Question

One of the packed absorption columns on your processing line requires significant maintenance with a total cost of $435,250. With this maintenance, the column is expected to operate for an additional 10 years before requiring additional maintenance that is estimated to cost $263,425. The additional maintenance will further extend the lifetime of the column for another 10 years. The current operating costs for the column are $2,745 per month.

As an alternative, your company could purchase a new packed absorption column with a total cost of $675,815 including removal of the old column and installation of the new column. The new column is expected to operate for 20 years with proper maintenance, which costs $1,275 per month. The operating costs for the new column are expected to be $2,545 per month.

a. Calculate the total present value of each option assuming an annual interest rate of 1.15% compounded monthly, and select the most economical option.

b.Convert the total present value to an equivalent uniform monthly cost for the 20- year lifetime of each option.

Answer 1

a). Number of years (N) = 10; Number of months (n) = 20*12 = 240

Annual interest rate (I) = 1.15%; Monthly interest rate (i) = 1.15%/12 = 0.0958%

Old column:

NPV = 435,250 + 263,425(P/F, I, N) + 2,745(P/A, i, n)

= 435,250 + 263,425/(1+1.15%)^10 + 2,745[(1+0.0958%)^240 -1]/0.0958%*((0.0958%+1)^240)

Note: [(1+0.0958%)^240 -1]/0.0958%*((0.0958%+1)^240) is the PV of annuity factor = 214.3084

= 435,250 + 588,276.56 + 588,299.27 = 1,258,488.82

New column:

NPV = 675,815 + 1,275(P/A, i, n) + 2,545(P/A, i, n)

= 675,815 + (1,275*214.3084) + (2,545*214.3084)

= 1,494,473.09

The old column appears to be the most economical column because it has a lower total NPV cost as compared to the new column.

b).

Capital recovery factor = (A/P, i, n) =[i*(1+i)^n]/[(1+i)^n-1] = [0.0958%*(1+0.0958%)^240]/[(1+0.0958%)^240-1] = 0.004666

Equivalent monthly cost for old column = NPV*capital recovery factor = 1,258,488.82*0.004666 = 5,872.33

Equivalent monthly cost for new column = NPV*capital recovery factor = 1,494,473.09*0.004666 = 6,973.47