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Question 1: [5pts each]
A. Calculate the future worth of the following 6-year cash transaction if the
interest rate is 10%, compounded annually. Draw the cash flow diagram.
Year Trx
1 $1000
2 $1200
3 $1400
4 $1600
5 $1800
6 $2000
B. Consider the following two investment opportunities. The investor’s MARR
is 15% and the investor only has enough funds to invest in one of the projects.
Which one should be chosen?
C. Use Excel (or equivalent application) to determine how long it will take for
an investment to triple in value at interest rates of 1%, 5%, 10%, 15%, 20%,
and 25%. Can you determine an approximate “Rule” for how to quickly
calculate how long it takes for an investment to triple in value?
Question 2: [10pts]
A company has decided to invest in a project to make a product. The initial
investment cost will be $1,000,000 to be spread over the first two years with
$700,000 in the first year and $300,000 in the second. The plan calls for producing
products at the following rates: 5,000 units in year 2; 10,000 in year 3; 30,000 in
year 4; 30,000 in year 5; $10,000 in year 6; and $5,000 in year 7. Products will be
sold for $50 each throughout the life of the project and cash operating expenses will
be $60,000 per year for years 2 through 7. Construct a cash flow diagram for the
project.
Question 3: [5pts each]
Air Links, a commuter airline company, is considering the replacement of one of its
baggage loading-unloading machines with a newer and more efficient one. The
relevant details for both machines are as follows:
• The current book value of the old machine is $50,000, and it has a remaining
useful life of five years. The salvage value expected from scrapping the old
machine at the end of five years is zero, but the company can sell the machine
now to another firm in the industry for $10,000.
• The new baggage-handling machine has a purchase price of $120,000 and an
estimated useful life of seven years. It has an estimated salvage value of
$30,000 and is expected to realize economic savings on electric-power usage,
labor, and repair costs and to reduce the amount of damaged luggage. In total,
annual savings of $50,000 will be realized if the new machine is installed.
The firm uses a MARR of 15%. Use any Annual Worth Method, address the
following questions:
A. What is the initial investment required for the new machine?
B. What are the cash flows for the defender in years zero to five?
C. Should the airline purchase the new machine?
Question 4: [10pts each]
The city of Toronto is considering two types of green water filtration subsystems.
Design A requires an initial investment of $500,000, with annual operating and
maintenance costs of 10% of the investment for the next 15 years. Design B needs
an investment of $250,000, with annual operating and maintenance costs of $75,000
per year for the next 15 years. Tax collections from Torontonians would be $85,000
per year. The interest rate is 6%, and no salvage value is associated with either
system.
A. Using Present Worth Analysis, which system should be selected and why?
B. If a new design (design C), which requires an initial outlay of $350,000 and
annual operating and maintenance costs of $65,000, is proposed, would your
answer to (A) change?
Question 5: [20pts]
SMART Robotix is planning to replace its old switchboard system, which has been
used in the company’s HQ for 10 years. This particular system, which has a current
market value of P, was installed for $100,000 and presumed a 15-year service life,
with no appreciable salvage value. Currently, the machine is costing the company
$20,000 a year, and these costs are presumed to be the same for the rest of its life.
SwitchT is proposing the company a new computerized switching system which
would require an investment of $200,000 for installation. The computerized system
is expected to have an economic life of 10 years, and a salvage value of $18,000.
One of the benefits of this new system is the reduction of operating cost to $5,000
per annum. No detailed agreement has been made with the sales representative about
the disposal of the old system.
Determine the range of resale values associated with the old system that would
justify installation of the new system at a MARR of 14%. Hint: use Annual
Equivalent Analysis
Sample Solution
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