Question

Replacement Analysis

Although the Chen Company's milling machine is old, it is still in relatively good working order and would last for another 10 years. It is inefficient compared to modern standards, though, and so the company is considering replacing it. The new milling machine, at a cost of $40,000 delivered and installed, would also last for 10 years and would produce after-tax cash flows (labor savings and depreciation tax savings) of $8,300 per year. It would have zero salvage value at the end of its life. The Project cost of capital is 10%, and its marginal tax rate is 35%.
Should Chen buy the new machine?

Yes? No?

Answer 1

The Net Present Value (NPV) of the Project

Year	Annual Cash flow ($)	Present Value factor at 10.00%	Present Value of Annual Cash flow ($)
1	8,300	0.909091	7,545.45
2	8,300	0.826446	6,859.50
3	8,300	0.751315	6,235.91
4	8,300	0.683013	5,669.01
5	8,300	0.620921	5,153.65
6	8,300	0.564474	4,685.13
7	8,300	0.513158	4,259.21
8	8,300	0.466507	3,872.01
9	8,300	0.424098	3,520.01
10	8,300	0.385543	3,200.01
TOTAL			50,999.91

Net Present Value (NPV) = Present value of annual cash inflows – Initial investment costs

= $50,999.91 - $40,000

= $10,999.91

DECISION

“YES”. Chen should buy the new machine, since the Net Present Value (NPV) of the Project is Positive $10,999.91.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.