Question

Your company is deciding whether to invest in a new machine. The new machine will increase cash flow by $325,000 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 $1,750,000. The cost of the machine will decline by $105,000 per year until it reaches $1,225,000, where it will remain.

If your required return is 13 percent, calculate the NPV if you purchase the machine today. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

NPV          $  

If your required return is 13 percent, calculate the NPV if you wait to purchase the machine until the indicated year. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

	NPV
Year 1	$
Year 2	$
Year 3	$
Year 4	$
Year 5	$
Year 6	$

Answer 1

Computation of NPV if we purchase the machine today:

Year	Cash flows ($)	Discounting factor@13%	Discounted cash flows
1	325000	0.8850	287610.6195
2	325000	0.7831	254522.6721
3	325000	0.6931	225241.3027
4	325000	0.6133	199328.5865
5	325000	0.5428	176396.9792
6	325000	0.4803	156103.5214
7	325000	0.425060644	138144.7092
8	325000	0.376159862	122251.9551
9	325000	0.332884833	108187.5708
10	325000	0.294588348	95741.2131

NPV if we purchase the machine today = investment + discounted cash flows from years 1 to 10

                                                                = (-$1750000) + $ 1763529.1297

                                                                 = $ 13529.1297

If we wait to purchase the machine, until to any indicated year, the NPV is as follows @ 13% return:

If we wait for 1 year, then NPV = investment + discounted cash flows from years 2 to 10 = (-$1750000)-$1475918.5102 = $ (-274081.4898)

Year	Cash flows ($)	Discounting factor@13%	Discounted cash flows
2	325000	0.7831	254522.6721
3	325000	0.6931	225241.3027
4	325000	0.6133	199328.5865
5	325000	0.5428	176396.9792
6	325000	0.4803	156103.5214
7	325000	0.425061	138144.7092
8	325000	0.37616	122251.9551
9	325000	0.332885	108187.5708
10	325000	0.294588	95741.2131
		Total	1475918.5102

If we wait for 2 years, then NPV = NPV = investment + discounted cash flows from years 3 to 10 = (- $ 1750000) - $1221395.8381 = $ -528604.1619

Year	Cash flows ($)	Discounting factor@13%	Discounted cash flows
3	325000	0.6931	225241.3027
4	325000	0.6133	199328.5865
5	325000	0.5428	176396.9792
6	325000	0.4803	156103.5214
7	325000	0.425061	138144.7092
8	325000	0.37616	122251.9551
9	325000	0.332885	108187.5708
10	325000	0.294588	95741.2131
		Total	1221395.8381

If we wait for 3 years, then NPV = investment + discounted cash flows from years 4 to 10 = (-$1750000)- $ 996154.5354 = $ -753845.4646

Year	Cash flows ($)	Discounting factor@13%	Discounted cash flows
4	325000	0.6133	199328.5865
5	325000	0.5428	176396.9792
6	325000	0.4803	156103.5214
7	325000	0.425061	138144.7092
8	325000	0.37616	122251.9551
9	325000	0.332885	108187.5708
10	325000	0.294588	95741.2131
		Total	996154.5354

If we wait until 4 years, then NPV = investment + discounted cash flows from years 5 to 10 = (-$1750000)- $ 796825.9489 = $ -953174.0511

Year	Cash flows ($)	Discounting factor@13%	Discounted cash flows
5	325000	0.5428	176396.9792
6	325000	0.4803	156103.5214
7	325000	0.425061	138144.7092
8	325000	0.37616	122251.9551
9	325000	0.332885	108187.5708
10	325000	0.294588	95741.2131
		Total	796825.9489

If we wait until 5 years, NPV = investment + discounted cash flows from years 6 to 10 = (-$1750000)- $ 620428.9697 = $ -1129571.0303

Year	Cash flows ($)	Discounting factor@13%	Discounted cash flows
6	325000	0.4803	156103.5214
7	325000	0.425061	138144.7092
8	325000	0.37616	122251.9551
9	325000	0.332885	108187.5708
10	325000	0.294588	95741.2131
		Total	620428.9697

If we wait until 6 years, NPV = investment + discounted cash flows from years 7 to 10 = (-$1750000)-$ 464325.4483 = $ -1285674.5517

Year	Cash flows ($)	Discounting factor@13%	Discounted cash flows
7	325000	0.425061	138144.7092
8	325000	0.37616	122251.9551
9	325000	0.332885	108187.5708
10	325000	0.294588	95741.2131
		Total	464325.4483