Question

Exercise 6.6: Details for 6 project proposals as are shown below. Find payback period,
NPW, EUAC, and NFW?
	Machine A	Machine B	Machine C	Machine D	Machine E	Machine F
Initial cost	($240,000)	($360,000)	($420,000)	($560,000)	($660,000)	($850,000)
Life of machine	3	4	5	6	7	9
MARR	9%	10%	11%	12%	13%	14%
Benefits in first year	$75,000	$92,000	$109,000	$126,000	$143,000	$131,000
Salvage cost (% of initial cost)	15%	14%	13%	15%	14%	13%
Increase in benefits each year	5%	6%	7%	8%	9%	5%

Answer 1

Machine A
Year	0	1	2	3
Initial cost	-240000
Salvage(240000*15%)				36000
Benefits		75000	78750	82688
Total Cash flows	-240000	75000	78750	118688
Cumulative cash flows	-240000	-165000	-86250	32438
Payback period=	2+(86250/118688)=
	2.73	Years
PV F at 9%(1/1.09^Yr.n)	1	0.91743	0.84168	0.77218
PV at 9%	-240000	68807	66282	91649
NPV	-13262
EUAC=
NPV/(PV Factor)
-13262/((1-1.09^-3)/0.09)=
-5239
NFW
Total Cash flows	-240000	75000	78750	118688
FW F at 9%(1*1.09^Yr.n)	1.295029	1.1881	1.09	1
FW at 9%	-310807	89108	85838	118688
FW at 9%				-17174

Machine B
Year	0	1	2	3	4
Initial cost	-360000
Salvage(360000*14%)					50400
Benefits		92000	97520	103371	109573
Total Cash flows	-360000	92000	97520	103371	159973
Cumulative cash flows	-360000	-268000	-170480	-67109	92865
Payback period=	3+(67109/159973)=
	3.42	Years
PV F at 10%(1/1.10^Yr.n)	1	0.90909	0.82645	0.75131	0.683013
PV at 9%	-360000	-243636	-140893	-50420	63428
NPV	-731521
EUAC=
NPV/(PV Factor)
-731521/((1-1.10^-4)/0.10)=
-230773.5178
NFW
Total Cash flows	-360000	92000	97520	103371	159973
FW F at 10%(1*1.10^Yr.n)	1.4641	1.331	1.21	1.1	1
FW at 10%	-527076	122452	117999	113708	159973
FW at 10%					-12943

Machine C
Year	0	1	2	3	4	5
Initial cost	-420000
Salvage(420000*13%)						54600
Benefits		109000	116630	124794	133530	142877
Total Cash flows	-420000	109000	116630	124794	133530	197477
Cumulative cash flows	-420000	-311000	-194370	-69576	63954	261431
Payback period=	3+(69576/133530)=
	3.52	Years
PV F at 11%(1/1.11^Yr.n)	1	0.90090	0.81162	0.73119	0.65873	0.59345
PV at 9%	-420000	98198	94660	91248	87960	117193
NPV	69259
EUAC=
NPV/(PV Factor)
-69529/((1-1.11^-5)/0.11)=
-18812.48305
NFW
Total Cash flows	-420000	109000	116630	124794	133530	197477
FW F at 11%(1*1.11^Yr.n)	1.685058	1.51807	1.367631	1.2321	1.11	1
FW at 11%	-707724	165470	159507	153759	148218	197477
FW at 11%						116706

Machine D
Year	0	1	2	3	4	5	6
Initial cost	-560000
Salvage(560000*15%)							84000
Benefits		126000	136080	146966	158724	171422	185135
Total Cash flows	-560000	126000	136080	146966	158724	171422	269135
Cumulative cash flows	-560000	-434000	-297920	-150954	7770	179192	448327
Payback period=	3+(150954/158724)=
	3.95	Years
PV F at 12%(1/1.12^Yr.n)	1	0.89286	0.79719	0.71178	0.63552	0.56743	0.50663
PV at 9%	-560000	112500	108482	104608	100872	97269	136352
NPV	100083
EUAC=
NPV/(PV Factor)
100083/((1-1.12^-6)/0.12)=
24343
NFW
Total Cash flows	-560000	126000	136080	146966	158724	171422	269135
FW F at 12%(1*1.12^Yr.n)	1.97382	1.76234	1.57352	1.40493	1.2544	1.12	1
FW at 12%	-1105341	222055	214125	206477	199103	191992	269135
FW at 12%							197547