Question

The Mowbot plant must replace an existing HVAC unit (doing nothing is not an option). You are evaluating two pieces of equipment. Each unit offers a saving in annual energy cost over the existing equipment.

Alternative                           Unit A              Unit B              Unit C

Up front cost                       $44,000           $65,000           $84,000

Operating cost/year           $1,900             $1,400             $900

Energy savings / year         $14,000           $16,500           $17,500

Salvage Value                      $2,000             $4,000             $5,000

Economic life, years                5                       7                       7

Mowbot’s MARR is 12%. Based on annual worth analysis (not incremental), which unit should you recommend?

Answer 1

Unit B should be selected

Explanation:-

Compute Annual Worth of each of the three Units

Annual Worth of Unit A

AW(A) = -$44,000 * (A/P, 12%, 5) - $1,900 + $14,000 + $2,000 *(A/F, 12%, 5)

Compute (A/P, 12%, 5)

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

       = [0.12 * (1 + 0.12)⁵] / [(1 + 0.12)⁵ - 1] = [0.12 * (1.12)⁵] / [(1.12)⁵ - 1] = [0.12 * 1.7623] / [1.7623 - 1]

       = 0.2115 / 0.7623 = 0.2774

Compute (A/F, 12%, 5)

       = r   / [(1 + r)ⁿ - 1]

       = 0.12 / [(1 + 0.12)⁵ - 1] = 0.12 / [(1.12)⁵ - 1] = 0.12 / [1.7623 - 1]

       = 0.12 / 0.7623 = 0.1574

AW(A) = (-$44,000 * 0.2774) - $1,900 + $14,000 + ($2,000 * 0.1574)

           = -$12,205.6 - $1,900 + $14,000 + $314.8

           = $209.20

Annual Worth of Unit B

AW(B) = -$65,000 * (A/P, 12%, 7) - $1,400 + $16,500 + $4,000 *(A/F, 12%, 7)

Compute (A/P, 12%, 7)

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

       = [0.12 * (1 + 0.12)⁷] / [(1 + 0.12)⁷ - 1] = [0.12 * (1.12)⁷] / [(1.12)⁷ - 1] = [0.12 * 2.2107] / [2.2107 - 1]

       = 0.2653 / 1.2107 = 0.2191

Compute (A/F, 12%, 7)

       = r   / [(1 + r)ⁿ - 1]

       = 0.12 / [(1 + 0.12)⁷ - 1] = 0.12 / [(1.12)⁷ - 1] = 0.12 / [2.2017 - 1]

       = 0.12 / 1.2017 = 0.0991

AW(B) = (-$65,000 * 0.2191) - $1,400 + $16,500 + ($4,000 * 0.0991)

           = -$14,241.50 - $1,400 + $16,500 + $396.4

           = $1,254.90

Annual Worth of Unit C

AW(C) = -$84,000 * (A/P, 12%, 7) - $900 + $17,500 + $5,000 *(A/F, 12%, 7)

   = (-$84,000 * 0.2191) - $900 + $17,500 + ($5,000 * 0.0991)

           = -$18,404.40 - $900 + $17,500 + $495.50

           = -$1,308.90

Annual Worth of Unit B is the highest. Unit B should be selected