Question

The internal rate of return method is used by Testerman Construction Co. in analyzing a capital expenditure proposal that involves an investment of $69,264 and annual net cash flows of $13,000 for each of the nine years of its useful life.

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 a present value factor for an
annuity of $1 which can be used in determining the internal rate of
return. If required, round your answer to three decimal places.

**b.** Using the factor determined in part (a) and
the present value of an annuity of $1 table above, determine the
internal rate of return for the proposal.

Answer #1

- The annuity amount is that amount which when multiplied by annual cash inflow equals the amount of initial investment.
- Internal Rate of Return is that of return rate that will lead to ‘zero’ Net Present Value when future cash inflows are discounted using this rate.
- Requirement ‘a’

à annuity figure of $1 calculation will be as follows:

$ 69,264 = $ 13,000 x $ 1 Annuity
factor for 9^{th} year

69,264 / 13,000 = $ 1 Annuity factor
for 9^{th} year

**$ 1 Annuity factor for 9 ^{th}
year = 5.328**

- Requirement ‘b’

$ 1 Annuity factor for 9^{th}
year calculated above = 5.328.

If you look closely as to where this
figure (5.328) is falling in the table of annuities provided in the
question, you’ll see that it falls under 12%, for 9^{th}
year.

**Hence, the Internal rate of Return =
12%**

Internal Rate of Return Method
The internal rate of return method is used by King Bros.
Construction Co. in analyzing a capital expenditure proposal that
involves an investment of $80,620 and annual net cash flows of
$20,000 for each of the nine years of its useful life.
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...

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...

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...

Net Present Value Method and Internal Rate of Return Method for
a service company
Keystone Healthcare Corp. is proposing to spend $228,160 on a
10-year project that has estimated net cash flows of $31,000 for
each of the 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...

Net Present Value Method and Internal Rate of Return Method for
a service company
Buckeye Healthcare Corp. is proposing to spend $79,611 on a
five-year project that has estimated net cash flows of $21,000 for
each of the five 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...

Net Present Value Method and Internal Rate of Return Method
Buckeye Healthcare Corp. is proposing to spend $93,150 on an
eight-year project that has estimated net cash flows of $15,000 for
each of the 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...

Internal Rate of Return Method for a Service Company
The Riverton Company, announced a $620,761 million expansion of
lodging properties, ski lifts, and terrain in Park City, Utah.
Assume that this investment is estimated to produce $151,000
million in equal annual cash flows for each of the first six years
of the project life.
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...

A project is estimated to cost $77,766 and provide annual net
cash flows of $26,000 for five 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
3.353
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...

The Riverton Company,
a ski resort, recently announced a $353,600 expansion to lodging
properties, lifts, and terrain. Assume that this investment is
estimated to produce $85,000 in equal annual cash flows for each of
the first seven years of the project life.
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...

Net Present Value Method and Internal Rate of Return Method for
a Service Company
Buckeye Healthcare Corp. is proposing to spend $186,725 on an
eight-year project that has estimated net cash flows of $35,000 for
each of the 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...

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