Your company is deciding whether to invest in a new machine. The new machine wil
ID: 2825410 • Letter: Y
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
$
NPV
Year 1
$
Year 2
$
Year 3
$
Year 4
$
Year 5
$
Year 6
$
Explanation / Answer
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 ($)
Discounting factor@13%
Discounted cash flows
7
325000
0.425061
138144.7092
8
325000
0.37616
122251.9551
9
325000
0.332885
108187.5708
10
325000
0.294588
95741.2131
Total
464325.4483
Year
Cash flows ($)
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
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