question archive Using the following initial cost and cash flow figures below for Projects 1 and 2, please answer the three questions (a, b, and c)
Using the following initial cost and cash flow figures below for Projects 1 and 2, please answer the three questions (a, b, and c)
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Using the following initial cost and cash flow figures below for Projects 1 and 2, please answer the three questions (a, b, and c).
Expected Net Cash Flows
Year Project 1 Project 2
0 -$1,000,000 -$1,000,000
1 520,000 150,000
2 300,000 425,000
3 280,000 800,000
Both of the projects have a cost of capital (r) of 11.5 percent (so r = 0.115 in decimal form).
a) What is Project 1's net present value (NPV)? Based on your answer for the NPV, should this project be accepted or rejected? Briefly explain.
b) Rounding your answer to the second decimal place, what is Project 2's internal rate of return (IRR)? Based on your answer for the IRR, should this project be accepted or rejected? Briefly explain.
c) Finally, what is the payback period (in years) for Project 2?
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a) What is Project 1's net present value (NPV)? Based on your answer for the NPV, should this project be accepted or rejected? Briefly explain.
NPV of Project-1 = $ (90,332.74)
NPV of Project-2 = $ 53,501.01
Hence
As per above calculation we should accept the Project-2, since NPV of this project is positive.
b) Rounding your answer to the second decimal place, what is Project 2's internal rate of return (IRR)? Based on your answer for the IRR, should this project be accepted or rejected? Briefly explain.
Therefore
IRR = 0.1397 OR 13.97%
Since the IRR(i.e.13.97%) is greater than Cost of capital (i.e.11.5%) we should accept the Project-2
c) Finally, what is the payback period (in years) for Project 2?
Payback Period = 2.53 Years
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Step-by-step explanation
a) What is Project 1's net present value (NPV)? Based on your answer for the NPV, should this project be accepted or rejected? Briefly explain.
Cost of capital = 11.5%
Calculation of Net Present Value of Projects
| Year | Cash Flows | PVF(11.5%,Year) | Present Values | ||
| Project -1 | Project-2 | Project -1 | Project-2 | ||
| 0 | $ (1,000,000.00) | $ (1,000,000.00) | 1.000 | $ (1,000,000.00) | $ (1,000,000.00) |
| 1 | $ 520,000.00 | $ 150,000.00 | 0.897 | $ 466,367.71 | $ 134,529.15 |
| 2 | $ 300,000.00 | $ 425,000.00 | 0.804 | $ 241,307.89 | $ 341,852.84 |
| 3 | $ 280,000.00 | $ 800,000.00 | 0.721 | $ 201,991.66 | $ 577,119.02 |
| Net Present Value | $ (90,332.74) | $ 53,501.01 | |||
Therefore
NPV of Project-1 = $ (90,332.74)
NPV of Project-2 = $ 53,501.01
Hence
As per above calculation we should accept the Project-2, since NPV of this project is positive.
b) Rounding your answer to the second decimal place, what is Project 2's internal rate of return (IRR)? Based on your answer for the IRR, should this project be accepted or rejected? Briefly explain.
As per formula
IRR = Lower Rate + [NPV at Lower Rate/(NPV at Lower Rate-NPV at Higher Rate)]*(Higher Rate - Lower Rate)
Where
Lower Rate = 12% (Assumed)
Higher Rate = 15% (Assumed)
Note- We can assume any rate as lower rate and higher rate but i suggest you always try to select two rates which have difference not more than 3-5% and higher rate give us negative NPV and Lower rate give us positive NPV.
NPV of Project-2 at above rates
| Year | Project -1 | PVF(15%,Year) | Present Value | PVF(12%,Year) | Present Value |
| 0 | $ (1,000,000.00) | 1.000 | $ (1,000,000.00) | 1.000 | $ (1,000,000.00) |
| 1 | $ 150,000.00 | 0.870 | $ 130,434.78 | 0.893 | $ 133,928.57 |
| 2 | $ 425,000.00 | 0.756 | $ 321,361.06 | 0.797 | $ 338,807.40 |
| 3 | $ 800,000.00 | 0.658 | $ 526,012.99 | 0.712 | $ 569,424.20 |
| Net Present Value | $ (22,191.17) | $ 42,160.17 | |||
Therefore
IRR = Lower Rate + [NPV at Lower Rate/(NPV at Lower Rate-NPV at Higher Rate)]*(Higher Rate - Lower Rate)
= 0.12 + [42,160.17/(42,160.17+22,191.17)]*(0.15 - 0.12)
= 0.12 + (0.6515*0.03)
= 0.12 + 0.0197
= 0.1397
Therefore
IRR = 0.1397 OR 13.97%
Since the IRR(i.e.13.97%) is greater than Cost of capital (i.e.11.5%) we should accept the Project-2
c) Finally, what is the payback period (in years) for Project 2?
Calculation of Payback period
| Year | Project -2 | Accumulated Cash Flow |
| 0 | $ (1,000,000.00) | $ (1,000,000.00) |
| 1 | $ 150,000.00 | $ (850,000.00) |
| 2 | $ 425,000.00 | $ (425,000.00) |
| 3 | $ 800,000.00 | $ 375,000.00 |
Payback Period = (T-1) + 1(CFr - CF)
Where
T = Year in which Accumulated Cash Flow is positive i.e. 3
CFr = ash Flow required in 3rd Year where Accumulated Balance become 0 i.e. $425,000.00
CF = Total Cash flow in 3rd year i.e. $800,000
Therefore
Payback Period = (T-1) + 1(CFr - CF)
= (3-1) + 1(425,000 - 800,000.00)
= 2 + 0.53
= 2.53 Years
Payback Period = 2.53 Years
