A new packaging machine will cost $57,000. The existing machine can be sold for $5,000 now and the new machine for $7,500 after its 10-year useful life. If the new machine reduces annual expenses by $5,000, what is the present worth at 25% of this investment?

Our answer is  $ 33,342

Explanation:

Initial investment = Cost of new machine - Salvage value of old machine = $ 57,000 - $ 5,000 = $ 52,000

Annual cost savings = $ 5,000

Present value of cash savings at a discount rate of 25% = Annuity x PVIFA 25%, 10 years + Salvage x PVIF 25%, 10th year= $ 5,000 x 3.5705 + $ 7,500 x 0.1074 = $ 17,852.5 + $ 805.5 = $ 18,658

Net present value = Present value of cash savings - Initial investment = $ 18,658 - $ 52,000 = $ ( 33,342 )