Question

A firm is considering whether to install a new computer system. The computer system costs $800,000 today and is expected to increase the firm’s productivity so much that the firm will earn $250,000 each year for four years starting one year from today. If the real interest rate is 10%, should the firm install the new computer system? (Make sure that you show the formula in your answer. Show your work.)

Answer 1

NPV of the project should be calculated here. If NPV is positive, the firm should install the system.

Formula and calculation:

Annual earnings = A = $250,000

Initial cost = IC = 800,000

r = rate of interest = 0.10

n = Number of years = 4

Hence,

NPV = [(A/r) {1 – (1 + r) ^ (- n)}] – IC

         = [(250,000/0.10) {1 – (1 + 0.10) ^ (- 4)}] – 800,000

         = [2,500,000 {1 – 1/1.10^4}] – 800,000

         = [2,500,000 {1 – 1/1.4641}] – 800,000

         = [2,500,000 {0.4641/1.4641}] – 800,000

         = [2,500,000 × 0.316986] – 800,000

         = 792,465 – 800,000

         = - 7,535

Conclusion: since NPV is negative, the initial cost can’t be recovered during the life time of the system; therefore, the firm should not install it.