses can be treated as growing perpetuities. Since production will decrease 7% per year while costs per barrel remain constant, the growth rate of expenses is: -7.0% To compute the growth rate of revenues, (1.05 x (1 -0.07)]-1=-0.0235 = -2.35% Therefore, the present value in 2021) of revenues beginning in 2022 is: PV OF 2021(INCOME) 76110551.76 0.1135 $670,577,548.52 Similarly, the present value (in 2021) of expenses beginning in 2022 is: Sheet1 EDIT @ 100% 11:40 PM a Palco a P ill Norton Security

? * C1 - Excel DEVELOPER - - Sign in FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW A PRODUCT NOTICE Excel hasn't been activated. To keep using Excel without interruption, activate before Sunday, March 1, 2020. Activate 152 X for - AB Therefore, the present value (in 2021) of revenues beginning in 2022 is: L P V OF 2021(INCOME) 76110551.76 0 .1135 $670,577,548.52| Similarly, the present value in 2021) of expenses beginning in 2022 is: P V OF 2021(EXPENSES) 36953769.29 0 .16 $230,961,058.09 PV OF 2021 $439,616,490.44 NOW discounting back three years to 2018, we find that the present value of dividends paid in 2022 and subsequent years is: $339,464,591.48 VALUE PV FACTOR @9% FOR 3 YEARS = (1+i)^n DIV IN 2022 $439,616,490.44 1.295029 $339,464,591.48 TOTAL VALUE OF COMPANY $467,199,827.87 PRESENT VALUE/SHARE(2018) NO OF SHARES O/S 8000000 PRESENT VALUE/SHARE(2018) $58.40 EPS/P RATIO EPS EPS/P 9.5 $0.16 Sheet1 + READY @ U -- + 100% 11:41 PM 2/28/2020

? * C1 - Excel DEVELOPER - - Sign in FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW A PRODUCT NOTICE Excel hasn't been activated. To keep using Excel without interruption, activate before Sunday, March 1, 2020. Activate G30 : * fic 1000000 2018 = 1.9*H4 0.07 YEARS PRODUCTION MILLION BARRELS) PRICEIBARREL COSTIBARREL 2019 =C6-1C6*A6) 61 26 12020 =D6-1D6*A6) 56 26 2021 =E6-(E6*A6) 51 2022 =F6-(F6*A6) =F7+[F7+H7) 26 0.05 166 26 26 REVENUE EXPENSES NET INCOME NET INCOME IN VALUES(IN MILLIONS) =C6 C7 =C6*C8 =C7-C8 =C6*C12 =D6*D7 =D6*D8 =D7-D8 =D6*D12 =E6*E7 =E6*E8 =E7-E8 =E6*E 12 =F6*F7 =F6*F8 =F7-F8 =F6*F12 =G6 G7 =G6*G8 =G7-G8 =G6 G12 PRESENT VALUE OF DIVIDENDS CALCULATIONS TO PAID IN 2019,2 YEARS I 2019 2020 2021 DIVIDENDS 61845000 49299300 38206957.5 PVFACTOR 9% 10.9174 0.8417 0.7722 PY OF DIVID =D19+E 19 =D20 E20 =D21E21 TOTAL =SUM(F19:F21) The present value of dividends to be paid in 2022 and FURTHER yea To compute the growth rate of revenues, (1.05 x (1 -0.07)] - 1= -0.0 Therefore, the present value (in 2021) of revenues beginning in 202: PV OF 2021 INCOME) = G6 G7 =0.09-(-0.0235) =C331D33 Similarly, the present value (in 2021) of expenses beginning in 2022 PY OF 2021(EXPENSES) =G11 =0.09-1-0.07] =0.09- =C371D37 PY OF 2021 =E33-E37 NOW discounting back three years to 2018, we find that the present VALUE PY FACTOR @9% FOR 3 YEARS = (1+i) în DIV IN 2022 =E39 1.295029 =C44/D44 TOTAL VALUE OF COMPANY =F23+E 44 A PRESENT VALUE/SHARE(2018) 49 50 Sheet1 + READY @ D -G H + 66% 11:42 PM 2/28/2020

? * C1 - Excel DEVELOPER - - Sign in FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW A PRODUCT NOTICE Excel hasn't been activated. To keep using Excel without interruption, activate before Sunday, March 1, 2020. Activate G30 : * fic E HA TOTAL =SUM(F19:F21) The present value of dividends to be paid in 2022 and FURTHER yea To compute the growth rate of revenues, [1.05 x (1 -0.07)] -1 = -0.0 Therefore, the present value (in 2021) of revenues beginning in 202: PY OF 2021(INCOME) = G6 G7 =0.09-1-0.0235) =C331D33 Similarly, the present value (in 2021) of expenses beginning in 2022 PY OF 2021 EXPENSES) =G11 =0.09-1-0.07 =C371D37 PY OF 2021 =E33-E 37 NOW discounting back three years to 2018, ve find that the present VALUE DIV IN 2022 PY FACTOR @9% FOR 3 YEARS = (1+i) n 1.295029 =E39 =C44/D44 TOTAL VALUE OF COMPANY =F23+E 44 PRESENT VALUE/SHARE(2018) NO OF SHARES O/S 8000000 PRESENT VALUE/SHARE(2018) =C47/C51 EPS/P RATIO EPS =C13/C51 =C57/C53 EPS/P Sheet1 + READY @ D -- H + 66% 11:42 PM 2/28/2020
bb-2) NO, IT IS NOT EQUAL TO 9%