Question

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 | 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 | 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 expected internal rate of
return of this project for six years, using the present value of an
annuity of $1 table above.

%

**b.** Identify the uncertainties that could reduce
the internal rate of return of this project?

All of these

Answer #1

1) | IRR = 12% | ||||||||

IRR: IRR stands for Internal rate of return, it is a rate where Net present value is zero. | |||||||||

Steps: To Calculate IRR, we took two random discount rate where at one present value is in negative while in other in positive. Here we took 20% and 28%. | |||||||||

Year |
Cash
Flows |
PVF |
PVF |
Present Value
at |
Present Value
at |
||||

10% |
15% |
10% |
15% |
||||||

0 | (620,761) | 1.00000 | 1.000 | (620,761) | (620,761) | ||||

1 | 151,000 | 0.90909 | 0.86957 | 137,273 | 131,304 | ||||

2 | 151,000 | 0.82645 | 0.75614 | 124,793 | 114,178 | ||||

3 | 151,000 | 0.75131 | 0.65752 | 113,449 | 99,285 | ||||

4 | 151,000 | 0.68301 | 0.57175 | 103,135 | 86,335 | ||||

5 | 151,000 | 0.62092 | 0.49718 | 93,759 | 75,074 | ||||

6 | 151,000 | 0.56447 | 0.43233 | 85,236 | 65,281 | ||||

Net Present
Value |
36,883 |
(49,304) |
|||||||

IRR = Lower Discount Rate + [Lower Rate NPV / (Lower Rate NPV - Higher Rate NPV)] * (Higher Discount Rate - Lower Discount Rate) | |||||||||

By putting above values in the give formula we get IRR = 12% | |||||||||

2) | Following are the uncertainicities | ||||||||

a) Fluctuation is cash flow | |||||||||

b) Change in market rate of interest during the project | |||||||||

c) Fluctuations in amount of initial investment | |||||||||

The Riverton Company, a ski resort, recently announced a
$872,590 expansion to lodging properties, lifts, and terrain.
Assume that this investment is estimated to produce $142,000 in
equal annual cash flows for each of the first 10 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...

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...

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...

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...

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...

Average Rate of Return, Cash Payback Period, Net Present Value
Method for a Service Company
Spanish Peaks Railroad Inc. is considering acquiring equipment
at a cost of $1,250,000. The equipment has an estimated life of
eight years and no residual value. It is expected to provide yearly
net cash flows of $312,500. The company’s minimum desired rate of
return for net present value analysis is 12%.
Present Value of an Annuity of $1 at
Compound Interest
Year
6%
10%
12%...

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...

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