Question

Your company is considering purchasing new machinery for the factory to upgrade and replace outdated equipment that will cost $4 Million right away. The machinery is projected to last 6 years, after which it can be sold for $500,000. The upgraded equipment will be able to produce more product and result in additional sales of $1.25 Million per year. Operating the new equipment will add $200,000 per year in expenses. Additionally, a one-time expense of $1.5 Million at the end of year 3 will be required to overhaul worn out parts. The company's MARR is 10%. Find the Net Present Worth of the project (enter it in the box below to the nearest dollar with no dollar sign).

Answer 1

Present Worth is -271,711

Explanation

PW = -$4,000,000 + $1,250,000 * (P/A, 10%, 6) - $200,000 * (P/A, 10%, 6) - $1,500,000 * (P/F, 10%, 3) +

          $500,000 * (P/F, 10%, 6)

Compute (P/F, 10%, 6)

      = (1 + i)^(-n)

      = (1 + 0.1)^(-6) = (1.1)^(-6) = 0.564474

Compute (P/F, 10%, 3)

      = (1 + i)^(-n)

      = (1 + 0.1)^(-3) = (1.1)^(-3) = 0.751315

Compute (P/A, 10%, 6)

      = [(1 + i)ⁿ - 1] / [i * (1 + i)ⁿ]

      = [(1 + 0.1)⁶ - 1] / [0.1 * (1 + 0.1)⁶] = [(1.1)⁶ - 1] / [0.1 * (1.1)⁶] = (1.771561 - 1 / (0.1 * 1.771561)

      = 0.771561 / 0.1771561 = 4.355261

PW = -$4,000,000 + ($1,250,000 * 4.355261) - ($200,000 * 4.355261) - ($1,500,000 * 0.751315) +

          ($500,000 * 0.564474)

      = -$4,000,000 + $5,444,076 - $871,052 - $1,126,973 + $282,237

      = -$271,711

Present Worth is -$271,711