Question

Exercise 6.7: Projects A to E have cash flows as shown in the table below. The Marr used to evaluate project is also shown.
Calculate NPW, NFW, and EUAW for each of these projects?
MARR	12%	7%	18%	6%	13%
Year	Project A	Project B	Project C	Project D	Project E
0	($36,000)	($56,000)	($25,000)	($278,000)	($321,000)
1	$5,000	$15,000	$5,000	$3,500	$40,000
2	$8,800	$17,400	$5,800	$40,600	$46,400
3	$10,208	$20,184	$6,728	$47,096	$53,824
4	$11,841	$23,413	$7,804	$54,631	$62,436
5	($13,736)	($27,160)	($9,053)	($63,372)	($72,426)
6	$15,934	$31,505	($10,502)	$73,512	$84,014
7	$18,483	$36,546	$12,182	$85,274	$97,456
8	$21,440		$14,131	$98,918	($113,049)
9	($24,871)			$114,745	$131,137
10	$33,824				$178,346

Answer 1

Present Worth PW = Cash Flow * PV Factor

PV Factor for Year n = 1/(1+r)ⁿ, where r is the MARR and n is the year

NPW = Σ Present Worth

Future Worth PW = Cash Flow * FV Factor

FV Factor for Year n = (1+r)ⁿ, where r is the MARR and n is the year

NFW = Σ Future Worth

Let the Equal Annual worth be P

=> P * sum of FV factor = NFW

MARR	12%		7%		18%		6%		13%
Year	Project A	FV Factor	Project B	FV Factor	Project C	FV Factor	Project D	FV Factor	Project E	FV Factor
0	-36000	1.00	-56000	1.00	-25000	1.00	-278000	1.00	321000	1.00
1	5000	1.12	15000	1.07	5000	1.18	3500	1.06	40000	1.13
2	8800	1.25	17400	1.14	5800	1.39	40600	1.12	46400	1.28
3	10208	1.40	20184	1.23	6728	1.64	47096	1.19	53824	1.44
4	11841	1.57	23413	1.31	7804	1.94	54631	1.26	62436	1.63
5	-13736	1.76	-27160	1.40	-9053	2.29	-63372	1.34	-72426	1.84
6	15934	1.97	31505	1.50	-10502	2.70	73512	1.42	84014	2.08
7	18483	2.21	36546	1.61	12182	3.19	85274	1.50	97456	2.35
8	21440	2.48			14131	3.76	98918	1.59	-113049	2.66
9	-24871	2.77					114745	1.69	131137	3.00
10	33824	3.11							178346	3.39
		20.65		10.26		19.09		13.18		21.81

Project A
Sum of FV Factor = 20.65
NFV = 150883.28
=> 20.65P = 150883.28 => P = $7306.70

Project B
Sum of FV Factor = 10.26
NFV = 103259.29
=> 10.26 = 103259.29 => P = $10064.26

Project C
Sum of FV Factor = 19.09
NFV = 58020.55
=> 19.09 = 58020.55 => P = $3039.32

Project D
Sum of FV Factor = 13.18
NFV = 395602.87
​​​​​​​=> 13.18 = 395602.87 => P = $30015.39

Project A
Sum of FV Factor = 21.81
NFV = 1574473.41
​​​​​​​=> 21.81 = 1574473.41 => P = $72190.44