51 In a new, highly automated factory, labor costs are expected to decrease at a
ID: 1141615 • Letter: 5
Question
51 In a new, highly automated factory, labor costs are expected to decrease at an rate of 4 %; material costs are expected to increase at an annual compound rate of 6%; and energy costs are expected to increase at an annual d rate of 7 %. The labor, material and energy costs the first year are $1.5 annual c million, S3.5 million, and $3.0 million. a. What will be the amount of each cost during the fifth year? b. Using an interest rate of 12 % compounded annually, what uniform annual costs over a 12-year period would be equivalent to the cumulative labor, material, and energy costs?Explanation / Answer
Let us draw the table for costs. Note that
(i) Labor cost in year N = Labor cost in year (N - 1) x 0.96
(ii) Material cost in year N = Material cost in year (N - 1) x 1.06
(iii) Energy cost in year N = Energy cost in year (N - 1) x 1.07
(iv) Total cost in year N = Labor cost in year N + Material cost in year N + Energy cost in year N
Therefore:
(a) In year 5,
Labor cost = $1.27 million
Material cost = $4.42 million
Energy cost = $3.93 million
(b) First we compute the Present Worth (PW) of total cost. Note that PV Factor in year N = (1.12)-N
Uniform annual cost = PW of Total cost / P/A(12%, 12) = $61.42 million / 6.1944** = $9.92 million
**From P/A Factor table
Year Labor Cost ($Million) Material Cost ($Million) Energy Cost ($Million) Total Cost ($Million) (A) (B) (C) (D) = (A) + (B) + (C) 1 1.5 3.5 3 8 2 1.44 3.71 3.21 8.36 3 1.38 3.93 3.43 8.75 4 1.33 4.17 3.68 9.17 5 1.27 4.42 3.93 9.63 6 1.22 4.68 4.21 10.11 7 1.17 4.96 4.50 10.64 8 1.13 5.26 4.82 11.21 9 1.08 5.58 5.15 11.82 10 1.04 5.91 5.52 12.47 11 1.00 6.27 5.90 13.17 12 0.96 6.64 6.31 13.92