Question

A firm is considering an investment in a new machine with a price of $16.7 million to replace its existing machine. The current machine has a book value of $6.4 million and a market value of $5.1 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 $6.8 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 $350,000 in net working capital. The required return on the investment is 10 percent and the tax rate is 25 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

NPV & IRR calculations for the new machine:

Formula	Year (n)	0	1	2	3	4
Price of new machine	Initial investment (II)	16,700,000
	Cost savings (Cs)		6,800,000	6,800,000	6,800,000	6,800,000
II/4	Depreciation (D)		4,175,000	4,175,000	4,175,000	4,175,000
Cs - D	Taxable income (Ti)		2,625,000	2,625,000	2,625,000	2,625,000
Ti*(1-Tax rate)	After-tax income (NI)		1,968,750	1,968,750	1,968,750	1,968,750
	Add: depreciation (D)		4,175,000	4,175,000	4,175,000	4,175,000
NI + D	Operating Cash Flow (OCF)		6,143,750	6,143,750	6,143,750	6,143,750
Recovery of NWC in Year 4	NWC investment	(350,000)				3,50,000
OCF + NWC-IO	Free Cash Flow (FCF)	(17,050,000)	6,143,750	6,143,750	6,143,750	6,493,750
1/(1+d)^n	Discount factor @ 10%	1.000	0.909	0.826	0.751	0.683
FCF*Discount factor	PV of FCF	(17,050,000)	5,585,227.27	5,077,479.34	4,615,890.31	4,435,318.63
Sum of all PVs	NPV	2,663,915.55
Using IRR function with FCFs	IRR	16.97%

NPV & IRR calculations for the old machine:

Formula	Year (n)	0	1	2	3	4
	Book value of the machine (BV)	6,400,000
	Market value of the machine (MV)	5,100,000
MV - (MV-BV)*Tax rate	Opportunity cost of not selling the machine (OC)	5,425,000
BV/4	Depreciation (D)		1,600,000	1,600,000	1,600,000	1,600,000
D*Tax rate	Operating Cash Flow (OCF)		400,000	400,000	400,000	400,000
OCF - OC	Free Cash Flow (FCF)	(5,425,000)	400,000	400,000	400,000	400,000
1/(1+d)^n	Discount factor @ 10%	1.000	0.909	0.826	0.751	0.683
FCF*Discount factor	PV of FCF	(5,425,000)	363,636.36	330,578.51	300,525.92	273,205.38
Sum of all PVs	NPV	(4,157,053.82)
Using IRR function with FCFs	IRR	-35.66%