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**Some Practice Questions in Engineering Economics**

Bruce A. Black Department of Electrical and Computer Engineering Rose-Hulman Institute of Technology

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**Cash Flow and Equivalence**

Time Value of Money Money can be invested at interest, so a given amount received today is worth more than the same amount received in the future.

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Example 1 Fifteen years ago $1000 was deposited in a bank account, and today it is worth $ The bank pays interest semi-annually. What was the nominal annual interest rate paid on this account?

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Example 2 A company puts $25,000 down and will pay $5,000 every year for the 10-year life of a machine. If the salvage value is zero and the interest rate is 10% compounded annually, what is the present value of the machine?

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Example 3 A machine costs $20,000 today and has an estimated scrap cash value of $2,000 after eight years. Inflation is 8% per year. The effective annual interest rate on money invested is 8%. How much money has to be set aside each year to replace the machine with an identical model eight years from now?

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Example 4 An oil company is planning to install a new pipeline to connect storage tanks to a processing plant 1500 m away. The connection will be needed for the forseeable future. Both 80 mm and 120 mm pipes are being considered. The annual interest rate is 8%.

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80 mm pipe 120 mm pipe Initial cost $ $2500 Service life years years Salvage value $ $ 300 Annual maint $ $ 300 Pump cost/hr $ $1.40 Pump operation 600 hr./yr hr./yr.

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Disregarding the initial and replacement pipe costs, what is the capitalized cost of the maintenance and pumping costs for the 80 mm pipe? What is the approximate uniform annual cost of the 80 mm pipe, considering all costs and expenses? What is the depreciation allowance for the 120 mm pipe in the first year? Use MACRS depreciation assuming a 10-year life.

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**Comparison of Alternatives**

Present Worth Mutually exclusive alternatives, same lives Annual Cost Assumes infinite renewal Rate of Return Interest rate that makes the present value zero Benefit-Cost Applies to public works projects. PW(benefits)/PW(costs) Break Even Does not use time-value of money by tradition

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Example 5 Warehouse A with a life of 10 years can be constructed now for $100,000 with no repair costs, and a salvage value of $10,000. Alternatively, warehouse B with a life of 12 years can be constructed for $70,000 now, with a salvage value of $5,000, but requires $18,000 of repairs every three years. Both have equal usefulness and are needed indefinitely. Assuming the cost of money is 6%, which warehouse is a better deal and by how much per year?

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Example 6 You purchased a lot for building your house four years ago for $20,000. Each year you paid $220 in property taxes. Each year you spent $80 in maintaining the lot. Now you are selling the lot and will get $25,000 after deducting the selling expenses. What is the rate of return on your investment?

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**Are there any questions?**

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