Question

X Company is unhappy with a machine that they bought just a year ago for $41,000. It is considering replacing it with a new machine that will save significant operating costs. Operating costs with the current machine are $69,000 per year; operating costs with the new machine are expected to be $45,000 per year. Both machines will last for 4 more years.The current machine can be sold immediately for $5,000 but will have no salvage value at the end of 4 years. The new machine will cost $68,000 and have a salvage value of $3,000 in 4 years.

Assuming a discount rate of 8%, what is the net present value of replacing the current machine?

Answer 1

Note :

Operating costs with the current machine = $69,000 per year

Operating costs with the  new machine = $45,000 per year

• Saving in operating costs due to replacement = $69,000 -  $45,000 = $24,000
• Intial outlay = Cost of new machine - Sales of current machine = $68,000 - $5,000 = $63,000

Answer :

Present value of intial outlay = $63,000 * 1 = $63,000

Present value of saving in operating costs =  $24,000 * PVIFA_{(8%, 4 years)} =  $24,000 * 3.31213 = $79,491

Present value of salvage value of new machine =  $3,000 * PVIF_{(8%, 4 years)} = $3,000 * 0.732503 = $2,205

Net present value of replacing the current machine :

Present value of saving in operating costs + Present value of salvage value of new machine - Present value of intial outlay

= $79,491 +$2,205 - $63,000 = $18,696