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	59	99
Spread ($ per pound)	1.14	1.14	1.14	1.14
Net revenues	0	0	67.26	112.86
Production costs	0	0	49.00	49.00
Transport	0	0	0	0
Other costs	0	39	39	39
Cash flow	–180	39	–20.74	–24.86
NPV (at r = 6%) = 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 6%. (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

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	-	-	67.26	112.86	112.86	112.86	112.86	112.86	112.86	112.86	112.86
[-] Production costs	E	-	-	49.00	49.00	49.00	49.00	49.00	49.00	49.00	49.00	49.00
[-] Transport	F	-	-	-	-	-	-	-	-	-	-	-
[-] Other costs	G	-	39.00	39.00	39.00	39.00	39.00	39.00	39.00	39.00	39.00	39.00
[-] 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)	-	(57.00)	(38.74)	6.86	6.86	6.86	6.86	6.86	6.86	6.86	6.86
Book Rate of Return	I = D / C from prior year		-31.67%	-23.91%	4.76%	5.44%	6.35%	7.62%	9.53%	12.70%	19.06%	38.11%
Calculation of Economic Income
Cash flows	J	(180.00)	(39.00)	(20.74)	24.86	24.86	24.86	24.86	24.86	24.86	24.86	24.86
Discount rate	K	6%
PV of cash flows at the beginning of the year	L = NPV(6%, Future cash flows)		82.14	126.07	154.38	138.78	122.24	104.72	86.14	66.45	45.58	23.45
PV of cash flows at the end of the year	M = NPV(6%, Future cash flows from next period)		126.07	154.38	138.78	122.24	104.72	86.14	66.45	45.58	23.45	-
Economic Depreciation	N = L - M		(43.93)	(28.30)	15.60	16.53	17.53	18.58	19.69	20.87	22.13	23.45
Economic Income	O = J - N		4.93	7.56	9.26	8.33	7.33	6.28	5.17	3.99	2.73	1.41

(a) the year-by-year book and economic profitability for investment in polyzone is calculated and shown in yellow highlighted rows.

(b) - 1 Economic rate of return = 6% (same as discount rate)

(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 = - 40.86

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

Hence, ROI = - 40.86 / 990 = - 4.13%