Deck 6: Annual Equivalent-Worth Analysis

Question 1

The City of Atlanta is considering adding new buses for its current mass-transit system that links from the
Hartsfield International Airport to major city destinations on non-stop basis. The total investment package is
worth $8 million and expected to last 10 years with a $750,000 salvage value. The annual operating and
maintenance costs for buses would be $2 million during the first year, and will grow by 5% each year over the
previous year thereafter. If the system is used for 600,000 trips per year, what would be the fair price to charge
per trip? Assume that the City of Atlanta uses 5% interest rate for any city-sponsored projects.

Answer 1

Question 2

You are considering a luxury apartment building project that requires an investment of $12,500,000. The
building has 50 units. You expect the maintenance cost for the apartment building to be $250,000 in the first
year, $300,000 in the second year, and will continue to increase by $50,000 in subsequent years. The cost to hire a
manager for the building is estimated to be $80,000 per year. After five years of operation the apartment
building can be sold for $14,000,000. What is the annual rent per apartment unit that will provide a return on
investment of 15%? Assume the building will remain fully occupied during the five-year ownership. (Do your
analysis before tax basis.)

Answer 2

Question 3

The City of Greenville has decided to build a softball complex on a piece of property donated by one of the city
residents. The city council has already voted to fund the project at a level of $800,000 (initial capital investment).
The city engineer has collected the following financial information for the project.
• Annual upkeep costs: $120,000
• Annual utility costs: $13,000
• Renovation costs: $50,000 for every 5 years
• Annual team user fees (revenues): $32,000
• Useful life: Infinite
• Interest rate: 5%.
If the city expects 40,000 visitors to the complex each year, what should be the minimum ticket price per
person, so that the city can break-even?

Answer 3

Question 4

Colgate Printing Co. (CPC) has the book binding contract for the Ralph Brown library. The library pays $25 per
book to CPC. CPC binds 1,000 books every year for the library. Ralph Brown library is considering the option of
binding the books in-house in the basement of the library complex. In order to do this, the library would have
to invest in a binding machine and other printing equipment at a cost of $100,000. The useful life of the machine
is 12 years, at the end of which time, the machine is estimated to have a salvage value of $12,000. The annual
operating and maintenance costs of the machine are estimated to be $10,000.
(a) Assuming an interest rate of 6%, what is the cost of binding per book for the in-house option?
(b) What annual volume of books in need of binding would make both the options (in-house versus
subcontracting) equivalent?

Question 5

Suppose that a young investor is considering investing $100 in an interest bearing account that pays 10% interest compounded annually. The investor's plan is to leave the money in the account for one year and then
Withdraw the principal plus all accrued interest. If the investor's MARR is known to be 10%, does the investor:
(a) Increase his/her wealth by an additional $10
(b) Break even on the investment
(c) The investor earns an additional $10 and also breaks even on the investment
(d) None of the above

Question 6

You have purchased a machine costing $30,000. The machine will be used for two years, at the end of which
time its salvage value is expected to be $18,000. The machine will be used 6,000 hours during the first year and
8,000 hours during the second year. The expected annual net savings will be $35,000 during the first year and
$42,000 during the second year. If your interest rate is 12%, what would be the equivalent net savings per
machine hour?

Question 7

Consider a piece of manufacturing equipment that has an installed cost of $100K. The equipment is expected to
generate $30K of annual energy savings during its first year of installation. The value of these annual savings is
expected to increase by 3% per year because of increased fuel costs. Assume that the equipment has a service
life of 5 years (or 3,000 operating hours per year) with no appreciable salvage value. Determine the equivalent
dollar savings per each operating hour at

Question 8

Consider a project with a first cost (investment) of $250,000, an annual O&M cost of $50,000, annual revenue of
$160,000, and a salvage value of $40,000 after a 10-year project life. Find the annual worth of the project
assuming an interest of 13% per year.

Question 9

A consumer product company is considering introducing a new shaving system called DELTA-4 in the market.
The company plans to manufacture 75 million units of DELTA-4 a year. The investment required at time 0 for
building the manufacturing plant is estimated to be $500 million, and the economic life of the project is assumed
to be 10 years with a salvage value of $120 million. The annual total operating expenses, including
manufacturing costs and overheads, are estimated to be $175 million. If the company's MARR is 25%, determine
the minimum price that the company should charge for a DELTA-4 shaving system (without considering any
tax effects).

Question 10

Your firm has purchased an injection molding machine at a cost of $100,000. The machine's useful life is
estimated to be 8 years. Your accounting department has estimated the capital cost for this machine at about
$25,455 per year. If your firm's MARR is 20%, how much salvage value do you think the accounting department
assumed at the end of 8 years?

Question 11

You just purchased a pin inserting machine to relieve some bottleneck problems that have been created in
manufacturing a PC board. The machine would cost $56,000 and has an estimated service life of 5 years. At that
time, the estimated salvage value would be $5,000. The machine is expected to operate 2,500 hours per year. The
expected annual operating and maintenance cost would be $6,000. If your firm's interest rate is 15%, what
would be the machine cost per operating hour?

Question 12

The following infinite cash flow series has a rate of return of 10%. Determine the unknown value of X.

Question 13

Two 150-horsepower (HP) motors are being considered for installation at a municipal sewage-treatment plant.
The first motor costs $4,500 and has an operating efficiency of 83% at full load. The second motor costs $3,600
and has an efficiency rating of 80% at full load. Both motors are projected to have zero salvage value after a life
of 10 years. The annual operating and maintenance cost (excepting power cost) amounts to 15% of the original
cost of each motor. The power costs are a flat 5 cents per kilowatt-hour. Determine the minimum number of
hours of full-load operation per year necessary to justify the purchase of the more expensive motor at i = 6%.