Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $650,000;the new one will cost $780,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $140,000 after five years. The old computer is beingdepreciated at a rate of $130,000 per year. It will be completely written off in three years. If we don'treplace it now, we will have to replace it in two years. We can sell it now for $230,000; in two years itwill probably be worth $90,000. The new machine will save us $125,000 per year in operating costs. The tax rate is 38 percent, and the discount rate is 14 percent.

Suppose we consider only whether we should replace the old computer now with­ out worrying aboutwhat's going to happen in two years. Calculate the NPV of the project.

{ Hint: In 2 years time you sell the old machine,s o you need to calculate the cashflows for it:

Aftertax salvage value = $90,000 + ($130,000 – 90,000)(.38) = $105,200}

Answer 1

The Details of the old machine being replaced

Old Cost	650000
Book Value	390000 (It has 3 years left)
Sale Value	230000

After tax salavge value = 230,000 +(390,000 -230,000)*0.38 = 290,800

The NPV of this project is as shown below:

Year	0	1	2	3	4	5
Proceeds from Sale of old Machine	290800
Cost of New Machine	-780000
Savings		125000	125000	125000	125000	125000
Depriciation		-156000	-156000	-156000	-156000	-156000
Profit before taxes		-31000	-31000	-31000	-31000	-31000
Taxes		-11780	-11780	-11780	-11780	-11780
Profit after taxes		-19220	-19220	-19220	-19220	-19220
Add back depreication		156000	156000	156000	156000	156000
After tax salavge value						86800
Net Cash flows	-489200	136780	136780	136780	136780	223580
NPV at 14%	$ 25,458.01

So, the NPV of the project without worrying about what's going to happen it two years is $25,458.01