Rincon, LLC is considering a project that will require an initial investment of
ID: 1104487 • Letter: R
Question
Rincon, LLC is considering a project that will require an initial investment of $750,000 with estimated net income of $135,000 per year for 10 years. (a) Determine the IROR, PI, and PW values at MARR = 12% per year. (b) For which of these measures is the project economically justified? (c) Reflect on the answers above and the breakeven i*. Is there any MARR value that will cause any of the three measures to result in different conclusions about the economic viability of the project? Explain your answer
Please help me this questions in details.
Explanation / Answer
Answer:
Ans a.
Year
Cash Flow
PVF@12%
PV
0
(750,000)
1.0000
(750,000)
1
135,000
0.8929
120,536
2
135,000
0.7972
107,621
3
135,000
0.7118
96,090
4
135,000
0.6355
85,795
5
135,000
0.5674
76,603
6
135,000
0.5066
68,395
7
135,000
0.4523
61,067
8
135,000
0.4039
54,524
9
135,000
0.3606
48,682
10
135,000
0.3220
43,466
NPW =
12,780
(NPW = Sum of PV calculated at the applicable MARR.
PVF is calculated by using following formula PVF for year n = 1/(1+MARR)n )
PI = (NPV+Initial Investment)/ Initial Investment = (12780+750000)/750000 = 1.017
IROR = 12.61% (approx), calculated as follows:
Step 1: calculate NPW using two discount rates (I have taken 10% and 15%)
Year
Cash Flow
PVF@10%
PV
Year
Cash Flow
PVF@15%
PV
0
(750,000)
1.0000
(750,000)
0
(750,000)
1.0000
(750,000)
1
135,000
0.9091
122,727
1
135,000
0.8696
117,391
2
135,000
0.8264
111,570
2
135,000
0.7561
102,079
3
135,000
0.7513
101,427
3
135,000
0.6575
88,765
4
135,000
0.6830
92,207
4
135,000
0.5718
77,187
5
135,000
0.6209
83,824
5
135,000
0.4972
67,119
6
135,000
0.5645
76,204
6
135,000
0.4323
58,364
7
135,000
0.5132
69,276
7
135,000
0.3759
50,752
8
135,000
0.4665
62,978
8
135,000
0.3269
44,132
9
135,000
0.4241
57,253
9
135,000
0.2843
38,375
10
135,000
0.3855
52,048
10
135,000
0.2472
33,370
NPV =
79,517
NPV =
(72,466)
Step 2: Calculate IRR using following formula:
IRR = Rate 1 + [ (NPV at Rate 1 x (rate 2 - rate 1) ) / (NPV at rate 1 - NPV at rate 2)]
= 0.10+[(79517*(.15-.10))/(79517 - (-72466))]
= 12.61%
Ans b: For all of these measures, the project is justified. The reasons are:
IROR: The IRR above MARR indicates that the rate of return at which the profit stops being profitable(the IROR) is higher than the current expected Rate of Return (the MARR).
PI: It is the ratio of the payoff of a project to its cost. A PI amount of greater than 1 indicates that we are earning a positive value from the project at the required discount rate/MARR.
NPW: Net present worth or Net present value is the cash flow from the project in present value terms, discounted at appropriate discount rate/MARR. A positive NPW indicates the project is giving us a positive cash inflow.
Ans c: A breakeven i* or IRR is the rate at which the NPV of the project is 0. An IRR which is greater than the required MARR indicates that the project is profitable and likely to be approved. However, comparing IRR with MARR has limitiations:
1. IRR can be accurately calcutaed only in case of projects when a cash outflow is followed by a series of cash inflows. If there are multiple cash outflows, the projects IRR calculations could be misleading and therefore not preferred.
2. IRR method looks at the rate of return rather than monetary size of the return. Eg. A return of $10 on invetment of $100 has high IRR of 10% compared to IRR of 5% on a project with $500 return on $10000, which has a higher net income in monetary terms.
Ans D: In the given question, all the three measures results in same conclusion, which can be seen as follows:
1. If the MARR = IRR, the NPW will be 0, the PI will be 1. Thus, the project will be at no profit, no loss situation.
2. If the MARR>IRR, the NPV will also be negetive and PI will be lower than 1. Thus, all the methods results in rejection of the project.
3. If the MARR<IRR, the NPV will be positive alonwith PI>1. Thus, Thus, all the methods results in selection of the project.
Year
Cash Flow
PVF@12%
PV
0
(750,000)
1.0000
(750,000)
1
135,000
0.8929
120,536
2
135,000
0.7972
107,621
3
135,000
0.7118
96,090
4
135,000
0.6355
85,795
5
135,000
0.5674
76,603
6
135,000
0.5066
68,395
7
135,000
0.4523
61,067
8
135,000
0.4039
54,524
9
135,000
0.3606
48,682
10
135,000
0.3220
43,466
NPW =
12,780
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