Problem 2.1
Find the correct numerical value for the following factors from the interest tables:
a. (F/P,10%,20)
b. (A/F,4%,8)
c. (P/A,8%,20)
d. (A/P,20%,28)
e. (F/A,30%,15)
Problem 2.2
What is the present worth of $30,000 in year 8 at an interest rate of 10% per year?
Problem 2.3
If an engineer invested $15,000 on January 1, 1991, into a retirement account that earned
6% per year interest, how much money will be in the account on January 1, 2016?
Problem 2.4
The Moller Skycar M400 is a flying car known as a personal air vehicle (PAV). The cost
is $995,000, and a $100,000 deposit holds one of the first 100 vehicles. Assume a buyer
pays the $885,000 balance 3 years after making the $100,000 deposit. At an interest rate
of 10% per year, determine the effective total cost of the PAV in year 3 using
(a) tabulated factors, and (b) a single-cell spreadsheet function.
Problem 2.5
What is the present worth of a future payment of $19,000 in year 7 if the interest rate is
10% per year using (a) the tabulated factor values in your book, (b) TVM functions on a
financial calculator, and (c) built-in functions on a spreadsheet?
Problem 2.6
Determine the amount of money a bank will loan to a developer who repays the loan by
selling 7 view lots at $120,000 each two years from now. Assume the bank’s interest rate
is 10% per year. Use (a) the tabulated factor values in your book, (b) TVM functions on a
financial calculator, and (c) built-in functions on a spreadsheet.
Problem 2.7
How much will be in an investment account 12 years from now if you deposit $3000 now
and $5000 four years from now and the account earns interest at a rate of 10% per year?
Use (a) tabulated factor values, (b) TVM functions on a financial calculator, and (c) built-
in functions on a spreadsheet.
Problem 2.8
Loadstar Sensors is a company that makes load/force sensors based on capacitive sensing
technology. The company wants to accumulate $30 million for plant expansion five years
from now. If the company already has $15 million in an investment account for the
expansion, how much more must the company add to the account now so that it will have
the $30 million 5 years from now? The account earns interest at 10% per year. Solve
using (a) tabulated factors, and (b) a spreadsheet. Compare the answers.
Problem 2.9
Meggitt Systems, a company that specializes in extreme-high-temperature
accelerometers, is investigating whether it should update equipment now or wait and do it
later. If the cost now is $280,000, what is the equivalent amount 2 years from now at an
interest rate of 12% per year?
Problem 2.10
By filling carbon nanotubes with miniscule wires made of iron and iron carbide,
incredibly thin nanowires can be extruded by blasting the carbon nanotubes with an
electron beam. If Gentech Technologies spends $12.7 million now in developing the
process, how much must be received in licensing fees each year for the next 8 years
(starting 1 year from now) to recover its investment at a 20% per year rate of return?
Problem 2.11
What is the present worth of a uniform series of 10 payments that begin one year from
now in the amount of $6000 if the interest rate is 10% per year?
Problem 2.12
How large of a repayment must an engineer make each year starting next year if she
borrows $60,000 now to start up her new consulting office and she promises to make
equal annual payments for 5 years. Assume the interest rate is 8% per year. Develop the
answer using (a) tabulated factor values, (b) a financial calculator, and (c) spreadsheet
functions.
Problem 2.13
Bodine Electric makes gear motors with a three-stage, selectively hardened gearing
cluster that is permanently lubricated. If the company borrows $20 million for a new
warehouse/distribution facility, what is the amount to repay the loan in six equal annual
payments? The loan’s interest rate is 10% per year.
Problem 2.14
A small oil company wants to replace its Micro Motion Coriolis flowmeters with
Emerson F-Series flowmeters in Hastelloy construction. The replacement process will
cost the company $50,000 three years from now. How much money must the company
set aside each year beginning one year from now in order to have the total amount in
three years? Assume the company will invest its funds at 20% per year.
Problem 2.15
Ametek Technical & Industrial Products (ATIP) manufactures brushless blowers for
boilers, foodservice equipment, and fuel cells. The company borrowed $17,000,000 for a
plant expansion and repaid the loan in eight annual payments of $2,737,680, with the first
payment made one year after the company received the money. What interest rate did
ATIP pay? Develop the answer using (a) tabulated factor values, (b) a financial
calculator, and (c) spreadsheet functions.
Problem 2.16
Assume the cost of homeland security border fence is $3 million per mile. If the life of
such a fence is 10 years, what is the equivalent annual cost of a 10-mile long fence at an
interest rate of 8% per year? Develop the answer using: (a) tabulated factor values, (b) a
financial calculator, and (c) spreadsheet functions.
Problem 2.17
The Border Patrol is considering the purchase of a new helicopter for aerial surveillance
of the New Mexico-Texas border with Mexico. A similar helicopter was purchased
4 years ago at a cost of $1,400,000. At an interest rate of 7% per year, what would be the
equivalent value today of that $1,400,000 expenditure?
Problem 2.18
Petroleum Products, Inc. is a pipeline company that provides petroleum products to
wholesalers in the Northern United States and Canada. The company is considering
purchasing insertion turbine flowmeters to provide better monitoring of pipeline integrity.
If these meters prevent one major disruption (through early detection of product loss)
valued at $600,000 four years from now, how much could the company afford to spend
now at an interest rate of 12% per year?
Problem 2.19
Sensotech, Inc., a maker of micro-electromechanical systems, believes it can reduce
product recalls by 10% if it purchases new software for detecting faulty parts at a cost of
$225,000. The minimum attractive rate of return is 15% per year.
a. How much does the company have to save each year for 4 years to recover its
investment?
b. What was the cost of recalls per year before the software was purchased if the
company exactly recovered its investment in 4 years from the 10% reduction?
Problem 2.20
Atlas Long-Haul Transportation is considering installing Valutemp temperature loggers
in all of its refrigerated trucks for monitoring temperatures during transit. If the systems
will reduce insurance claims by $100,000 two years from now, how much should the
company be willing to spend now if it uses an interest rate of 12% per year?
Problem 2.21
The current cost of liability insurance for a consulting firm is $65,000 per year. If the cost
is expected to increase by 4% each year, what will be the cost 5 years from now?
Problem 2.22
How much money could RTT Environmental Services borrow to finance a site
reclamation project if it expects revenues of $280,000 per year over a 5-year cleanup
period? Expenses associated with the project are expected to be $90,000 per year.
Assume the interest rate is 10% per year.
Problem 2.23
Arctic and Antarctic regions are harsh environments in which to take data. A TempXZ
3000 portable temperature recorder can take and store 32,767 measurements at −40 to
150 °C. A research team from the University of Nova Scotia needs 20 of the recorders,
and they are trying to decide whether they should buy them now at $649 each or purchase
them 2 years from now, which is when they will be deployed. At an interest rate of 8%
per year, how much can each recorder cost in 2 years to render their decision indifferent?
Problem 2.24
Since many U.S. Navy aircraft are at or near their usual retirement age of 30 years,
military officials want a precise system to assess when aircraft should be taken out of
service. A computational method developed at Carnegie Mellon maps in 3-D the
microstructure of aircraft materials in their present state so that engineers can test them
under different conditions of moisture, salt, dirt, etc. Military officials can then determine
if an aircraft is fine, is in need of overhaul, or should be retired. If the 3-D system allows
the Navy to use one airplane 2 years longer than it normally would have been used,
thereby delaying the purchase of a $20 million aircraft for 2 years, what is the present
worth of the assessment system at an interest rate of 8% per year?
Problem 2.25
GE Marine Systems is planning to supply a Japanese shipbuilder with aero-derivative gas
turbines to power 11DD-class destroyers for the Japanese Self-Defense Force. The buyer
can pay the total contract price of $2,100,000 two years from now, when the turbines will
be needed, or an equivalent amount now. At an interest rate of 10% per year, what is the
equivalent amount now?
Problem 2.26
A maker of mechanical systems can reduce product recalls by 25% if it purchases new
packaging equipment. The cost of the new equipment is expected to be $40,000 four
years from now. How much could the company afford to spend now, instead of 4 years
from now, if it uses a minimum attractive rate of return of 12% per year?
Problem 2.27
a. How much money could Tesla-Sino Inc., a maker of superconducting magnetic energy
storage systems, spend each year on new equipment in lieu of spending $850,000 five
years from now, if the company’s rate of return is 18% per year?
b. What is the spreadsheet function to display an answer with the correct sign sense to the
annual cash flows?
Problem 2.28
French car maker Renault signed a $95 million contract with ABB of Zurich,
Switzerland, for automated underbody assembly lines, body assembly workshops, and
line control systems. If ABB will be paid in 3 years, when the systems are ready, what is
the present worth of the contract at 12% per year interest?
Problem 2.29
What is the future worth six years from now of a present cost of $375,000 to Corning,
Inc. at an interest rate of 10% per year?
Problem 2.30
A pulp and paper company is planning to set aside $150,000 now for possibly replacing
its large synchronous refiner motors. If the replacement isn’t needed for 8 years, how
much will the company have in the account if it earns interest at a rate of 8% per year?
Problem 2.31
Automationdirect, which makes 6-inch TFT color touch screen HMI panels, is examining
its cash flow requirements for the next 5 years. The company expects to replace office
machines and computer equipment at various times over the 5-year planning period.
Specifically, the company expects to spend $7000 two years from now, $9000 four years
from now, and $15,000 five years from now. Determine the present worth of the planned
expenditures at an interest rate of 10% per year using (a) tabulated factors, and (b) a
financial calculator.
Problem 2.32
A proximity sensor attached to the tip of an endoscope could reduce risks during eye
surgery by alerting surgeons to the location of critical retinal tissue. If a certain eye
surgeon expects that by using this technology, he will avoid lawsuits of $0.6 and $1.35
million 2 and 5 years from now, respectively, how much could he afford to spend now if
his out-of-pocket costs for the lawsuits would be only 10% of the total amount of each
suit? Use an interest rate of 10% per year.
Problem 2.33
Irvin Aerospace of Santa Ana, CA, just received a 5-year contract to develop an advanced
space capsule airbag landing attenuation system for NASA’s Langley Research Center.
The company’s computer system uses fluid structure interaction modeling to test and
analyze each airbag design concept. What is the present worth of the contract at 10% per
year interest if the annual cost for 5 years is $8 million per year?
Problem 2.34
Julong Petro Materials, Inc. ordered $10 million worth of seamless tubes for its drill
collars from the Timken Company of Canton, Ohio. (A drill collar is the heavy tubular
connection between a drill pipe and a drill bit.) At 10% per year interest, what is the
annual worth of the purchase over a 10-year amortization period?
Problem 2.35
Improvised explosive devices (IEDs) are responsible for many deaths in times of war.
Unmanned ground vehicles (robots) can be used to disarm the IEDs and to perform other
tasks as well. The robots cost $140,000 each and the U.S. Army signed a contract to
purchase 4000 of them now. What is the equivalent annual cost of the contract if it is
amortized over a 4-year period at 10% per year interest?
Problem 2.36
The U.S. Navy’s robotics lab at Point Loma Naval Base in San Diego is developing
robots that will follow a soldier’s command or operate autonomously. If one robot would
prevent injury to soldiers or loss of equipment valued at $1.5 million per year, how much
could the military afford to spend now on the robot and still recover its investment in
4 years at 8% per year?
Problem 2.37
PCM Thermal Products uses austenitic nickel-chromium alloys to manufacture resistance
heating wire. The company is considering a new annealing-drawing process to reduce
costs. If the new process will cost $3.25 million dollars now, how much must be saved
each year to recover the investment in 6 years at an interest rate of 15% per year?
Problem 2.38
A green algae, chlamydomonas reinhardtii, can produce hydrogen when temporarily
deprived of sulfur for up to 2 days at a time. How much could a small company afford to
spend now to commercialize the process if the net value of the hydrogen produced is
$280,000 per year? Assume the company wants to earn a rate of return of 18% per year
and recover its investment in 8 years.
Problem 2.39
HydroKlean LLC, an environmental soil cleaning company, borrowed $3.5 million to
finance startup costs for a site reclamation project. How much must the company receive
each year in revenue to earn a rate of return of 25% per year for the 5-year project
period?
Problem 2.40
A VMB pressure regulator allows gas suppliers and panel builders to provide compact
gas handling equipment, thereby minimizing the space required in clean rooms. Veritech
Micro Systems is planning to expand its clean room to accommodate a new product
design team. The company estimates that it can reduce the space in the clean room by
7 square meters if it uses the compact equipment. If the cost of construction for a clean
room is $5000 per square meter, what is the annual worth of the savings at 10% per year
interest if the cost is amortized over 10 years?
Problem 2.41
New actuator element technology enables engineers to simulate complex computer-
controlled movements in any direction. If the technology results in cost savings in the
design of new roller coasters, determine the future worth at 12% per year in year 6 for
estimated savings of $70,000 now and $90,000 two years from now using (a) tabulated
factors, and (b) spreadsheet functions.
Problem 2.42
Under an agreement with the Internet Service Providers (ISPs) Association, SBC
Communications reduced the price it charges ISPs to resell its high-speed digital
subscriber line (DSL) service from $458 to $360 per year per customer line for the next
5 years. A particular ISP, which has 20,000 customers, plans to pass 90% of the savings
along to its customers. What is the total present worth of these savings at an interest rate
of 10% per year?
Problem 2.43
Southwestern Moving and Storage wants to have enough money to purchase a new
tractor-trailer in 5 years at a cost of $290,000. If the company sets aside $100,000 in year
2 and $75,000 in year 3, how much will the company have to set aside in year 4 in order
to have the money it needs? Assume investments earn 9% per year. Solve using
(a) tabulated factors, and (b) spreadsheet functions.
Problem 2.44
Vision Technologies, Inc., is a small company that uses ultra-wideband technology to
develop devices that can detect objects (including people) inside buildings, behind walls,
or below ground. The company expects to spend $100,000 per year for labor and
$125,000 per year for supplies for three years before a product can be marketed. At an
interest rate of 15% per year, what is the total equivalent present worth of the company’s
expenses?
Problem 2.45
How many years will it take Rexchem, Inc. to accumulate $400,000 for a chemical feeder
if the company deposits $50,000 each year, starting one year from now, into an account
that earns interest at 12% per year?
Problem 2.46
How many years will it take for money to increase to three times the initial amount at an
interest rate of 10% per year?
Problem 2.47
Acceleron is planning future expansion with a new facility in Indianapolis. The company
will make the move when its real estate sinking fund has a total value of $1.2 million. If
the fund currently has $400,000 and the company adds $50,000 per year, how many years
will it take for the account to reach the desired value? The fund earns interest at a rate of
10% per year.
Problem 2.48
The defined benefits pension fund of G-Tech Electronics has a net value of $2 billion.
The company is switching to a defined contribution pension plan, but it guaranteed the
current retirees that they will continue to receive their benefits as promised. If the
withdrawal rate from the fund is $158 million per year starting 1 year from now, how
many years will it take to completely deplete the fund if the conservatively managed fund
grows at a rate of 7% per year?
Problem 2.49
Silastic-LC-50 is a liquid silicone rubber designed to provide high clarity, superior
mechanical properties, and short cycle time for high speed manufacturers. One high-
volume manufacturer used it to achieve smooth release from molds. The company’s
projected growth would result in silicon costs of $26,000 next year and costs increasing
by $2000 per year through year 5. The interest rate is 10% per year. (a) What is the
present worth of these costs using tabulated factors? (b) How is this problem solved using
a spreadsheet? Using a financial calculator?
Problem 2.50
Calculate the equivalent annual cost of fuel for mail trucks that records indicate costs
$72,000 in year one, increasing by $1000 per year through year five. Use an interest rate
of 8% per year.
Problem 2.51
A company that manufactures air-operated drain valve assemblies budgeted $84,000 per
year for repair components over the next five years. Assume the company uses an interest
rate of 10% per year. (a) If the company expects to spend $15,000 in year 1, what is the
annual increase (arithmetic gradient) that the company expects in the cost of the parts?
(b) Comment on the size of the arithmetic gradient compared to the first year cost.
Problem 2.52
A company that manufactures a revolutionary aeration system combining coarse and fine
bubble aeration components had costs this year (year 1) of $9,000 for check valve
components. Based on completion of a new contract with a distributor in China and
volume discounts, the company expects this cost to decrease. If the cost in year 2 and
each year thereafter decreases by $560, what is the equivalent annual cost for a five-year
period at an interest rate of 10% per year?
Problem 2.53
For the cash flows shown, determine the value of G that makes the present worth in year
0 equal to $14,000. The interest rate is 10% per year.
Year 0 1 2 3 4
Cash flow, $ per year — 8000 8000-G 8000-2G 8000-3G
Problem 2.54
Allen Bradley claims that its XM1Z1A and XM442 electronic over-speed detection relay
modules provide customers a cost-effective monitoring and control system for turbo
machinery. Estimates indicate the equipment will provide more efficient turbine
performance to the extent of $20,000 in year 1, $22,000 in year 2, and amounts
increasing by $2000 per year. How much can Mountain Power and Light spend now and
recover its investment in 10 years, if interest is 10% per year?
Problem 2.55
A low-cost non-contact temperature measuring tool may be able to identify railroad car
wheels that are in need of repair long before a costly structural failure occurs. If the
BNSF railroad saves $100,000 in year 1, $110,000 in year 2, and amounts increasing by
$10,000 each year for five years, what is the future worth of the savings in year 5 at an
interest rate of 10% per year?
Problem 2.56
Southwest Airlines hedged the cost of jet fuel by purchasing options that allowed the
airline to purchase fuel at a fixed price for 5 years. If the market price of fuel was
$0.50 per gallon higher than the option price in year 1, $0.60 per gallon higher in year 2,
and amounts increasing by $0.10 per gallon higher through year 5, what was the present
worth of SWA’s savings per gallon? Use i = 10% per year.
Problem 2.57
NMTeX Oil company owns several gas wells in Carlsbad, NM. Income from the
depleting wells has been decreasing according to an arithmetic gradient for the past five
years. If the interest rate is 10% per year and income in year 1 from well no. 24 was
$390,000 and it decreased by $15,000 each year thereafter, (a) what was the income in
year 3, and (b) what was the equivalent annual worth of the income through year 5?
Problem 2.58
The present worth of income from an investment that follows an arithmetic gradient is
projected to be $475,000. The income in year one is expected to be $25,000. What is the
gradient each year through year 6 at an interest rate of 10% per year?
Problem 2.59
Very Light Jets (VLJs) are one-pilot, two-engine jets that weigh 10,000 pounds or less
and have only five or six passenger seats. Since they cost half as much as the most
inexpensive business jets, they are considered to be the wave of the future. MidAm
Charter purchased five planes so that it can initiate service to small cities that have
airports with short runways. MidAm expects revenue of $1 million in year one,
$1.2 million in year two and amounts increasing by $200,000 per year thereafter. If the
company’s MARR is 10% per year, what is the future worth of the revenue through the
end of year 5? Solve using both tabulated factors and spreadsheet functions.
Problem 2.60
The future worth in year 10 of income associated with a fixed-income investment is
guaranteed to be $500,000. If the cash flow in year 1 is $20,000, how much would the
arithmetic gradient have to be at the interest rate of 10% per year?
Problem 2.61
Fomguard LLC of South Korea developed a hightech fiber-optic fencing mesh (FOM)
that contains embedded sensors that can differentiate between human and animal contact.
In an effort to curtail illegal entry into the United States, a FOM fence has been proposed
for some sections of the U.S. border with Canada. The cost for erecting the fence in year
1 is expected to be $7 million, decreasing by $500,000 each year through year 5. At an
interest rate of 10% per year, what is the equivalent uniform annual cost of the fence for
years 1 to 5?
Problem 2.62
For the cash flow series shown, determine the future worth in year 5 at an interest rate of 10% per
year.
Year 1 2 3 4 5
Cash Flow, $ 300,000 275,000 250,000 225,000 200,000
Problem 2.63
Verizon Communications said it plans to spend $22.9 billion to expand its fiber-optic
Internet and television network so that it can compete with cable-TV providers like
Comcast Corp. If the company attracts 950,000 customers in year one and grows its
customer base by a constant amount of 15% per year, what is the future worth of the total
subscription income in year 5? Estimates indicate that income will average $800 per
customer per year. Assume Verizon uses a MARR of 10% per year.
Problem 2.64
The cost for manufacturing a component used in intelligent interface converters was
$23,000 the first year. The company expects the cost to increase by 2% each year.
Calculate the present worth of this cost over a five-year period at an interest rate of 10%
per year.
Problem 2.65
Many companies offer retirement plans wherein the company matches the contributions
made by the employee up to 6% of the employee’s salary. An engineer planning for her
retirement expects to invest the maximum of 6% each year. Her salary in year one is
$60,000 and is expected to increase by 4% each year. Including the employer’s
contributions, how much will she have in her account at the end of 20 years if interest
accrues at 7% per year?
Problem 2.66
A concept car that will get 100 miles per gallon and carry four persons would have a
carbon-fiber and aluminum composite frame with a 900 cc three-cylinder
turbodiesel/electric hybrid power plant. The extra cost of these technologies is estimated
to be $11,000. (a) If gasoline savings over a comparable conventional car would be $900
in year one, increasing by 10% each year, what is the present worth of the savings over a
10-year period at an interest rate of 8% per year? (b) Compare the present worth values to
determine if the extra cost is recovered by fuel savings.
Problem 2.67
The National Institute on Drug Abuse has spent $15 million on clinical trials to find out
whether two vaccines can end the bad habits of nicotine and cocaine addiction. A Swiss
company is now testing an obesity vaccine. If the vaccines are semi-successful such that
treatment costs and medical bills are reduced by an average of $15,000 per person per
year, what is the annual worth of the vaccines for 10 million beneficiaries in year one and
an additional 15% people each year through year 5? Use an interest rate of 8% per year.
Problem 2.68
Find the annual worth in years 1 through 10 of an investment that starts at $8000 in year
1 and increases by 10% each year. The interest rate is 10% per year.
Problem 2.69
The effort required to maintain a scanning electron microscope is known to increase by a
fixed percentage each year. A high-tech equipment maintenance company has offered its
services for a fee that includes automatic increases of 8% per year after year 1. A biotech
company that wanted to use the service offered $65,000 as pre-payment for a 3-year
contract to take advantage of a temporary tax loophole. If the biotech company used an
interest rate of 10% per year in determining how much it should offer, what was the
service fee amount that it assumed for year 1?
Problem 2.70
Hughes Cable Systems plans to offer its employees a salary enhancement package that
has revenue sharing as its main component. Specifically, the company will set aside 1%
of total sales for year-end bonuses for all its employees. The sales are expected to be $5
million the first year, $5.5 million the second year, and amounts increasing by 10% each
year for the next 5 years. At an interest rate of 8% per year, what is the equivalent annual
worth in years 1 through 5 of the bonus package?
Problem 2.71
Determine how much money will be in an investment account that starts at $5000 in year
1 and increases each year thereafter by 15% per year. Use an interest rate of 10% per year
and a 12-year time period.
Problem 2.72
The present worth in year 10 of a decreasing geometric gradient series was calculated
using tabulated factors to be $80,000. If the interest rate was 10% per year and the annual
rate of decrease was 8% per year, determine the cash flow amount in year 1 using
(a) tabulated factors, and (b) the Goal Seek tool in Excel. (Hint: See Appendix A,
section A.4).
Problem 2.73
Altmax Ltd, a company that manufactures automobile wiring harnesses, has budgeted
P = $400,000 now to pay for a certain type of wire clip over the next 5 years. If the
company expects the cost of the clips to increase by 4% each year, what is the expected
cost in year 3 if the company uses an interest rate of 10% per year?
Problem 2.74
Thomasville Furniture Industries offers several types of high-performance fabrics that are
capable of withstanding chemicals as harsh as chlorine. A Midwestern manufacturing
company that uses fabric in several products has a report showing that the present worth
of fabric purchases over a specified 5-year period was $900,000. If the costs are known to
have increased geometrically by 5% per year during that time and the company uses an
interest rate of 15% per year for investments, what was the cost of the fabric in year 1?
Problem 2.75
A small northern California consulting firm wants to start a recapitalization pool for
replacement of network servers. If the company invests $5000 at the end of year 1 but
decreases the amount invested by 5% each year, how much will be in the account 5 years
from now? Interest is earned at a rate of 8% per year.
Problem 2.76
A company that manufactures purgeable hydrogen sulfide monitors is planning to make
deposits such that each one is 5% smaller than the preceding one. What must be the
deposit at the end of year 1 if the deposits will extend through year 10 and the fourth
deposit is $1250? Use an interest rate of 10% per year.
Problem 2.77
Akron Coating and Adhesives (ACA) produces a hot melt adhesive that provides a strong
bond between metals and thermoplastics when used for weather stripping, seals, gaskets,
hand grips for tools, appliances, etc. ACA claims that by eliminating a primer coat,
manufacturers can cut costs and reduce scrap. If Porter Cable is able to save $60,000 now
and $40,000 per year thereafter by switching to the new adhesive, what is the present
worth of the savings for three years at an interest rate of 10% per year?
Problem 2.78
Attenuated Total Reflectance (ATR) is a method for looking at the surfaces of materials
that are too opaque or too thick for standard transmission methods. A manufacturer of
precision plastic parts estimates that ATR spectroscopy can save the company $8000 per
year by reducing returns of out-of-spec parts. What is the future worth of the savings if
they start now and extend through year 4? Use i = 10% per year.
Problem 2.79
To improve crack detection in aircraft, the U.S. Air Force combined ultrasonic inspection
procedures with laser heating to identify fatigue cracks. Early detection of cracks may
reduce repair costs by an estimated $200,000 per year. If the savings start now and
continue through year 5, determine the equivalent future worth in year 5 of these savings
at an interest rate of 10% per year.
Problem 2.80
An entrepreneurial new civil engineering graduate started a lab for testing endocrine
disrupting compounds. The lab just broke even the first year, but in years 2 through 5, it
made a profit of $97,000 each year. What is the present worth in year 0 of the profit at an
interest rate of 10% per year?
Problem 2.81
A mechanical engineer who is anticipating paying for his daughter’s college education
plans to start depositing money now (year 0) and continue through year 17. If he deposits
$5000 each year, how much will his daughter be able to withdraw each year starting in
year 18 and continuing through year 22? Assume the account earns interest at 8% per
year.
Problem 2.82
For the cash flows shown, calculate the future worth in year 8 at i = 10% per year.
Year 0 1 2 3 4 5 6
Cash flow, $ 100 100 100 200 200 200 200
Problem 2.83
An Air Force Research
Laboratory has spent $62 million
over a decade developing and testing the Active Denial System, a device which uses
energy beams to allow soldiers to break up unruly mobs without firing a shot. Another $9
million will be spent over the next two years. Assume the $62 million was spent evenly
in years 1 through 10 and that the $9 million will be expended evenly in years 11 and 12.
What is the total future worth of the expenditures in year 12 at an interest rate of 8% per
year? Solve using (a) tabulated factors, and (b) write the calculator function to find the
future worth.
Problem 2.84
Calculate the annual cost for years 1 through 9 of the following series of disbursements.
Use an interest rate of 10% per year. Solve using (a) factors and (b) a spreadsheet.
Year Disbursement,$ Year
Disbursement, $
Problem 2.85
A company that manufactures digital pressure gauges just borrowed $10,000,000 with the
understanding that it will make annual payments of $2,000,000 for three years starting
next year, and then pay off the balance in year 4. If the interest rate is 8% per year, how
much will the company owe at the end of year 4?
Problem 2.86
a. For the cash flow revenues shown, find the value of CF3 that makes the equivalent
annual worth in years 1 through 7 equal to exactly $200. The interest rate is 10% per
year.
0
5,000
5
5,000
1
4,000
6
5,000
2
4,000
7
5,000
3
4,000
8
5,000
4
4,000
9
5,000
Year
Cash flow, $
Year
Cash flow, $
b. Use a spreadsheet to
find CF3.
Problem 2.87
Some studies have shown that
taller men tend to earn higher
salaries than equally qualified men of shorter stature. Homotrope growth hormone can
increase a child’s height at a cost of $50,000 per inch. Clyde’s parents wanted him to be
3″ taller than he was projected to be. They paid $50,000 per year for the treatments for
three years beginning on their son’s 8th birthday. How much extra money would Clyde
have to earn per year from his 26th through 60th birthdays (a total of 35 years) in order to
justify their expenditure? Use i = 8% per year.
Problem 2.88
Calculate the future worth in year 7 of Merchant Trucking Company’s cash flows. Use an
interest rate of 10% per year.
Year 0 1 2 3 4 5 6 7
Cash Flow, $ million 450 -40 200 200 200 200 200 200
Problem 2.89
The by-product department of Iowa Packing utilizes a cooker that has the cost stream
shown. Determine the annual worth for years 1 through 5 of the costs at an interest rate of
10% per year. Costs are in $1000 units.
Year
Cost, $
0
850
1
300
2
400
3
400
4
400
5
500
Problem 2.90
An entrepreneurial electrical engineer approached a large water utility with a proposal
that promises to reduce the utility’s power bill by at least 15% through installation of
patented surge protectors. The proposal states that the engineer will not be paid for the
first year, but beginning in year 2, she will receive three equal, annual payments that are
0
200
4
200
1
200
5
200
2
200
6
200
3
CF
3
7
200
equivalent to 60% of the power bill savings achieved in year 1 due to the protectors.
Assuming that the utility’s power bill of $1 million per year is reduced by 15% after
installation of the surge protectors, what is (a) the present worth in year 0 of the uniform
payments to the engineer, and (b) their future worth in year 4? Use an interest rate of 10%
per year.
Problem 2.91
Metropolitan Water Utility is planning to upgrade its SCADA system for controlling well
pumps, booster pumps, and disinfection equipment so that everything can be controlled
from one site. The first phase will reduce labor and travel costs by an estimated $31,000
per year. The second phase will reduce costs by an estimated $20,000 per year. If phase I
will occur in years 1 through 3 and phase II in years 4 through 8, what is (a) the present
worth of the savings, and (b) the equivalent annual worth for years 1 through 8 of the
savings? Use an interest rate of 8% per year. Solve using tabulated factors and a
spreadsheet.
Problem 2.92
Infrared thermometers by Delta Thermal Products are compatible with type K
thermocouples and can provide rapid non-contact measurement capabilities at a cost of
$135 per unit. A small private electric utility company plans to purchase 100 of the
thermometers now and 500 more 1 year from now, if the anticipated savings in labor
costs can be realized. At an interest rate of 12% per year, what is the equivalent annual
worth of the savings over a study period of years 1 through 5 that justifies the equipment
purchases?
Problem 2.93
Encon Systems, Inc. sales revenues for a product line introduced 7 years ago is shown.
Use tabulated factors, a calculator or a spreadsheet to calculate the equivalent annual
worth over the 7 years using an interest rate of 10% per year.
Year
Revenue,
$
Year
Revenue, $
0
4,000,000
4
5,000,000
1
4,000,000
5
5,000,000
2
4,000,000
6
5,000,000
3
4,000,000
7
5,000,000
Problem 2.94
Cisco’s gross revenue (the percentage of total revenue left after subtracting the cost of
goods sold) was 70.1% of total revenue over a 4-year period. If the total revenue per year
was $5.8 billion for the first two years and $6.2 billion for the last 2, find the future worth
of the gross revenue series in year 4 at an interest rate of 14% per year.
Problem 2.95
Calculate (a) the annual worth for years 1–8 and (b) the future worth in year 8 of the
following series of incomes and expenses. The interest rate is 10% per year.
Year
Income, $
Expense, $
0
20,000,000
1–5
8,000,000
1,000,000
6–8
9,000,000
2,000,000
Problem 2.96
A supplier of certain suspension system parts for General Motors wants to have a
contingency fund that it can draw on during down periods of the economy. The company
wants to have $15 million in the fund 5 years from now. If the company deposits
$1.5 million now, determine the uniform amount to add at the end of each of the next
5 years to reach its goal, provided the fund earns 10% per year. Solve using (a) tabulated
factors, and (b) the Goal Seek tool in Excel. (Hint: See Appendix A, Section A.4.)
Problem 2.97
A rural utility company provides standby power to pumping stations using diesel-
powered generators. An alternative has arisen whereby the utility could use a
combination of wind and solar power to run its generators, but it will be a few years
before the alternative energy systems are available. The utility estimates that the new
systems will result in savings of $15,000 per year for 3 years, starting 2 years from now
and $25,000 per year for 4 more years after that, i.e., through year 8. At an interest rate of
8% per year, determine the equivalent annual worth for years 1 through 8 of the projected
savings.
Problem 2.98
The cost of energy for operating high-lift pumps in a water distribution system was
$1.4 million for the first three years. Beginning in year four, the cost increased by
$30,000 each year for the next 12 years. What is the present worth in year 0 of these
energy costs at an interest rate of 6% per year?
Problem 2.99
A chemical engineer saving for his retirement deposited $10,000 into a stock fund at
t = 0. In year one and each year thereafter through year 20, he increased the deposit by
$1500. If the rate of return on the investments is 12% per year, how much will his
retirement account be worth at the end of year 20?
Problem 2.100
An industrial engineering consulting firm signed a lease agreement for simulation
software. Calculate the present worth in year 0 if the lease requires a payment of $30,000
now and amounts increasing by 5% per year through year 7. Use an interest rate of 10%
per year.
Problem 2.101
A build to operate (BTO) company signed a contract to operate several industrial
wastewater treatments plants for 10 years. The contract will pay the company
$2.5 million now and amounts increasing by $200,000 each year through year 10. At an
interest rate of 10% per year, what is the present worth of the contract now? Solve using
(a) tabulated factors, and (b) a spreadsheet.
Problem 2.102
Nippon Steel’s expenses for heating and cooling one of its large manufacturing facilities
are expected to increase according to an arithmetic gradient beginning in year 2. The
costs are expected to be $550,000 now (year 0), $550,000 in year 1, and increases by
$40,000 each year through year 12. What is the equivalent annual worth in years 1–12 of
the costs at an interest rate of 10% per year?
Problem 2.103
Lifetime Savings Accounts, known as LSAs, allow people to invest after-tax money
without being taxed on any of the gains. An engineer began his LSA by investing
$10,000 five years ago and increased his deposit by $1000 each year, including a deposit
today. How much will be in the account immediately after today’s deposit (after a total of
6 deposits), if the account grew at a rate of 12% per year?
Problem 2.104
A software company that installs systems for inventory control using RFID technology
spent $600,000 per year for the past 3 years in developing their latest product. The
company wants to recover its investment in 5 years beginning now. If the company
signed a contract that will pay $250,000 now and amounts increasing by a uniform
amount each year through year 5, how much must the increase be each year? Use an
interest rate of 15% per year.
Problem 2.105
The future worth in year 8 for the cash flow series shown is $20,000. At an interest rate
of 10% per year, what is the value of the cash flow labeled x in year 4?
Problem 2.106
The annual worth for years 1 through 8 of the cash flows shown is $30,000. What is the
amount of the cash flow labeled x in year 3, if i = 10% per year? Solve using (a) tabulated
factors, and (b) a spreadsheet.
Problem 2.107
Wrangler Western has some of its jeans stonewashed under a contract with independent
U.S. Garment Corp. If U.S. Garment’s operating cost per machine is $22,000 per year for
years 1 and 2 and then it increases by 8% per year through year 10, what is the present
worth in year 0 of the machine operating cost at an interest rate of 10% per year?
Problem 2.108
Union Pacific is considering the elimination of a railroad grade crossing by constructing a
dual track overpass. The railroad subcontracts for maintenance of its crossing gates at
$11,500 per year. Beginning 4 years from now, however, the costs are expected to
increase by 10% per year into the foreseeable future (that is, $12,650 in year 4, $13,915
in year 5, etc.). If the railroad uses a 10-year study period and an interest rate of 15% per
year, how much could the railroad afford to spend now on the overpass in lieu of the
maintenance contracts?
Problem 2.109
McCarthy Construction is trying to bring the company-funded portion of its employee
retirement fund into compliance with HB-301. The company has already deposited
$500,000 in each of the last 5 years. Beginning in year 6, McCarthy will increase its
deposits by 15% per year through year 20. How much will be in the fund immediately
after the last deposit, if the fund grows at a rate of 12% per year? Solve using
(a) tabulated factors, and (b) a spreadsheet.
Problem 2.110
San Antonio is considering various options for providing water in their 50-year plan,
including desalting. One brackish aquifer is expected to yield desalted water that will
generate revenue of $4.1 million per year for the first 4 years, after which less production
will decrease revenue by 10% each year. If the aquifer will be totally depleted in
20 years, what is the present worth of the desalting option at an interest rate of 6% per
year?
Problem 2.111
Revenue from gas wells that have been in production for at least 5 years tends to follow
a decreasing geometric gradient. One particular rights holder received royalties of $4000
per year for years 1 through 6, but beginning in year 7, income decreased by 15% per
year through year 14. What was the future value in year 14 if all of the income was
invested at 10% per year?
Problem 2.112
A mechanical engineer conducting an economic analysis of wireless technology
alternatives discovered that the F/G factor values were not in his table. He decided to
create the (F/G,i,n) factor values himself. He did so by:
a. Multiplying the (F/A,i,n) and (A/G,i,n) values
b. Dividing (F/A,i,n) values by (A/G,i,n) values
c. Multiplying the (F/A,i,n) and (P/G,i,n) values
d. Multiplying the (P/G,i,n) and (A/F,i,n) values
Problem 2.113
The amount of money that would be accumulated in 10 years from an initial investment
of $1000 at an interest rate of 8% per year is closest to:
a. $2160
b. $2290
c. $2418
d. $2643
Problem 2.114
A manufacturer of triaxial accelerometers wants to have $2,800,000 available 10 years
from now so that a new product line can be initiated. If the company plans to deposit
money each year, starting one year from now, the equal amount to deposit each year at
6% per year interest in order to have the $2,800,000 available immediately after the last
deposit is closest to:
a. $182,000
b. $188,500
c. $191,300
d. $212,400
Problem 2.115
Yejen Industries Ltd. invested $10,000,000 in manufacturing equipment for producing
small wastebaskets. If the company uses an interest rate of 15% per year, the amount of
money it will have to earn each year to recover its investment in 7 years is closest to:
a. $2,403,600
b. $3,530,800
c. $3,941,800
d. $4,256,300
Problem 2.116
An engineer planning for retirement decides that she wants to have income of $100,000
per year for 20 years with the first withdrawal beginning 30 years from now. If her
retirement account earns interest at 8% per year, the annual amount she would have to
deposit for 29 years beginning 1 year from now is closest to:
a. $7360
b. $8125
c. $8670
d. $9445
Problem 2.117
A winner of the state lottery was given two choices: receive a single lump sum payment
now of $50 million or receive 21 uniform payments, with the first payment to be made
now, and the rest to be made at the end of each of the next 20 years. At an interest rate of
4% per year, the amount of the 21 uniform payments that would be equivalent to the
$50 million lump-sum payment is closest to:
a. $3,152,000
b. $3,426,800
c. $3,623,600
d. $3,923,800
Problem 2.118
The equivalent amount of money that can be spent seven years from now in lieu of
spending $50,000 now at an interest rate 18% per year is closest to:
a. $15,700
b. $159,300
c. $199,300
d. $259,100
Problem 2.119
Income from sales of an injector-cleaning gasoline additive has been averaging
$100,000 per year. At an interest rate of 18% per year, the future worth of the income in
years 1–5 is closest to:
a. $496,180
b. $652,200
c. $715,420
d. $726,530
Problem 2.120
The maker of a motion-sensing towel dispenser is considering adding new products to
enhance offerings in the area of touchless technology. If the company does not expand its
product line now, it will definitely do so in 2 years. Assume the interest rate is 10% per
year. The amount the company can afford to spend now if the cost 2 years from now is
estimated to be $100,000 is closest to:
a. $75,130
b. $82,640
c. $91,000
d. $93,280
Problem 2.121
Assume you borrow $10,000 today and promise to repay the loan in two payments, one
in year 2 and the other in year 4, with the one in year 4 being only half as large as the one
in year 2. At an interest rate of 10% per year, the size of the payment in year 4 will be
closest to:
a. $4280
b. $3975
c. $3850
d. $2335
Problem 2.122
Chemical costs associated with a packed-bed flue gas incinerator (for odor control) have
been decreasing uniformly for 5 years because of increases in efficiency. If the cost in
year 1 was $100,000 and it decreased by $5,000 per year through year 5, the present
worth of the costs at 10% per year is closest to:
a. $344,800
b. $402,200
c. $485,700
d. $523,300
Problem 2.123
If you borrow $24,000 now at an interest rate of 8% per year and promise to repay the
loan with payments of $3000 per year starting one year from now, the number of
payments that you will have to make is closest to:
a. 8
b. 11
c. 14
d. 17
Problem 2.124
You deposit $1000 now and you want the account to have a value as close to $8870 as
possible in year 20. Assume the account earns interest at 10% per year. The year in which
you must make another deposit of $1000 is
a. 6
b. 8
c. 10
d. 12
Problem 2.125
Maintenance costs for a regenerative thermal oxidizer have been increasing uniformly for
5 years. If the cost in year 1 was $8000 and it increased by $900 per year through year 5,
the present worth of the costs at an interest rate of 10% per year is closest to:
a. $31,670
b. $33,520
c. $34,140
d. $36,500
Problem 2.126
At an interest rate of 8% per year, the present worth in year 0 of a lease that requires a
payment of $9,000 now and amounts increasing by 8% per year through year 7 is closest
to:
a. $60,533
b. $65,376
c. $72,000
d. $69,328
Solution 2.1
Solution 2.2
P = 30,000(P/F,10%,8)
Solution 2.3
Solution 2.4
(b) Spreadsheet function is = -FV(10%,3,,100000) + 885000
Solution 2.5
(a) P = 19,000(P/F,10%,7)
Solution 2.6
Solution 2.7
(a) F = 3000(F/P,10%,12) + 5000(F/P,10%,8)
Solution 2.8
Solution 2.9
Solution 2.10
Solution 2.11
Solution 2.12
(a) A = 60,000(A/P,8%,5)
Solution 2.13
Solution 2.14
Solution 2.15
(a) 17,000,000(A/P,i,8) = 2,737,680
Solution 2.16
(a) A = 3,000,000(10)(A/P,8%,10)
Solution 2.17
Solution 2.18
P = 600,000(P/F,12%,4)
Solution 2.19
(a) A = 225,000(A/P,15%,4)
Solution 2.20
P = 100,000((P/F,12%,2)
Solution 2.21
Solution 2.22
Solution 2.23
Solution 2.24
The value of the system is the interest saved on $20 million for 2 years.
Solution 2.25
Solution 2.26
Solution 2.27
(a) A = 850,000(A/F,18%,5)
Solution 2.28
Solution 2.29
Solution 2.30
Solution 2.31
(b) Three calculator functions are added.
Solution 2.32
= $133,406
Solution 2.33
Solution 2.34
Solution 2.35
Solution 2.36
P = 1,500,000(P/A,8%,4)
Solution 2.37
Solution 2.38
P = 280,000(P/A,18%,8)
Solution 2.39
= $1,301,475
Solution 2.40
A = 5000(7)(A/P,10%,10)
Solution 2.41
(a) F = 70,000(F/P,12%,6) + 90,000(F/P,12%,4)
Solution 2.42
Solution 2.43
(a) Let CF4 be the amount in year 4
Solution 2.44
Solution 2.45
Solution 2.46
Solution 2.47
Solve for n by trial and error:
Solution 2.48
Solve for n by trial and error (in $ thousands):
By interpolation, n is between 32 and 33, and close to 32 years.
Solution 2.49
Solution 2.50
Solution 2.51
(a) 84,000 = 15,000 + G(A/G,10%,5)
Solution 2.52
Solution 2.53
Solution 2.54
P = 20,000(P/A,10%,10) + 2000(P/G,10%,10)
Solution 2.55
Solution 2.56
Solution 2.57
(a) Income = 390,000 – 2(15,000)
Solution 2.58
Solution 2.59
Factors: First find P and then convert to F
Solution 2.60
Convert F to A or P and then plug values into A/G or P/G equation.
Using A:
Solution 2.61
Solution 2.62
First find P and then convert to F
Solution 2.63
P = 950,000(800)(P/A,10%,5) + 950,000(800)(0.15)(P/G,10%,5)
Solution 2.64
Solution 2.65
Find present worth of geometric gradient, then F after 20 years
Solution 2.66
Solution 2.67
First find P and then convert to A. (in million-people units)
Solution 2.68
First find P and then convert to A
Solution 2.69
Solve for A1 in geometric gradient equation
Solution 2.70
Solve for P in geometric gradient equation and then convert to A
Solution 2.71
First find P and then convert to F
Solution 2.72
(b) Read Section A.4 first. Enter series into cells with any starting value for year
Solution 2.73
Solve for A1 in geometric gradient equation and then find cost in year 3
Solution 2.74
Solve for A1 in geometric gradient equation
Solution 2.75
First find P and then convert to F
Solution 2.76
Solution 2.77
Solution 2.78
F = 8000(F/A,10%,5)
Solution 2.79
Solution 2.80
P = 97,000(P/A,10%,4)(P/F,10%,1)
Solution 2.81
Use this F value as a present worth to calculate A for the next 5 years
Solution 2.82
Solution 2.83
Solution 2.84
(a) 1. For $5000 in year 0, find A in years 1-9
(b)
Solution 2.85
Find the future worth Fpaid of 3 payments in year 4
Find total amount owed Fowed after 4 years
Solution 2.86
(a) First find present worth of A = $200 in years 1 through 7
(b) Use PMT with an embedded NPV function to calculate annual equivalent.
Solution 2.87
Find P in year 7, move to year 25, and then solve for A
Solution 2.88
Find P in year 0 then convert to F. In $ million units,
Solution 2.89
Solution 2.90
Power savings = 1,000,000(0.15) = $150,000
Solution 2.91
= $24,932
Spreadsheet:
Solution 2.92
Solution 2.93
Find F in year 7 and convert to A
Solution 2.94
In $ billion units,
Solution 2.95
(a) Net income, years 1-8 = $7,000,000
Solution 2.96
Solution 2.97
First find F in year 8 and then solve for A
Solution 2.98
In $ million units
Solution 2.99
Solution 2.100
Find P in year -1 for geometric gradient, than move to year 0 to find P
Solution 2.101
(a) Factors: Find P in year –1 using gradient factor and then move forward 1 year
Solution 2.102
Solution 2.103
Find P in year –6 using arithmetic gradient factor and then find F today
Solution 2.104
Move development cost to year –1 and set equal to income
Solution 2.105
Move $20,000 to year 0, add and subtract $1600 in year 4 to use gradient, and solve for x
Solution 2.106
(a) Add and subtract $2400 and $2600 in periods 3 and 4, respectively, to use gradient
Solution 2.107
Find P in year 1 for geometric gradient; move back to year 0
Solution 2.108
Find P in year 2, then move back to year 0
Solution 2.109
(a) Find P in year 4 for the geometric gradient, then move all cash flows to future
(b) Spreadsheet
Solution 2.110
Find P in year 3, then find present worth of all cash flows
Solution 2.111
Find P in year 5, then find future worth of all cash flow:
Solution 2.112
Solution 2.113
Solution 2.114
Solution 2.115
Solution 2.116
Solution 2.117
Solution 2.118
Solution 2.119
Solution 2.120
P = 100,000(P/F,10%,2)
Solution 2.121
10,000 = 2x(P/F,10%,2) + x(P/F,10%,4)
Solution 2.122
P = 100,000(P/A,10%,5) – 5000(P/G,10%,5)
Solution 2.123
Solution 2.124
1000(F/P,10%,20) + 1000(F/P,10%,n) = 8870
Solution 2.125
Solution 2.126
P-1 = A1(n/1+i)
