# Present Value and final decisions

Bottom Up Diaper Service is considering the purchase of a new industrial washer. It can purchase a high-efficiency washer for \$12 000 or an ordinary washer for \$9 000. The installation and delivery charge is \$480. The high-efficiency washer lasts for 8 years while the ordinary washer lasts only 6 years. The operating cost totals to \$1500/year for the high-efficiency washer and \$1600/year for the ordinary washer. Both washers will be depreciated using straight-line method. Neither will have salvage value at the end of life. The firm's tax rate is 40%

a) Assume that the cost of capital for the firm is 12%, what is the present value of the total costs (including capital outlay and operating costs) for the high-efficiency washer and ordinary waster, respectively?

b) Assume that the washers would have to replaced once they are junked at the end of their life, which washer should the firm purchase? Why?

 Curlyben Posts: 18,726, Reputation: 8983 Admin & Wine Expert #2 Feb 10, 2010, 04:20 AM
Thank you for taking the time to copy your homework to AMHD.
 shadow429 Posts: 2, Reputation: 1 New Member #3 Feb 10, 2010, 09:19 AM

I don't know the answer I spent like an hour on it alone, trying to figure out exactly how to find the answer... I'm so confused and I've tried so many different ways of doing it that I have no idea where to go from anymore...
 ArcSine Posts: 961, Reputation: 523 Senior Member #4 Feb 10, 2010, 11:04 AM
Picking the best machine involves your calculation of what's called "equivalent annual cost".

First determine the after-tax cash flows for both machines. All the info for this calc is there, with the SL depreciation assumption, and the given tax rate.

Next, calculate the NPV for each machine, by discounting the after-tax cash flows at the given cost of capital.

Finally, determine the annuity amount which has the same NPV as each machine, where the annuity's life is the same as that of the machine. For example, for the high-efficiency machine, what annual, level payment (annuity), with 8 payments, has the same NPV as the machine? Similarly, what 6-year annuity, one payment per year, has the same NPV as the ordinary washer?

The annuity that you calculate--one for each machine--represents each machine's "equivalent annual cost". Then you just go with the one that has the lower EAC.

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