Question

Cisco, Inc., has a proposal from the Engineering Planning Division to invest Cisco retained earnings in the design, testing, and development of the next generation of smart grids useful in the Internet of Things (IoT) environment. The initial investment projection is $4,000,000 in year 0, $2,100,000 in year 3, and $87,320 in years 11 and beyond. At i = 10% per year, calculate the infinite-life equivalent annual cost in years 0 through infinity of the proposal.

The infinite-life equivalent annual cost is determined to be $  .

Answer 1

As per the question the Cisco Inc., has a proposal to invest in smart grids project

Initial investment of the project (I) = $4,000,000

The investment in the year 3 is =$2,100,000

The investment in the year 11 and beyond =$87,320

i = 10% = 0.1

When Life of the project (N) = ∞ (infinite)

Thought the investment from the year 11 and beyond indicates and investment for an infinite period, so we need to calculate the present worth of the investment at the year 10

The present worth of the investment at year 10= $87,320(P/A,10%,∞) =$87,320/0.1=873,200

Present worth of the cost = $4,000,000 + $2,100,000(P/F,10%,3) + $873200(P/F,10%,10)

Present worth of the cost = $4,000,000 + $2,100,000(0.751315) + $873,200(0.385543)

Present worth of the cost = $4,000,000 + $1,577,761.5 + $336,656.15 = $5,914,417.65

The infinite life equivalent annual cost (A) =?

Present worth of the cost = The infinite life equivalent annual cost x (P/A,10%,∞) =A/i

Present worth of the cost = A/i

A = (Present worth of the cost) x i = $5,914,417.65 x 0.1 = $591,441.76

The infinite life equivalent annual cost (A) = $591,441.76