Question

A firm is considering an investment in a new machine with a price of $17.2 million to replace its existing machine. The current machine has a book value of $6.8 million and a market value of $5.5 million. The new machine is expected to have a 4-year life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save $7.0 million in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine, it will also need an investment of $390,000 in net working capital. The required return on the investment is 10 percent and the tax rate is 24 percent. The company uses straight-line depreciation. What is the NPV of the decision to purchase a new machine? (Do not round intermediate calculations and enter your answer in dollars, not millions, rounded to 2 decimal places, e.g., 1,234,567.89.) What is the IRR of the decision to purchase a new machine? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) What is the NPV of the decision to purchase the old machine? (A negative amount should be indicated by a minus sign. Do not round intermediate calculations and enter your answer in dollars, not millions, rounded to 2 decimal places, e.g., 1,234,567.89.) What is the IRR of the decision to purchase the old machine? (A negative amount should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. )

Answer 1

Calculation of Net Present value of new machinery

Calculation of Present value of cash inflows of new machinery-

Year	Saving in operating costs	Depreciation	Cash flow before tax	Tax @24%	Cash flow after tax	Add back depreciation	Sale value of Old Machinary	Net cash inflows	PV factor @10%	PV of net cash flow
1	7000000	4300000	2700000	648000	2052000	4300000	5500000	11852000	0.909090909	10774545.45
2	7000000	4300000	2700000	648000	2052000	4300000	0	6352000	0.826446281	5249586.78
3	7000000	4300000	2700000	648000	2052000	4300000	0	6352000	0.751314801	4772351.62
4	7000000	4300000	2700000	648000	2052000	4300000	0	6352000	0.683013455	4338501.47
Total Present value of net cash flow										25134985.32

Calculation of Present value of cash outflows of new machinery-

= Purchase cost of Machinery + Working capital introduced

= 17200000 + 390000

= $17590000

Net present value (NPV) = PV of cash inflows - PV of cash outflows

= 25134985.32 - 17590000

= $7544985.31

Calculation of IRR of New machinery

Formula of IRR = In excel type =IRR(values)

Values should be combination of negative and positive values.

Year	0	1	2	3	4
Cash Flows	-17590000	11852000.00	6352000.00	6352000.00	6352000.00

On the above apply the formula and the IRR will be 32%

Calculation of Net Present value of old machinery

Calculation of Present value of cash inflows of old machinery-

Year	Saving in investment in new machine	Saving in Working capital	Tax saving on Depreciation	Tax saving on operating cost	Net cash inflows	PV factor @10%	PV of net cash flow
1	11700000	4300000	408000	1680000	18088000	0.909090909	16443636.36
2	0	0	408000	1680000	2088000	0.826446281	1725619.83
3	0	0	408000	1680000	2088000	0.751314801	1568745.30
4	0	0	408000	1680000	2088000	0.683013455	1426132.09
Total Present value of net cash inflows							21164133.6

Calculation of Present value of cash outflows of old machinery-

Year	Operating costs	PV factor @10%	PV of operating cost
1	7000000	0.909090909	6363636.36
2	7000000	0.826446281	5785123.97
3	7000000	0.751314801	5259203.61
4	7000000	0.683013455	4781094.19
Total Present value of operating cost			22189058.12

Net present value (NPV) = PV of cash inflows - PV of cash outflows

= 21164133.6 - 22189058.12

= $-1024924.53

Calculation of IRR of old machinery

Formula of IRR = In excel type =IRR(values)

Values should be combination of negative and positive values.

Year	1	2	3	4
Cash Outflows	-7000000	-7000000	-7000000	-7000000
Cash Inflows	18088000	2088000	2088000	2088000

On the above apply the formula and the IRR will be 5%