Question

our company is deciding whether to invest in a new machine. The new machine will increase cash flow by $330,000 per year. You believe the technology used in the machine has a 10-year life; in other words, no matter when you purchase the machine, it will be obsolete 10 years from today. The machine is currently priced at $1,700,000. The cost of the machine will decline by $102,000 per year until it reaches $1,190,000, where it will remain. If your required return is 14 percent, calculate the NPV today. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) If your required return is 14 percent, calculate the NPV for the following years. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16. A negative answer should be indicated by a minus sign.) Should you purchase the machine? Yes No If so, when should you purchase it? Today One year from now Two years from now

Answer 1

NPV = - Initial investment + C / R x [1 - (1 + R)^-N]

where C = annual cash flows = $ 330,000, R = discount rate = 14% and N = Remaining life of the machine.

The machine is currently priced at $1,700,000. The cost of the machine will decline by $102,000 per year until it reaches $1,190,000, where it will remain.

Please see the table below for NPV.

NPV has been calculated at the end of every period using the formula: NPV = - Initial investment + C / R x [1 - (1 + R)^-N]

= - Initial investment + 330,000 / 14% x [1 - (1 + 14%)^-N]

Time, t	Remaining Life, N = 10 - t	Initial Investment ($)	NPV ($)
0	10	1,700,000	21,318.16
1	9	1,598,000	34,302.71
2	8	1,496,000	34,825.08
3	7	1,394,000	21,140.60
4	6	1,292,000	- 8,739.72
5	5	1,190,000	- 57,083.28
6	4	1,190,000	- 228,474.94
7	3	1,190,000	- 423,861.43
8	2	1,190,000	- 646,602.03
9	1	1,190,000	- 900,526.32

Yes, I will purchase the machine.

I will purchase it when the NPV is maximum. It's maximum at t= 2. Hence, I will purchase it two years from now.