We must compute the annual worth of each process and compare them in order to determine which one the organization should choose based on an examination of annual worth during a three-year research period.
PLAN A
- First cost (C_A) = $2,000,000
- Annual operating cost (A_A) = $60,000
- Salvage value (S_A) = 10% of the first cost = 0.10 * $2,000,000 = $200,000
FORMULA PLAN A
- AW_A = A_A + (A_A - S_A) * (P/A, i, n)
SOLUTION
- i = 12% per year
- n = 3 years
- P/A, 12%, 3 = 1 - (1 + 0.12)^-3 / 0.12 = 1 - (1.12)^-3 / 0.12 ≈ 2.4013
PLAN A
AW_A = $60,000 + ($60,000 - $200,000) * 2.4013 ≈ -$240,780.20
PLAN B
First cost (C_B) = $795,000
Annual operating cost for year 1 (A_B1) = $85,000
Annual operating cost for year 2 and beyond (A_B2) = $46,000
FORMULA PLAN B
- AW_B = A_B1 + (A_B2 - C_B) * (P/A, i, n)
Calculate the present worth factor (P/A, i, n) using the same values as before:
P/A, 12%, 3 ≈ 2.4013
PLAN B
AW_B = $85,000 + ($46,000 - $795,000) * 2.4013 ≈ $159,983.20
COMPARE
Plan B is the better choice as it has a positive annual worth of approximately $159,983.20 over the 3-year study period, while Plan A has a negative annual worth of approximately -$240,780.20.