Question

"Consider the cash flow for an investment project with MARR = 17.4%. Determine the annual equivalent worth for the project. The cash flow for years 0 through 4 in dollars is as follows:
-4,100
1,600
1,700
1,300
540"

Answer 1

Year	Cash Flow	PV Factor Formula	PV Factor @ 17.4%	PV
0	$           (4,100.00)	1/(1+0.174)^0	1	$                           (4,100.00)
1	$              1,600.00	1/(1+0.174)^1	0.851788756	$                             1,362.86
2	$              1,700.00	1/(1+0.174)^2	0.725544086	$                             1,233.42
3	$              1,300.00	1/(1+0.174)^3	0.618010294	$                                 803.41
4	$                  540.00	1/(1+0.174)^4	0.52641422	$                                 284.26
			NPV	$                               (416.04)

Equivalent annual worth = NPV/A_r,t

A_r,t = [1 – 1/(1+r)^t]/r

r = Rate of interest = 17.4 % or 0.174

t = No. of periods = 4

A_r,t = [1 – 1/(1+0.174)⁴]/0.174

      = [1 – 1/ (1.174)⁴]/0.174

      = [1 – (1/ 1.899644732)]/0.174

      = (1 – 0.52641422)/0.174

      = 0.47358578/0.174

      = 2.721757356

Equivalent annual worth = $ (416.04)/ 2.721757356 = $ (152.86)