Question

Problem 12-13 (algorithmic) Question Help A potential project has an initial capital investment of $85,000. Net annual revenues minus expenses are estimated to be $40,000 (A$) in the first year and to increase at the rate of 6.76% per year. The useful life of the primary equipment, however, is uncertain, as shown in the following table. Assume that im = MARR = 16% per year and f= 3% per year. Useful Life, Years (N) ܢ ܢ ܚ P(N) 0.02 0.12 0.34 0.22 0.18 0.12 ܠܛ ܗ ܗ a. What are the E(PW) and SD(PW) for this project based on this information? E(P ound to the nearest hundreds.)

Answer 1

Initial Capital investment is $ 85,000 (Column 1)

Net Revenue increases @ 6.76% (Column 2)

Discounted revenue @ MARR 16% (Column 3) Calculated as

Revenuex 1.16

PW(N) is cumulative net outcome of the project up to the year (Column 4)

Probability of useful life of the project is p(N) (Column 5)

Summation of PW(N) X p(N) is E(PW) (Column 6)

Variance of Present Worth is

V(PW) = E(PW)? - E(PW)

and Standard Deviation of Present worth is

SD(PW) = V(PW)

Year	Cost	Revenue	Discounted Revenue @ 16%	PW(N)	p(N)	PW(N)*p(N)	PW(N)^2	p(N)*PW(N)^2
0	$ 85,000.00		$                  (85,000.00)
1		$ 40,000.00	$                    34,482.76	$                  (50,517.24)	0.02	$ (1,010.34)	$ 2,55,19,91,676.58	$          5,10,39,833.53
2		$ 42,704.00	$                    31,736.03	$                  (18,781.21)	0.12	$ (2,253.75)	$      35,27,33,955.81	$          4,23,28,074.70
3		$ 45,590.79	$                    29,208.09	$                    10,426.88	0.34	$    3,545.14	$      10,87,19,761.28	$          3,69,64,718.83
4		$ 48,672.73	$                    26,881.51	$                    37,308.39	0.22	$    8,207.85	$ 1,39,19,16,051.05	$        30,62,21,531.23
5		$ 51,963.00	$                    24,740.26	$                    62,048.65	0.18	$ 11,168.76	$ 3,85,00,35,437.95	$        69,30,06,378.83
6		$ 55,475.70	$                    22,769.57	$                    84,818.23	0.12	$ 10,178.19	$ 7,19,41,31,554.37	$        86,32,95,786.52
					E(PW)	$ 29,835.84	E[(PW)^2]	$    1,99,28,56,323.65
							V(PW)	$    1,10,26,79,053.21
							SD(PW)	$                    33,206.61