Exercise 26.10: Replacing Existing Equipment

Exhibit 26-3 Present Value of $1 Payable in n Periods

Number Present Value of $1 Due in n Periods * of Periods ( n ) Discount Rate |

1% 1½% 5% 6% 8% 10% 12% 15% 20% |

1 .990 .985 .952 .943 .926 .909 .893 .870 .833 |

2 .980 .971 .907 .890 .857 .826 .797 .756 .694 |

3 .971 .956 .864 .840 .794 .751 .712 .658 .579 |

4 .961 .942 .823 .792 .735 .683 .636 .572 .482 |

5 .951 .928 .784 .747 .681 .621 .567 .497 .402 |

6 .942 .915 .746 .705 .630 .564 .507 .432 .335 |

7 .933 .901 .711 .665 .583 .513 .452 .376 .279 |

8 .923 .888 .677 .627 .540 .467 .404 .327 .233 |

9 .914 .875 .645 .592 .500 .424 .361 .284 .194 |

10 .905 .862 .614 .558 .463 .386 .322 .247 .162 |

20 .820 .742 .377 .312 .215 .149 .104 .061 .026 |

24 .788 .700 .310 .247 .158 .102 .066 .035 .013 |

36 .699 .585 .173 .123 .063 .032 .017 .007 .001 |

*The present value of $1 is computed by the formula p 5 1 / (1 + 1 i )
n , where p is the present value of $1, i is the discount rate, and n
is the number of periods until the future cash flow will occur. Amounts
in this table have been rounded to three decimal places and are shown
for a limited number of periods and discount rates. Many calculators are
programmed to use this formula and can compute present values when the
future amount is enter

ed along with values for i and n.

EXHIBIT 26–4 Present Value of a $1 Annuity Receivable Each Period for n Periods

Number Present Value of $1 to Be Received Periodically for n Periods of Periods (n) Discount Rate |

1% 1½% 5% 6% 8% 10% 12% 15% 20% |

1 0.990 0.985 0.952 0.943 0.926 0.909 0.893 0.870 0.833 |

2 1.970 1.956 1.859 1.833 1.783 1.736 1.690 1.626 1.528 |

3 2.941 2.912 2.723 2.673 2.577 2.487 2.402 2.283 2.106 |

4 3.902 3.854 3.546 3.465 3.312 3.170 3.037 2.855 2.589 |

5 4.853 4.783 4.329 4.212 3.993 3.791 3.605 3.352 2.991 |

6 5.795 5.697 5.076 4.917 4.623 4.355 4.111 3.784 3.326 |

7 6.728 6.598 5.786 5.582 5.206 4.868 4.564 4.160 3.605 |

8 7.652 7.486 6.463 6.210 5.747 5.335 4.968 4.487 3.837 |

9 8.566 8.361 7.108 6.802 6.247 5.759 5.328 4.772 4.031 |

10 9.471 9.222 7.722 7.360 6.710 6.145 5.650 5.019 4.192 |

20 18.046 17.169 12.462 11.470 9.818 8.514 7.469 6.259 4.870 |

24 21.243 20.030 13.799 12.550 10.529 8.985 7.784 6.434 4.937 |

36 30.108 27.661 16.547 14.621 11.717 9.677 8.192 6.623 4.993 |

EnterTech has noticed a significant decrease in the profitability of its line of portable CD players. The production manager believes that the source of the trouble is old, inefficient equipment used to manufacture the product. The issue raised, therefore, is whether EnterTech should (1) buy new equipment at a cost of $120,000 or (2) continue using its present equipment. It is unlikely that demand for these portable CD players will extend beyond a five-year time horizon. EnterTech estimates that both the new equipment and the present equipment will have a remaining useful life of five years and no salvage value. The new equipment is expected to produce annual cash savings in manufacturing costs of $34,000, before taking into consideration depreciation and taxes. However, management does not believe that the use of new equipment will have any effect on sales volume. Thus, its decision rests on the magnitude of the potential cost savings. The old equipment has a book value of $100,000. However, it can be sold for only $20,000 if it is replaced. EnterTech has an average tax rate of 40 percent and uses straight-line depreciation for tax purposes. The company requires a minimum return of 12 percent on all investments in plant assets.

a. Compute the net present value of the new machine using the tables in Exhibits 26–3 and 26–4.

b. What nonfinancial factors should EnterTech consider?

c. If the manager of EnterTech is uncertain about the accuracy of the cost savings estimate, what actions could be taken to double-check the estimate?