Question

Your company is deciding whether to invest in a new machine. The new machine will increase cash flow by $318,000 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 $1,710,000. The cost of the machine will decline by $105,000 per year until it reaches $1,185,000, where it will remain. If your required return is 13 percent, calculate the NPV 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.)

Answer 1

Calculation of net present value
Net present value	Present value of cash inflow - Present value of cash outflow
Calculation of net present value if machine is purchased today
Year	Cash flow	Discount factor @ 13%	Present value
0	-$1,710,000	1.00000	-$1,710,000
1	$318,000	0.88496	$281,415.93
2	$318,000	0.78315	$249,040.65
3	$318,000	0.69305	$220,389.95
4	$318,000	0.61332	$195,035.36
5	$318,000	0.54276	$172,597.66
6	$318,000	0.48032	$152,741.29
7	$318,000	0.42506	$135,169.28
8	$318,000	0.37616	$119,618.84
9	$318,000	0.33288	$105,857.38
10	$318,000	0.29459	$93,679.09
NPV			$15,545.43
Calculation of net present value if machine is purchased after one year
Year	Cash flow	Discount factor @ 13%	Present value
0	-$1,605,000	1.00000	-$1,605,000
1	$318,000	0.88496	$281,415.93
2	$318,000	0.78315	$249,040.65
3	$318,000	0.69305	$220,389.95
4	$318,000	0.61332	$195,035.36
5	$318,000	0.54276	$172,597.66
6	$318,000	0.48032	$152,741.29
7	$318,000	0.42506	$135,169.28
8	$318,000	0.37616	$119,618.84
9	$318,000	0.33288	$105,857.38
NPV at end of year 1			$26,866.33
Discount factor @ 13%			0.88496
NPV today			$23,775.51
Calculation of net present value if machine is purchased after 2 years
Year	Cash flow	Discount factor @ 13%	Present value
0	-$1,500,000	1.00000	-$1,500,000
1	$318,000	0.88496	$281,415.93
2	$318,000	0.78315	$249,040.65
3	$318,000	0.69305	$220,389.95
4	$318,000	0.61332	$195,035.36
5	$318,000	0.54276	$172,597.66
6	$318,000	0.48032	$152,741.29
7	$318,000	0.42506	$135,169.28
8	$318,000	0.37616	$119,618.84
NPV at end of year 2			$26,008.95
Discount factor @ 13%			$0.78315
NPV today			$20,368.83
Calculation of net present value if machine is purchased after 3 years
Year	Cash flow	Discount factor @ 13%	Present value
0	-$1,395,000	1.00000	-$1,395,000
1	$318,000	0.88496	$281,415.93
2	$318,000	0.78315	$249,040.65
3	$318,000	0.69305	$220,389.95
4	$318,000	0.61332	$195,035.36
5	$318,000	0.54276	$172,597.66
6	$318,000	0.48032	$152,741.29
7	$318,000	0.42506	$135,169.28
NPV at end of year 3			$11,390.12
Discount factor @ 13%			$0.69305
NPV today			$7,893.92
Calculation of net present value if machine is purchased after 4 years
Year	Cash flow	Discount factor @ 13%	Present value
0	-$1,290,000	1.00000	-$1,290,000
1	$318,000	0.88496	$281,415.93
2	$318,000	0.78315	$249,040.65
3	$318,000	0.69305	$220,389.95
4	$318,000	0.61332	$195,035.36
5	$318,000	0.54276	$172,597.66
6	$318,000	0.48032	$152,741.29
NPV at end of year 4			-$18,779.17
Discount factor @ 13%			$0.61332
NPV today			-$11,517.61
Calculation of net present value if machine is purchased after 5 years
Year	Cash flow	Discount factor @ 13%	Present value
0	-$1,185,000	1.00000	-$1,185,000
1	$318,000	0.88496	$281,415.93
2	$318,000	0.78315	$249,040.65
3	$318,000	0.69305	$220,389.95
4	$318,000	0.61332	$195,035.36
5	$318,000	0.54276	$172,597.66
NPV at end of year 5			-$66,520.46
Discount factor @ 13%			$0.5428
NPV today			-$36,104.64
Calculation of net present value if machine is purchased after 6 years
Year	Cash flow	Discount factor @ 13%	Present value
0	-$1,185,000	1.00000	-$1,185,000
1	$318,000	0.88496	$281,415.93
2	$318,000	0.78315	$249,040.65
3	$318,000	0.69305	$220,389.95
4	$318,000	0.61332	$195,035.36
NPV at end of year 6			-$239,118.12
Discount factor @ 13%			$0.4803	1/(1.13^6)
NPV today			-$114,852.86
Yes the machine should be purchased after one year as it provides highest NPV