Consider the cash flow for an investment project with MARR

\"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\"

Solution

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)