A new computer system will require an initial outlay of $22,500, but it will increase the firm’s cash flows by $4,500 a year for each of the next 6 years.

A new computer system will require an initial outlay of $22,500, but it will increase the firm’s cash flows by $4,500 a year for each of the next 6 years.

a. Calculate the NPV and decide if the system is worth installing if the required rate of return is 8%.
 


Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations.

a.
NPV_8% = −$22,500 + [$4,500 × Annuity factor (8%, 6periods)]
                                            = −$22,500 + $4,500 ×  [10.08 −  10.08 × (1.08)6]= $1,697.04


b.
NPV_14% = −$22,500 + [$4,500 × Annuity factor (13%,6 periods)]
                                                 =  −$22,500 + $4,500 ×  [10.13 −  10.13 × (1.13)6]= − $4,511.03


c.
IRR = discount rate (r), which is the solution to the following equation:

$8 ×  [1r −  1r × (1+ r)6]= $22,500  ⇒  r= IRR= 5.47%


[Using a financial calculator, enter PV = (−)22,500; PMT = 4,500; FV = 0; n = 6, compute i.]

The project will be rejected for any discount rate above this rate.