FE Environmental Engineering Economics Practice Problems

The current FE Environmental specification assigns 5-8 of the 110 exam questions to Engineering Economics. Form A contains 5 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A 30,000 m $^{3}$ /d water treatment plant must select a disinfection process for a 20-year study period. Ultraviolet disinfection has a capital cost of USD 850,000, annual operation and maintenance of USD 62,000, and a salvage value of USD 90,000 at the end of year 20. Sodium hypochlorite disinfection has a capital cost of USD 520,000, annual operation and maintenance of USD 105,000, and no salvage value. At an interest rate of 6% per year, the present worth advantage of the ultraviolet alternative is most nearly:

(A)USD 163,000
(B)USD 191,000
(C)USD 253,000
(D)USD 452,000

Show worked solution

Answer: (B)

Ultraviolet disinfection is cheaper in present worth by roughly USD 191,000, because USD 43,000 per year of avoided operating cost outweighs its USD 330,000 capital premium.

Equal 20-year lives permit a direct present-worth comparison of the two cost streams at 6% per year.

(P / A, 6%, 20) = \frac{1 - ( 1.06 ) ^{- 20}}{0.06} = 11.470

(P / F, 6%, 20) = (1.06)^{- 20} = 0.3118

Salvage enters the ultraviolet stream as a single credit at year 20, discounted like any other future amount.

P W_{U V} = 850, 000 + 62, 000 (11.470) - 90, 000 (0.3118) = 1, 533, 000 USD

Hypochlorite buys a lower first cost at the price of a much heavier chemical and labor burden every year.

P W_{C l} = 520, 000 + 105, 000 (11.470) = 1, 724, 000 USD

Discounted savings of 43,000 USD per year, plus the residual credit, more than repay the 330,000 USD capital premium.

Δ P W = 1, 724, 000 - 1, 533, 000 = 191, 000 USD

FE Reference Handbook — Engineering Economics: Present Worth Analysis, Uniform Series Present Worth Factor

Why the other choices appear

(A)Omits the year-20 salvage credit entirely, giving 1,724,342 - 1,561,135 = 163,000 USD.
(C)Credits the full 90,000 USD salvage without discounting it, giving 1,724,342 - 1,471,135 = 253,000 USD.
(D)Compounds the salvage forward with (F/P, 6%, 20) = 3.207 instead of discounting it, crediting 288,600 USD and giving 1,724,342 - 1,272,493 = 452,000 USD.