Question

Use the cash flows and competitive spreads shown in the table below.

		($ millions)
	Year 0	Year 1	Year 2	Years 3–10
Investment	180
Production (millions of pounds per year)	0	0	48	88
Spread ($ per pound)	1.03	1.03	1.03	1.03
Net revenues	0	0	49.44	90.64
Production costs	0	0	38.00	38.00
Transport	0	0	0	0
Other costs	0	28	28	28
Cash flow	–180	28	–16.56	–24.64
NPV (at r = 7%) = 0

Assume the dividend payout ratio each year is 100%.

a. Calculate the year-by-year book and economic profitability for investment in polyzone production. Assume straight-line depreciation over 10 years and a cost of capital of 7%. (Negative answers should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Enter your income answers in millions rounded to 2 decimal places and enter the rate of return as a percent rounded to 2 decimal places.)

Period:	0	1	2	3	4	5
Book income ($)
Book rate of return (%)
Economic income ($)

	6	7	8	9	10
Book income ($)
Book rate of return (%)
Economic income ($)

b-1. What is the economic rate of return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Economic rate of return             %

b-2. Now compute the steady-state book rate of return (ROI) for a mature company producing polyzone. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

ROI             %

Answer 1

Part (a) The year-by-year book and economic profitability for investment in polyzone is calculated and shown in yellow highlighted rows. Yellow highlighted rows are your answers.

Parameter	Linkage	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8	Year 9	Year 10
Investment	A	180.00
Depreciation	B = A / 10		18.00	18.00	18.00	18.00	18.00	18.00	18.00	18.00	18.00	18.00
Year end book value	C = 180 - accumulated depreciation	180.00	162.00	144.00	126.00	108.00	90.00	72.00	54.00	36.00	18.00	-
Calculation of Book Income & Book Rate of Return
Net revenues	D	-	-	49.44	90.64	90.64	90.64	90.64	90.64	90.64	90.64	90.64
[-] Production costs	E	-	-	38.00	38.00	38.00	38.00	38.00	38.00	38.00	38.00	38.00
[-] Transport	F	-	-	-	-	-	-	-	-	-	-	-
[-] Other costs	G	-	28.00	28.00	28.00	28.00	28.00	28.00	28.00	28.00	28.00	28.00
[-] Depreciation	B (from above)	-	18.00	18.00	18.00	18.00	18.00	18.00	18.00	18.00	18.00	18.00
Book Income	D - (E+F+G+B)	-	(46.00)	(34.56)	6.64	6.64	6.64	6.64	6.64	6.64	6.64	6.64
Book Rate of Return	I = D / C from prior year		-25.56%	-21.33%	4.61%	5.27%	6.15%	7.38%	9.22%	12.30%	18.44%	36.89%
Calculation of Economic Income
Cash flows	J	(180.00)	(28.00)	(16.56)	24.64	24.64	24.64	24.64	24.64	24.64	24.64	24.64
Discount rate	K	7%
PV of cash flows at the beginning of the year	L = NPV(7%, Future cash flows)		87.88	122.03	147.13	132.79	117.45	101.03	83.46	64.66	44.55	23.03
PV of cash flows at the end of the year	M = NPV(7%, Future cash flows from next period)		122.03	147.13	132.79	117.45	101.03	83.46	64.66	44.55	23.03	-
Economic Depreciation	N = L - M		(34.15)	(25.10)	14.34	15.34	16.42	17.57	18.80	20.11	21.52	23.03
Economic Income	O = J - N		6.15	8.54	10.30	9.30	8.22	7.07	5.84	4.53	3.12	1.61

(b) - 1 Economic rate of return will be same as the discount rate, as given in the question. At some point in the question, NPV is being calculated at 7%. Hence economic rate of return = 7%

(b) - 2 Steady state ROI = Sum of Book income over the life of 10 years = Add all the elements in the row titled Book Income = - 27.44

Investments = Sum of year end book value over the life = add the elements in the row titled Year end book value = 990

Hence, ROI = - 27.44 / 990 = - 2.77%