The following are intended to be practice problems to better understand the economic formulae that are used in engineering economic analysis.
1) You have an old car, which you can sell now for $500. Antique collectors say the car ought to be worth $2,000 in 10 years. You anticipate that savings accounts will earn an average of 5% during this period. What is the prudent economic decision - "sell or hold" ?
2) Your newly born child will start college in 18 years. You anticipate college will cost $10,000 for each of the four years.
A) How much should you save (uniformly) each of these 18 years, assuming you do no further saving once the child has started college, and that the "annuity" should be such as to pay out $10,000 per year for each of those four years. Assume a 3% savings account interest rate. (Note that this is a two-part problem.) Assume that you make the investment at the beginning of each of the 18 years - i.e. first payment during the first week the baby was born, the seond ayment at the end of year I, beginning of year 2, etc.
B) The stock market has typically had an average return of 11% per year, over the last 50 years. There is no guarantee on mutual fund earnings, but suppose you did invest in a stock mutual fund that did earn 11% per year each year. Recalculate the above problem for this higher, i.e. 11%, return on investment.
3) This problem compares the "sinking fund" method of making a purchase vs the loan method of purchasing a car. You want to buy a new $20,000 car. Savings accounts earn 3%, but the car loans cost 8% on four-year loans. You now have an old car worth $2,000, depreciating at the rate of 20% per year. You have a job that allows you to set aside $5,000 a year toward the purchase of a car. Consider two conditions:
a) You buy the car now, on time ($20,000 less trade in value of $2000).
b) You save until you can pay cash (less trade).
Assume new car prices do not change during the next few years.
When can you buy the new car if you adopted plan (b) - i.e. how many months from now, the beginning of these exercise?
ii) What is your net worth (car plus savings) four years from now, for BOTH a) and b)?
Assume that both the new car and the used will depreciate 25% per year by the declining balance method.
4) 4.1) What is the loan payment, monthly, on a $200,000 mortgage at 5% for :
a) 30 years, b) 20 years, c) 10 years ?
What is the total sum you paid to the bank for each of these conditions?
2) Redo the problem for current long term mortgage interest rates of 6%.
5) An oil company drills a well that costs $2 million, and has a 50% chance of producing 120 barrels a day (i.e. on average, two wells drilled, total production = 120 barrels per day). Estimate the ROI, based on the current cost of oil (about $50 per barrel).
6) Health care is a major issue today. Costs appear out of control. One such concern os the expense of special diagnostic equipment, such as MRI (magnetic resonance imaging) machines, for which a typical installation at a hospital will cost about $3 million.
The hospital will probably attempt to amortize it over a period of 5 years (the technology changes so rapidly, that in 5 years they may need to replace it). Assume the cost of capital to a hospital is 7%.
a) If the MM is used 5 days per week, taking images of 50 patients per week, what is the capital cost component that should be charged to the bill of each patient? (Don't include any operating expenses, or profit in this part of the answer.)
b) If the MRI machine is better utilized, by faster imaging techniques being employed, and the machine being used for longer hours, so that 150 patients can be processed each week, what is the capital cost charge now, per patient?
A large electric generating power plant is to be built. The utility has two choices:
a) A Nuclear Plant, 1200 MW net output. Expected construction cost = $1.8 billion, spread out uniformly over 5 years, on a construction loan that carries 8% interest.
No payments on construction costs or interest can be made until the plant starts operating, according to Missouri law passed in 1977. Thus, interest on the construction loan must be paid by further borrowing. Once started, the plant is expected to employ a total of 900 people (average salary per person = $60,000 (with a 1.4 multiplier for benefits).
Other annual costs for consultants, supplies, services, fees, etc. will be $50 million per year. Fuel cost will be 0.5 cents per kWh, and a capacity factor of 85% over the years is expected. Once the plant starts operation, the construction loan and interest that it bore will be changed to a bonded indebtedness at 7% for 30 years.
b) A 1200 MW new coal-fired plant with necessary pollution controls, can be built for $1.6 billion. It will take 4 years to build, and interest may be paid during construction (or may be borrowed and added to construction costs).
The bonded indebtedness on the plant will be at 7% interest for 30 years. The plant will employ 300 people, at an average salary of $45,000 (with a 1.4 multiplier for benefits). Fuel cost and scrubber material and ash disposal cost is expected to average 1.8 cents per kWh. Other annual costs for supplies, taxes, fees, etc. will total $30 million per year.
Assume that the plant will achieve an overall capacity factor of 85% As a utility executive or engineer, perform an economic analysis to determine the cost of electricity produced by each plant (cents per kWh), and decide which plant is most economical, over its lifetime.
For the final answer, you might reflect on uncertainties involving the costs over the lifetime of each plant, and any political implications that might be pertinent in making the final decision.