Probability and Engineering Economy

Maintenance costs for a small bridge with an expected 50-year life are estimated to be $1,000 each year for the first 5 years, followed by $10,000 expenditure in year 15 and $10,000 expenditure in year 30. If r = 10% per year, what is the Present Worth (PW)?

A public utility is trying to decide between two different sizes of pipe for a new water main. A 250-mm line will have an initial cost of $40,000, whereas a 300-mm line will cost $46,000. Since there is more head loss through the 250-mm pipe, the pumping cost for the smaller line is expected to be $2500 per year more than for the 300-mm line. If the pipes are expected to last for 15 years, which size should be selected if the interest rate is 12% per year? Use an annual-worth analysis.

A bi-level mall is under construction. It is planned to install only 9 escalators at the start, although the ultimate design calls for 16. The question arises in the design as to whether to provide necessary facilities (stair supports, wiring conduits, motor foundations, etc.), which would permit the installation of the additional escalators at only the cost of their purchase and installation, or to defer investment in these facilities until the escalators need to be installed.

Option 1: Provide these facilities now for all 7 future escalators at $200,000.

Option 2: Defer the facility investment as needed. It is planned to install 2 more escalators in 2 years, 3 more in 5 years, and the last 2 in 8 years. The installation of these facilities at the time they are required is estimated to cost $100,000 in year 2, $160,000 in year 5, and $140,000 in year 8. Additional annual expenses are estimated at $3,000 for each escalator facility installed. At an interest rate of 12%, which option is preferred based on the net present worth?

A certain factory building has an old lighting system, and electricity for the building costs, on average, $20,000 a year. A lighting consultant tells the factory supervisor that the lighting bill could be reduced to $8,000 a year if $50,000 were invested in relighting the factory building. If the new lighting system is installed, an incremental maintenance cost of $3,000 per year will be incurred. If the new lighting system is estimated to have a life of 20 years, what is the net annual benefit for this investment in new lighting? Consider the MARR to be 12%. Both the new and old lighting system has zero salvage value.

A new highway is to be constructed with two alternative designs. Design A calls for concrete pavement costing $90 per foot with a 20-year life; two paved ditches costing $3 per foot each; and three box culverts every mile, each costing $9,000 and having a 20- year life. Annual maintenance will cost $1,800 per mile; the culverts must be cleaned every five years at a cost of $450 each per mile. Design B calls for bituminous pavement costing $45 per foot with a 10-year life, two grass ditches costing $1.50 per foot each; and three pipe culverts every mile, each costing $2,250 and having a 10-year life. The replacement culverts will cost $2,400 each. Annual maintenance will cost $2,700 per mile; the culverts must be cleaned yearly at a cost of $225 each per mile; and the annual ditch maintenance will cost $1.50 per foot per ditch.

Compare the two designs worth per mile for a 20-year period. Find the most economical design on the basis of annual worth and present worth if the MARR is 6% per year.

6. The Development Corporation has a 30-year lease on a plot of land. Estimates of the annual expenses and revenues of various types of structures on the property are as shown in the accompanying table. Each structure is expected to have a market value equal to 20% of its capital investment at the end of a 30-year analysis period. If MARR is 12% per year on all investments, which structure (if any) should be selected? Use the AW method.

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Alternatives Apartment house Theater Department store Office building

Capital investment

$300,000 200,000 250,000 400,000

Annual Revenues Less Expenses

$69,000 40,000 55,000 76,000

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Angel investor Jerry Kodra is looking to invest $12,000 between two possible teams. The first team led by Evan Najjar will require an initial investment of $10,000. The second team led by Mary Fleurat will require an initial investment of $12,000. Evan and Mary both have an initial discussion with Jerry’s financial advisors, who determine that their projects are likely to get sold for $11,000 and $13,500 respectively after year 1. The MARR for Jerry’s firm is 5%. What are the IRRs for the investments? If both Evan and Mary approach Jerry, how should Jerry allocate his funds and why? Justify clearly.

Investment A costs $14,000 while investment B costs $65,000. Annual costs associated with investment A is $14,000 while that with investment B is $9,000. Useful life of A is 5 years while that of B is 20 years. Market value @ end of useful life of A and B is $8,000 and $13,000, respectively. If the study period = 20 years, which alternative is preferred? Use discount rate=5%. Hint: First draw a cash flow diagram.

Mr. Ronald Drump can “adopt a highway” with an expected life of 20-years by agreeing to pay $2,000 per year for the next 8 years, $5,000 per year over the next 12 years and $7,500 in year 20. What is the present worth of the “adoption” if the average interest rate over the 20 year period is r = 10% per year.

10. For each of the following costs, state if the costs are (1) fixed or variable, (2) direct or indirect, and (3) recurring or non-recurring. Give a one sentence explanation why.

Wages paid to temporary workers

Property taxes on factory building

Property taxes on administrative building

Sales commission paid to salespeople

Electricity for machinery and equipment in the plant

Heat and air-conditioning for the plant

Salaries paid to design engineers

Regular maintenance on machinery and equipment

Basic raw materials used in production

Factory fire insurance

Water (for a facility that does not use water in production)

Office rent

11. A loan company lends money at 1.25% per month, compounded monthly.

What are the nominal and effective annual interest rates?

How many years will it take an investment to double itself if interest is

compounded monthly?

The company is considering the option of investing $20,000 in high-risk stocks

over the next 5 years. The projections for the next several years are as follows: a 3% return for a best case with a probability of 70%, a –4% return (i.e., loss) for a worst case with a probability of 30%. Is the stock investment more attractive to the company that the loan investment?

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