Question

Net Present Value—Unequal Lives

Project 1 requires an original investment of $50,300. The project will yield cash flows of $12,000 per year for five years. Project 2 has a calculated net present value of $14,600 over a three-year life. Project 1 could be sold at the end of three years for a price of $49,000.

Use the **Present Value of $1 at Compound
Interest** and the **Present Value of an Annuity of $1
at Compound Interest** tables shown below.

Present Value of $1 at Compound
Interest |
|||||

Year |
6% |
10% |
12% |
15% |
20% |

1 | 0.943 | 0.909 | 0.893 | 0.870 | 0.833 |

2 | 0.890 | 0.826 | 0.797 | 0.756 | 0.694 |

3 | 0.840 | 0.751 | 0.712 | 0.658 | 0.579 |

4 | 0.792 | 0.683 | 0.636 | 0.572 | 0.482 |

5 | 0.747 | 0.621 | 0.567 | 0.497 | 0.402 |

6 | 0.705 | 0.564 | 0.507 | 0.432 | 0.335 |

7 | 0.665 | 0.513 | 0.452 | 0.376 | 0.279 |

8 | 0.627 | 0.467 | 0.404 | 0.327 | 0.233 |

9 | 0.592 | 0.424 | 0.361 | 0.284 | 0.194 |

10 | 0.558 | 0.386 | 0.322 | 0.247 | 0.162 |

Present Value of an Annuity of $1 at
Compound Interest |
|||||

Year |
6% |
10% |
12% |
15% |
20% |

1 | 0.943 | 0.909 | 0.893 | 0.870 | 0.833 |

2 | 1.833 | 1.736 | 1.690 | 1.626 | 1.528 |

3 | 2.673 | 2.487 | 2.402 | 2.283 | 2.106 |

4 | 3.465 | 3.170 | 3.037 | 2.855 | 2.589 |

5 | 4.212 | 3.791 | 3.605 | 3.352 | 2.991 |

6 | 4.917 | 4.355 | 4.111 | 3.784 | 3.326 |

7 | 5.582 | 4.868 | 4.564 | 4.160 | 3.605 |

8 | 6.210 | 5.335 | 4.968 | 4.487 | 3.837 |

9 | 6.802 | 5.759 | 5.328 | 4.772 | 4.031 |

10 | 7.360 | 6.145 | 5.650 | 5.019 | 4.192 |

**a.** Determine the net present value of Project 1
over a three-year life with residual value, assuming a minimum rate
of return of 12%. If required, round to the nearest dollar.

$

**b.** Which project provides the greatest net
present value?

Project 2

Answer #1

**A. Determination of NPV**

**NPV=Present value of cash flows- Initial
Investment**

**Initial Investment=50300**

**Present Value of future cash flows= 12000 PVAF(12%,3yr)+
49000 PVIF(12%,3)**

**Present Value of future cash flows=
(12000*2.402)+(49000*0.712)**

**Present Value of future cash flows=
28824+34888**

**Present Value of future cash flows=63712**

**So, NPV of Project= 63712-50300**

**NPV of Project=13412**

**B. It is not clear which required rate of return is to
be used, so we are using 12%. Further it is clear that net present
value of project 1 will always be greater when it will be sold in
3year.**

**NPV of Project A= 13412**

**NPV of Project B= 14600**

**Conclusion- Project B has greater NPV.**

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Project 1 requires an original investment of $76,700. The
project will yield cash flows of $12,000 per year for seven years.
Project 2 has a calculated net present value of $16,500 over a
five-year life. Project 1 could be sold at the end of five years
for a price of $56,000.
Use the Present Value of $1 at Compound
Interest and the Present Value of an Annuity of $1
at Compound Interest tables shown below.
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Project 1 requires an original investment of $54,000. The
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Project 2 has a calculated net present value of $10,800 over a
six-year life. Project 1 could be sold at the end of six years for
a price of $41,000.
Use the Present Value of $1 at Compound
Interest and the Present Value of an Annuity of $1
at Compound Interest tables shown below.
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Project 1 requires an original investment of $71,000. The
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Project 2 has a calculated net present value of $20,500 over a
six-year life. Project 1 could be sold at the end of six years for
a price of $57,000.
Use the Present Value of $1 at Compound
Interest and the Present Value of an Annuity of $1
at Compound Interest tables shown below.
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Net Present Value—Unequal Lives
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Project 2 has a calculated net present value of $8,300 over a
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Use the Present Value of $1 at Compound
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at Compound Interest tables shown below.
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A project is estimated to cost $454,730 and provide annual net
cash flows of $74,000 for 10 years.
Present Value of an Annuity of $1 at
Compound Interest
Year
6%
10%
12%
15%
20%
1
0.943
0.909
0.893
0.870
0.833
2
1.833
1.736
1.690
1.626
1.528
3
2.673
2.487
2.402
2.283
2.106
4
3.465
3.170
3.037
2.855
2.589
5
4.212
3.791
3.605
3.352
2.991
6
4.917
4.355
4.111
3.784
3.326
7
5.582
4.868
4.564
4.160
3.605
8
6.210
5.335
4.968...

A project is estimated to cost $191,850 and provide annual net
cash flows of $50,000 for eight years.
Present Value of an Annuity of $1 at
Compound Interest
Year
6%
10%
12%
15%
20%
1
0.943
0.909
0.893
0.870
0.833
2
1.833
1.736
1.690
1.626
1.528
3
2.673
2.487
2.402
2.283
2.106
4
3.465
3.170
3.037
2.855
2.589
5
4.212
3.791
3.605
3.352
2.991
6
4.917
4.355
4.111
3.784
3.326
7
5.582
4.868
4.564
4.160
3.605
8
6.210
5.335
4.968...

Net Present Value A project has estimated annual net cash flows
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minimum acceptable rate of return of 12%. Use the Present Value of
an Annuity of $1 at Compound Interest table below. Present Value of
an Annuity of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1
0.943 0.909 0.893 0.870 0.833 2 1.833 1.736 1.690 1.626 1.528 3
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A project has estimated annual net cash flows of $11,250 for
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acceptable rate of return of 15%. Use the Present Value of
an Annuity of $1 at Compound Interest table below.
Present Value of an Annuity of $1 at
Compound Interest
Year
6%
10%
12%
15%
20%
1
0.943
0.909
0.893
0.870
0.833
2
1.833
1.736
1.690
1.626
1.528
3
2.673
2.487
2.402
2.283
2.106
4...

1.
Project 1 requires an original investment of $63,600. The
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Project 2 has a calculated net present value of $12,300 over a
three-year life. Project 1 could be sold at the end of three years
for a price of $53,000.
Use the Present Value of $1 at Compound
Interest and the Present Value of an Annuity of $1
at Compound Interest tables shown below.
Present Value of $1...

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Present Value of an Annuity of $1 at
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6%
10%
12%
15%
20%
1
0.943
0.909
0.893
0.870
0.833
2
1.833
1.736
1.690
1.626
1.528
3
2.673
2.487
2.402
2.283
2.106
4
3.465
3.170
3.037
2.855
2.589
5
4.212
3.791
3.605
3.353
2.991
6
4.917
4.355
4.111
3.785
3.326
7
5.582
4.868
4.564
4.160
3.605
8
6.210
5.335
4.968...

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