question archive consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$ 364,000 –$ 52,000 1 46,000 25,000 2 68,000 22,000 3 68,000 21,500 4 458,000 17,500 Whichever project you choose, if any, you require a return of 11 percent on your investment
consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$ 364,000 –$ 52,000 1 46,000 25,000 2 68,000 22,000 3 68,000 21,500 4 458,000 17,500 Whichever project you choose, if any, you require a return of 11 percent on your investment
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consider the following two mutually exclusive projects:
| Year | Cash Flow (A) | Cash Flow (B) | |||||
| 0 | –$ | 364,000 | –$ | 52,000 | |||
| 1 | 46,000 | 25,000 | |||||
| 2 | 68,000 | 22,000 | |||||
| 3 | 68,000 | 21,500 | |||||
| 4 | 458,000 | 17,500 | |||||
Whichever project you choose, if any, you require a return of 11 percent on your investment.
a-1. What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
a-2. If you apply the payback criterion, which investment will you choose?
Project A
Project B
b-1. What is the discounted payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
b-2. If you apply the discounted payback criterion, which investment will you choose?
Project A
Project B
c-1. What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
c-2. If you apply the NPV criterion, which investment will you choose?
Project A
Project B
d-1. What is the IRR for each project? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
d-2. If you apply the IRR criterion, which investment will you choose?
Project A
Project B
e-1. What is the profitability index for each project? (Do not round intermediate calculations and round your answers to 3 decimal places, e.g., 32.161.)
e-2. If you apply the profitability index criterion, which investment will you choose?
Project A
Project B
f. Based on your answers in (a) through (e), which project will you finally choose?
Project A
Project B
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a-1. What is the payback period for each project?
Project A
| Year | 0 | 1 | 2 | 3 | 4 |
| Cashflow(in $) | (364,000) | 46,000 | 68,000 | 68,000 | 458,000 |
| Cumulative Cashflow(in $) | (364,000) | (318,000) | (250,000) | (182,000) | 276,000 |
Payback Period = A+(B/C)
where
A - last period containing negative cumulative cash flow
B - absolute value of cumulative cash flow in A
C - cash flow during the period after A
Payback Period = 3 + (182000/458000)
= 3 + 0.39737991266
= 3.40 Years
Project B
| Year | 0 | 1 | 2 | 3 | 4 |
| Cashflow(in $) | (52,000) | 25,000 | 22,000 | 21,500 | 17,500 |
| Cumulative Cashflow(in $) | (52,000) | (27,000) | (5,000) | 16,500 | 34,000 |
Payback period = 2 + (5000/21500)
= 2 + 0.23255813953
= 2.23 years
a-2. If you apply the payback criterion, which investment will you choose?
Project B as it has lower Payback period.
b-1. What is the discounted payback period for each project?
Project A
| Year | 0 | 1 | 2 | 3 | 4 |
| Cashflow(in $) | (364,000) | 46,000 | 68,000 | 68,000 | 458,000 |
| PVF @11% | 1 | 0.901 | 0.812 | 0.731 | 0.659 |
| Discounted Cashflow (Cash flow * PVF) | (364,000) | 41,441 | 55,190 | 49,721 | 301,699 |
| Cumulative Cashflow(in $) | (364,000) | (322,559) | (267,368) | (217,647) | 84,052 |
Discounted Payback Period = 3 + (217647/301699)
= 3 + 0.72140444615
= 3.72 Years
Project B
| Year | 0 | 1 | 2 | 3 | 4 |
| Cashflow(in $) | (52,000) | 25,000 | 22,000 | 21,500 | 17,500 |
| PVF @11% | 1 | 0.901 | 0.812 | 0.731 | 0.659 |
| Discounted Cashflow (Cash flow * PVF) | (52,000) | 22,523 | 17,856 | 15,721 | 11,528 |
| Cumulative Cashflow(in $) | (52,000) | (29,477) | (11,622) | 4,099 | 15,627 |
Discounted payback period = 2+(11622/15721)
= 2 + 0.73926595
= 2.74 years
b-2. If you apply the discounted payback criterion, which investment will you choose?
Project B as it has lower Lower Discounted Payback period.
c-1. What is the NPV for each project?
Project A
| ear | 0 | 1 | 2 | 3 | 4 |
| Cashflow(in $) | (364,000) | 46,000 | 68,000 | 68,000 | 458,000 |
| PVF @11% | 1 | 0.901 | 0.812 | 0.731 | 0.659 |
| Discounted Cashflow (Cash flow * PVF) | (364,000.00) | 41,441.44 | 55,190.33 | 49,721.01 | 301,698.79 |
NPV = PV of Inflows - PV of Outflows
= (41441.44+55190.33+49721.01+301698.79) - 364000
= 448051.57-364000
= 84051.57
Project B
| Year | 0 | 1 | 2 | 3 | 4 |
| Cashflow(in $) | (52,000) | 25,000 | 22,000 | 21,500 | 17,500 |
| PVF @11% | 1 | 0.901 | 0.812 | 0.731 | 0.659 |
| Discounted Cashflow (Cash flow * PVF) | (52,000) | 22,522.52 | 17,855.69 | 15,720.61 | 11,527.79 |
NPV = (22522.52+17855.69+15720.61+11527.79)-52000
= 67626.62-52000
= 15626.62
c-2. If you apply the NPV criterion, which investment will you choose?
Project A as it has Higher NPV
d-1. What is the IRR for each project?
Project A
IRR is the rate at which NPV=0. ie: PV of inflows = PV of outflows. It is calculated by trial and error method.
Lets find NPV at say 18%.
| Year | 0 | 1 | 2 | 3 | 4 |
| Cashflow(in $) | (364,000) | 46,000 | 68,000 | 68,000 | 458,000 |
| PVF @18% | 1 | 0.847 | 0.718 | 0.609 | 0.516 |
| Discounted Cashflow (Cash flow * PVF) | (364,000.00) | 38,983.05 | 48,836.54 | 41,386.90 | 236,231.30 |
NPV1 = (38983.05+48836.54+41386.90+236231.30) - 364000
= 365437.80-364000
= 1437.80
Since NPV is positive, Take a higher rate say 19%
| Year | 0 | 1 | 2 | 3 | 4 |
| Cashflow(in $) | (364,000) | 46,000 | 68,000 | 68,000 | 458,000 |
| PVF @19% | 1 | 0.840 | 0.706 | 0.593 | 0.499 |
| Discounted Cashflow (Cash flow * PVF) | (364,000.00) | 38,655.46 | 48,019.21 | 40,352.28 | 228,390.29 |
NPV2 = (38655.46+48019.21+40352.28+228390.29)-364000
= 355417.23-364000
= -8582.77
IRR = R1 + ((NPV1 * (R2 - R1)) / (NPV1 - NPV2))
= 18+((1437.80*(19-18)) / (1437.80+8582.77)
= 18+(1437.80/10020.57)
= 18+0.14348485166v
= 18.14%
Project B
Lets find NPV at say 25%
| Year | 0 | 1 | 2 | 3 | 4 |
| Cashflow(in $) | (52,000) | 25,000 | 22,000 | 21,500 | 17,500 |
| PVF @25% | 1 | 0.800 | 0.640 | 0.512 | 0.410 |
| Discounted Cashflow (Cash flow * PVF) | (52,000.00) | 20,000.00 | 14,080.00 | 11,008.00 | 7,168.00 |
NPV = (20000+14080+11008+7168)-52000
= 52256-52000
= 256
Since NPV is positive, Take a higher rate say 26%
| Year | 0 | 1 | 2 | 3 | 4 |
| Cashflow(in $) | (52,000) | 25,000 | 22,000 | 21,500 | 17,500 |
| PVF @26% | 1 | 0.794 | 0.630 | 0.500 | 0.397 |
| Discounted Cashflow (Cash flow * PVF) | (52,000.00) | 19,841.27 | 13,857.39 | 10,747.98 | 6,943.14 |
NPV = (19841.27+13857.39+10747.98+6943.14)-52000
= 51389.79-52000
= -610.22
IRR = R1 + ((NPV1 * (R2 - R1)) / (NPV1 - NPV2))
= 25 + ((256*(26-25)) / (256+610.22))
= 25 + (256/866.22)
= 25+0.29553693057
= 25.30%
d-2. If you apply the IRR criterion, which investment will you choose?
A project is acceptable when IRR is greater than required rate of return. Project B as this has higher IRR.
e-1. What is the profitability index for each project?
Project A
Profitability index = PV of future Cash Flows / Initial Investment
= 448051.57/364000
= 1.231
Project B
Profitability index = PV of future Cash Flows / Initial Investment
= 67626.62/52000
= 1.301
e-2. If you apply the profitability index criterion, which investment will you choose?
Project B as it has Higher Profitability index.
f. Based on your answers in (a) through (e), which project will you finally choose?
Project A as it has higher NPV as NPV supercedes all other evaluation technique.
