Question

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 |

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.** Compute the net present value, using a rate
of return of 10%. Use the table of present value of an annuity of
$1 presented above. If required, round to the nearest dollar. Use
the minus sign to indicate a negative net present value.

Present value of annual net cash flows | $ |

Less amount to be invested | $ |

Net present value | $ |

**b.** Based on the analysis prepared in part (a),
is the rate of return (1) more than 10%, (2) 10%, or (3) less than
10%?

**c.** Determine the internal rate of return by
computing a present value factor for an annuity of $1 and using the
table of the present value of an annuity of $1 presented
above.

%

Answer #1

Solution:

**a)Calculation of Net Present Value :**

Net Present Value = Present Value of Net Cash Inflow - Intial Amount to be Invested

Here,

Present Value of Cash Inflow = Net Cash Flows * Compound PV factor of $1 Annuity @ 10 % for 10 Years

= $ 31,000 * 6.145

= $ 190,495

Therefore,

Net Present Value = $190,495 - $ 228,160

**Net Present Value = ( $37,665)**

**b)**

Based on analysis calculated above Net present Value is Negative
at 10 %. Therefore the rate of return of the project is
**less than 10%.**

**c)** **Calculation of Internal Rate of
Return**

Present Value Factor = Initial Investment / Annual Cash Inflow

= $ 228,160 / $31,000

= 7.360

As we can see in Annuity Table for $1 given in question, Compound PV Factor of $1 Annuity @ 6% for 10 Years is 7.360

**Therefore, Internal Rate of Return will be =
6%**

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...

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...

Keystone Healthcare Corp. is proposing to spend $150,570 on a
10-year project that has estimated net cash flows of $30,000 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
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...

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 $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...

Buckeye Healthcare Corp. is proposing to spend $120,640 on a
seven-year project that has estimated net cash flows of $29,000 for
each of the seven 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...

Buckeye Healthcare Corp. is proposing to spend $124,072 on a
nine-year project that has estimated net cash flows of $26,000 for
each of the nine 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...

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