Question

Your company is deciding whether to invest in a new machine. The new machine will increase cash flow by $316,000 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 $1,690,000. The cost of the machine will decline by $106,000 per year until it reaches $1,160,000, where it will remain.

If your required return is 13 percent, calculate the NPV if you purchase the machine today. What is the NPV if you wait to purchase the macine until each year indicated below?

Answer 1

NPV :
NPV means Net Present Value
NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.

PVF = 1/(1+r)^n

r - required rate of return = 13 %

n - no. of the period discounting

Part A

Year	CF	PVF @13 %	Disc CF
0	$   -1,690,000.00	1.0000	$   -1,690,000.00
1	$        316,000.00	0.8850	$        279,646.02
2	$        316,000.00	0.7831	$        247,474.35
3	$        316,000.00	0.6931	$        219,003.85
4	$        316,000.00	0.6133	$        193,808.72
5	$        316,000.00	0.5428	$        171,512.14
6	$        316,000.00	0.4803	$        151,780.65
7	$        316,000.00	0.4251	$        134,319.16
8	$        316,000.00	0.3762	$        118,866.52
9	$        316,000.00	0.3329	$        105,191.61
10	$        316,000.00	0.2946	$          93,089.92
	NPV		$          24,692.94

Part B : cost of the machine will decline by $106,000 per year until it reaches $1,160,000

Cash flows for machine if purchse after each year to reach machine value $1,160,000

	Purchase After	Year 1		Year 2		Year 3		Year 4		Year 5
Year	PVF @ 13 % (a)	CF (b)	Disc CF (a*b)	CF (c)	Disc CF (a*c)	CF (d)	Disc CF (a*d)	CF (e)	Disc CF (a*e)	CF (f)	Disc CF (a*f)
1	0.8850	$ -1,584,000.00	$ -1,401,769.91
2	0.7831	$ 316,000.00	$       247,474.35	$ -1,478,000.00	$ -1,157,490.80
3	0.6931	$ 316,000.00	$       219,003.85	$       316,000.00	$       219,003.85	$ -1,372,000.00	$ -950,864.82
4	0.6133	$ 316,000.00	$       193,808.72	$       316,000.00	$       193,808.72	$       316,000.00	$   193,808.72	$ -1,266,000.00	$ -776,461.51
5	0.5428	$ 316,000.00	$       171,512.14	$       316,000.00	$       171,512.14	$       316,000.00	$   171,512.14	$       316,000.00	$   171,512.14	$ -1,160,000.00	$ -629,601.53
6	0.4803	$ 316,000.00	$       151,780.65	$       316,000.00	$       151,780.65	$       316,000.00	$   151,780.65	$       316,000.00	$   151,780.65	$       316,000.00	$   151,780.65
7	0.4251	$ 316,000.00	$       134,319.16	$       316,000.00	$       134,319.16	$       316,000.00	$   134,319.16	$       316,000.00	$   134,319.16	$       316,000.00	$   134,319.16
8	0.3762	$316,000.00	$       118,866.52	$       316,000.00	$       118,866.52	$       316,000.00	$   118,866.52	$       316,000.00	$   118,866.52	$       316,000.00	$   118,866.52
9	0.3329	$ 316,000.00	$       105,191.61	$       316,000.00	$       105,191.61	$       316,000.00	$   105,191.61	$       316,000.00	$   105,191.61	$       316,000.00	$   105,191.61
10	0.2946	$316,000.00	$         93,089.92	$       316,000.00	$         93,089.92	$       316,000.00	$     93,089.92	$       316,000.00	$     93,089.92	$       316,000.00	$     93,089.92
		NPV	$         33,277.01	NPV	$         30,081.77	NPV	$     17,703.89	NPV	$      -1,701.51	NPV	$    -26,353.67

please comment if any further explanation is required.