Question

Rooney, Inc. is considering a new machine for its largest product line. The cash flows are:
Installed Purchase Price $ 40,000
Reduced Cost of Materials $ 6,000 per year
Labor Savings $ 9,000 per year
Increase in Working Capital (for Year 0 and 1 only) $5,000
Depreciable Life (zero salvage value) 4 years
Economic Life 8 years
Required Return 12%
Tax Rate 40%

1. What is the NPV of this machine if it does not replace any other?

2. Suppose the machine replaces another machine with the following characteristics: Book Value of Old Machine $ 6,000
Market Value of Old Machine $ 4,000
Remaining Depreciable Life of Old Machine 6 years

Assume the old machine was not expected to have any salvage value and compute the NPV of the New Machine.

Please show all steps. Don't round off until you get to the end.

Answer 1

1.NPV of this machine if it does not replace any other
Purchase price of new m/c		-40000
PV of After-tax reduced cost of materials(6000*(1-40%))	3600*4.96764 =	17883.50
PV of After-tax labor savings(9000*(1-40%))	5400*4.96764=	26825.26
Yr.0 increase in NWC		-5000
Recovery of NWC at end Yr.1	5000/1.12^1=	4464.29
PV of depn. Tax shields(40000/4)*40%	10000*40%*3.03735=	12149.40
NPV of the new machine purchase		16322.45

2.NPV of this machine if it does replace an old machine
ATCF on sale of old m/c(Wkgs.)		4800
PV of depn. Tax shields on Old m/c lost(6000/6*40%)	400*4.11141=	-1644.56
Purchase price of new m/c		-40000
PV of After-tax reduced cost of materials(6000*(1-40%))	3600*4.96764=	17883.50
PV of After-tax labor savings(9000*(1-40%))	9000*(1-40%)*4.96764	26825.26
Yr.0 increase in NWC		-5000
Recovery of NWC at end Yr.1	5000/1.12^1=	4464.29
PV of depn. Tax shields(40000/4)*40%	10000*40%*3.03735=	12149.40
NPV of the replacement decision		19477.88
NOTE: P/A Factors used:
P/A,i=12%,n=4 yrs. = (1-1.12^-4)/0.12=	3.03735
P/A,i=12%,n= 8 yrs.=(1-1.12^-8)/0.12=	4.96764
P/A,i=12%,n= 6 yrs.=(1-1.12^-6)/0.12=	4.11141

Workings:
ATCF on sale of old m/c
MV of old m/c	4000
BV of old m/c	6000
Loss on sale(6000-4000)	2000
Cash out flow saved due to loss(2000*40%)	800
ATCF on sale of old m/c(4000+800)	4800

As the NPV of the REPLACEMENT decision is greater,($ 19477.88 > $ 16322.45) it is RECOMMENDED to Replace the old m/c.