Question

Rapid Wave is considering purchasing a water park in Oakland, California, for $1,950,000. The new facility will generate annual net cash inflows of $500,000 for eight years. Engineers estimate that the facility will remain useful for eight years and have no residual value. The company uses straight-line depreciation. Its owners want payback in less than five years and an ARR of 10% or more. Management uses a 14% hurdle rate on investments of this nature

1.	Compute the payback​ period, the​ ARR, the​ NPV, and the approximate IRR of this investment.​ (If you use the tables to compute the​ IRR, answer with the closest interest rate shown in the​ tables.)
2.	Recommend whether the company should invest in this project.

Answer 1

Calculation of Payback Period: Step 1: Depreciation per year can be calculated as follows: Assuming Straight line depreciation, depreciation per year can be calculated as follows Initial cost Life of Machine Salvage value Depreciation per year $1,950,000 8 years -(Investment- Salvage Value)/Expected life of equipment 243,750(D9-D11)/D10 13 14 15 16 17 18 Step2: Now free cash flow can be calculated using following data as follows: Initial investment Net Cash inflow Depreciation per year $1,950,000 $500,000 $243,750.00 ear Investment Net Cash Inflow Salvage Value Free cash flow ($1,950,000 21 $500,000 $500,000 $500,000 $500,000 $500,000 $500,000$500,000 $500,000 $1,950,000 S500,000 $500,000 $500,000 $500,000$500,000 $500,000 $500,000 $500,000 Step3: Payback period is calculated as below: Payback ear Free Cash Flow Cumulative cash flow is the when investment amount is recovered 27 ($1,950,000)丨 ($1,950,000 $500,000| $500,000| ($950,000 S500,000| S500,000| 500,000 $500,000 $500,000 50,000$550,000$1,050,000 $1,550,000 $2,050,000 $500,000 29 ) ($1,450,000 31 32 Payback period is when cumulative free cash flow becomes zero. It can be seen from above that cumulative cash flow becomes zero between year 3 and year 4 To estimate the exact payback period cumulative free cash flow can be proprated over the years as follows: Payback period .90-G27+(0-G29)/(H29-G29) 37 Hence Payback period is 3.90 39 Calculation of ARR: 41 Unadjusted rate of return (ARR) is calculated by dividing increase in future income with initial investment Step1: Calculation of initial investment Intial investment investment 1,950,000 47 Step2: Calculation of increase in future income Increase in revenue Depreciation per year Increase in Net Income $500,000 ($243,750.00) $256,250 51 52 Step3: Calculation of unadjusted rate of return Unadjusted rate of return Given the following data Increase in net income Initial Investment Unadjusted rate of return =increase in net income/Initial investment $256,250 $1,950,000 57 -Increase in net income/Initial investment 13.14% :055/D56 59 Hence ARR of the project is 13.14% 61

ti HA NPV Calculation: NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment ven the fol ear Cash Flow Discount Rate (i) (Assumed) (P/F.i.n) for each year Present F*(P/F,i,n) Present value if future cash flows llowing cash flow and WACC, NPV for the project can be calculated as follows: ($1,950,000$500,000$500,000 $500,000$500,000 $500,000$500,000 $500,000 $500,000 14.0% 0.88 0.77 0.67 0.59 0.52 0.46 0.40 0.35 Value of cash flows FC $438,596.49 $384,733.76 $337,485.76 $296,040.14 $259,684.33 $227,793.27 $199,818.66 $175,279.53 $2,319,431.95SUM(E71:L71) NPV for Project -Present value fo future cash flows-Initial investment $369,431.95 D72+D68 Hence NPV for Project is $369,431.95 IRR Calculation IRR is the rate at which NPV of the project will be zero i.e Given the following cash flow IRR can be calculated as below ear Free Cash Flow 0 S500000 $500,000 o- -$1950000+$50000 IRR can be found using hit and trial method for above equation. IRR can also be found using IRR function in excel as follows: ear Free Cash Flow 19.46% ะเ RRI D96:L96 Hence IRR of the project is 19.46% Since Payback period is 3.90 which is less than the cutoff payoff period of 5 ARR is 13.14% which is higher than the minimum required ARR of 10%, NPV of the project is positive and IRR of the project is 19.46% which is higher than hurdle rate of 14%, therefore project satisfies all the criteria and hence it should be accepted. 105 106
Formula sheet

A	B	C	D	E	F	G	H	I	J	K	L
2
3
4
5		Calculation of Payback Period:
6
7		Step 1: Depreciation per year can be calculated as follows:
8		Assuming Straight line depreciation, depreciation per year can be calculated as follows:
9		Initial cost	1950000
10		Life of Machine	8	years
11		Salvage value	0
12		Depreciation per year	=(Investment - Salvage Value)/Expected life of equipment
13			=(D9-D11)/D10	=(D9-D11)/D10
14		Step2: Now free cash flow can be calculated using following data as follows:
15		Initial investment	=D9
16		Net Cash inflow	500000
17		Depreciation per year	=D13
18
19		Year	0	=D19+1	=E19+1	=F19+1	=G19+1	=H19+1	=I19+1	=J19+1	=K19+1
20		Investment	=-D9
21		Net Cash Inflow		=$D$16	=$D$16	=$D$16	=$D$16	=$D$16	=$D$16	=$D$16	=$D$16
22		Salvage Value									=D11
23		Free cash flow	=D20	=E21	=F21	=G21	=H21	=I21	=J21	=K21	=L21+L22
24
25		Step3: Payback period is calculated as below:
26		Payback period is the period when investment amount is recovered.
27		Year	0	=D27+1	=E27+1	=F27+1	=G27+1	=H27+1	=I27+1	=J27+1	=K27+1
28		Free Cash Flow	=D23	=E23	=F23	=G23	=H23	=I23	=J23	=K23	=L23
29		Cumulative cash flow	=D28	=D29+E28	=E29+F28	=F29+G28	=G29+H28	=H29+I28	=I29+J28	=J29+K28	=K29+L28
30
31		Payback period is when cumulative free cash flow becomes zero.
32		It can be seen from above that cumulative cash flow becomes zero between year 3 and year 4.
33
34		To estimate the exact payback period cumulative free cash flow can be proprated over the years as follows:
35		Payback period	=G27+(0-G29)/(H29-G29)	=G27+(0-G29)/(H29-G29)
36
37		Hence Payback period is	=D35
38
39
40		Calculation of ARR:
41		Unadjusted rate of return (ARR) is calculated by dividing increase in future income with initial investment.
42
43		Step1: Calculation of initial investment
44
45		Intial investment investment	=D9
46
47		Step2: Calculation of increase in future income
48		Increase in revenue	=D16
49		Depreciation per year	=-D17
50		Increase in Net Income	=D48+D49
51
52		Step3: Calculation of unadjusted rate of return
53		Unadjusted rate of return	=Increase in net income/Initial investment
54		Given the following data
55		Increase in net income	=D50
56		Initial Investment	=D45
57		Unadjusted rate of return	=Increase in net income/Initial investment
58			=D55/D56	=D55/D56
59
60		Hence ARR of the project is	=D58
61
62
63
64		NPV Calculation:
65		NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment.
66		Given the following cash flow and WACC, NPV for the project can be calculated as follows:
67		Year	0	1	2	3	4	5	6	7	8
68		Cash Flow	=D23	=E23	=F23	=G23	=H23	=I23	=J23	=K23	=L23
69		Discount Rate (i) (Assumed)	0.14
70		(P/F,i,n) for each year		=1/((1+$D69)^E67)	=1/((1+$D69)^F67)	=1/((1+$D69)^G67)	=1/((1+$D69)^H67)	=1/((1+$D69)^I67)	=1/((1+$D69)^J67)	=1/((1+$D69)^K67)	=1/((1+$D69)^L67)
71		Present Value of cash flows = FCF*(P/F,i,n)		=E68*E70	=F68*F70	=G68*G70	=H68*H70	=I68*I70	=J68*J70	=K68*K70	=L68*L70
72		Present value if future cash flows	=SUM(E71:L71)	=SUM(E71:L71)
73
74		NPV for Project	=Present value fo future cash flows - Initial investment
75			=D72+D68	=D72+D68
76
77		Hence NPV for Project is	=D75
78
79
80
81		IRR Calculation
82
83		IRR is the rate at which NPV of the project will be zero i.e.
84		Given the following cash flow IRR can be calculated as below:
85
86		Year	0	=D86+1	=E86+1	=F86+1	=G86+1	=H86+1	=I86+1	=J86+1	=K86+1
87		Free Cash Flow	=D23	=E23	=F23	=G23	=H23	=I23	=J23	=K23	=L23
88
89
90
91
92		IRR can be found using hit and trial method for above equation.
93
94		IRR can also be found using IRR function in excel as follows:
95		Year	0	=D95+1	=E95+1	=F95+1	=G95+1	=H95+1	=I95+1	=J95+1	=K95+1
96		Free Cash Flow	=D87	=E87	=F87	=G87	=H87	=I87	=J87	=K87	=L87
97		IRR	=IRR(D96:L96)	=IRR(D96:L96)
98
99		Hence IRR of the project is	=D97
100
101
102		2)
103
104		Since Payback period is 3.90 which is less than the cutoff payoff period of 5,
105		ARR is 13.14% which is higher than the minimum required ARR of 10%,
106		NPV of the project is positive and IRR of the project is 19.46% which is higher than hurdle rate of 14%,
107		therefore project satisfies all the criteria and hence it should be accepted.
108