Question

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 |

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.** Compute the net present value, using a rate
of return of 12%. Use the table of present value of an annuity of
$1 presented above. **If required, round your answers to the
nearest dollar.** If required, 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 internal rate of return (1) more than 12%, (2) 12%, or (3)
less than 12%?

**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:**

Computation of NPV | ||||

Particulars | Period | Amount | PV factor at 12% | Present Value |

Cash outflows: | ||||

Initial investment | 0 | $186,725.00 | 1 | $186,725 |

Present Value of Cash outflows (A) | $186,725 | |||

Cash Inflows | ||||

Annual cash inflows | 1-8 | $35,000.00 | 4.9680 | $173,880 |

Present Value of Cash Inflows (B) | $173,880 | |||

Net Present Value (NPV) (B-A) | -$12,845 |

**Solution b:**

As NPV is negative, therefore internal rate of return is less than 12%.

**Solution c:**

Present value factor at IRR = Initial investment / Annual cash inflows

= $186,725 / $35,000 = 5.335

Refer PV factor table at period 8, this factor falls at IRR = 10%

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