Question

Seth Fitch owns a small retail ice cream parlor. He is considering expanding the business and has identified two attractive alternatives. One involves purchasing a machine that would enable Mr. Fitch to offer frozen yogurt to customers. The machine would cost $7,680 and has an expected useful life of three years with no salvage value. Additional annual cash revenues and cash operating expenses associated with selling yogurt are expected to be $6,120 and $840, respectively.

Alternatively, Mr. Fitch could purchase for $9,560 the equipment necessary to serve cappuccino. That equipment has an expected useful life of four years and no salvage value. Additional annual cash revenues and cash operating expenses associated with selling cappuccino are expected to be $8,400 and $2,270, respectively.

Income before taxes earned by the ice cream parlor is taxed at an effective rate of 20 percent.

   

Required

Determine the payback period and unadjusted rate of return (use average investment) for each alternative. (Round your answers to 2 decimal places.)

	Alternative 1		Alternative 2
Payback period		years		years
Unadjusted rate of return		%		%

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J
2
3		Alternative 1:
4		Initial investment	7680
5		Estimated Life	3	Years
6		Salvage Value	0
7		Additional Revenue	6120
8		Operating Expense	840
9		Depreciation per Year	=(D4-D6)/D5	=(D4-D6)/D5	(Assuming Straight line depreciation)
10		Cash flow for alternative 1:
11		Year	0	1	2	3
12		Investment	=-D4
13		Additional Revenue		=$D7	=$D7	=$D7
14		Cash Expense		=-$D8	=-$D8	=-$D8
15		Depreciation Expense		=-$D9	=-$D9	=-$D9
16		EBIT		=SUM(E13:E15)	=SUM(F13:F15)	=SUM(G13:G15)
17		Tax Expense (20%)		=-E16*20%	=-F16*20%	=-G16*20%
18		EBIT*(1-T)		=E16+E17	=F16+F17	=G16+G17
19		Add Depreciation		=-E15	=-F15	=-G15
20		Net Cash flow	=D12	=E18+E19	=F18+F19	=G18+G19
21
22		Calculation of Payback period for Alternative 1:
23		Payback period is the period when investment amount is recovered.
24		Year	0	=D24+1	=E24+1	=F24+1
25		Net Cash Flow	=D20	=E20	=F20	=G20
26		Cumulative cash flow	=D25	=E25+D26	=F25+E26	=G25+F26
27		Payback period is when cumulative free cash flow becomes zero.
28		It can be seen from above that cumulative cash flow becomes zero between year 1 and year 2.
29
30		To estimate the exact payback period cumulative free cash flow can be proprated over the years as follows:
31		Payback period	=E24+(0-E26)/(F26-E26)	=E16+(0-E18)/(F18-E18)
32
33		Hence Payback period is	=D31	Years
34
35
36		Calculation of unadjusted rate of return for Altenative 1:
37		Unadjusted rate of return can be calculated as follows:
38
39		Unadjusted rate of return	=Increase in net income / Initial Investment
40
41		Increase in net income	=Incremental Revenue - Incremental Cost
42			=E18	=E18
43
44		Initial investment	=-D26
45
46		Unadjusted rate of return	=Incremental Accounting income / Initial Investment
47			=D42/D44	=D42/D44
48
49		Hence Unadjusted rate of return for alternative 1 is	=D47
50
51		Alternative 2:
52		Initial investment	9560
53		Estimated Life	4	Years
54		Salvage Value	0
55		Additional Revenue	8400
56		Operating Expense	2270
57		Depreciation per Year	=(D52-D54)/D53
58		Cash flow for Alternative 2:
59		Year	0	1	2	3
60		Investment	=-D52
61		Additional Revenue		=$D55	=$D55	=$D55
62		Cash Expense		=-$D56	=-$D56	=-$D56
63		Depreciation Expense		=-$D57	=-$D57	=-$D57
64		EBIT		=SUM(E61:E63)	=SUM(F61:F63)	=SUM(G61:G63)
65		Tax Expense (20%)		=-E64*20%	=-F64*20%	=-G64*20%
66		EBIT*(1-T)		=E64+E65	=F64+F65	=G64+G65
67		Add Depreciation		=-E63	=-F63	=-G63
68		Net Cash flow	=D60	=E66+E67	=F66+F67	=G66+G67
69
70		Calculation of Payback period for Alternative 2:
71		Payback period is the period when investment amount is recovered.
72		Year	0	=D72+1	=E72+1	=F72+1
73		Net Cash Flow	=D68	=E68	=F68	=G68
74		Cumulative cash flow	=D73	=E73+D74	=F73+E74	=G73+F74
75		Payback period is when cumulative free cash flow becomes zero.
76		It can be seen from above that cumulative cash flow becomes zero between year 1 and year 2.
77
78		To estimate the exact payback period cumulative free cash flow can be proprated over the years as follows:
79		Payback period	=E72+(0-E74)/(F74-E74)	=E72+(0-E74)/(F74-E74)
80
81		Hence Payback period is	=D79	Years
82
83
84		Calculation of unadjusted rate of return for Alternative 2:
85		Unadjusted rate of return can be calculated as follows:
86
87		Unadjusted rate of return	=Increase in net income / Initial Investment
88
89		Increase in net income	=Incremental Revenue - Incremental Cost
90			=E66	=E66
91
92		Initial investment	=-D74
93
94		Unadjusted rate of return	=Incremental Accounting income / Initial Investment
95			=D90/D92	=D90/D92
96
97		Hence Unadjusted rate of return for Alternative 2 is	=D95
98
99		Hence,
100			Alternative 1	Alternative 2
101		Payback Period (Years)	=D33	=D81
102		Unadjusted Rate of return	=D49	=D97
103