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CHAPTER
2
Time Value of Money
1. A contractor borrowed $250,000 from a bank at an interest rate of 6% to purchase new
construction equipment. What annual payment must the contractor make if the loan is to be
paid off in 10 years?
2. A grader costs $350,000 to purchase and is expected to have a useful life of 8 years. Annual
operating, maintenance, and labor costs are estimated to be $35,000 per year, and the salvage
value after 8 years of use is estimated to be $50,000. At an interest rate of 9%, what is the
present worth equivalent cost to the contractor of owning and operating the grader?
3. Using an interest rate of 12%, find the equivalent uniform annual cost for a piece of
construction equipment that has an initial purchase cost of $80,000, an estimated economic
life of 8 years, and an estimated salvage value of $10,000. Annual maintenance will amount
to $600 per year and periodic overhauls costing $1,000 each will occur at the end of the 2nd,
4th, and 6th years.
4. A company owns a fleet of trucks and operates its own maintenance shop. A certain type of
truck, normally used for 5 years, has an initial cost of $45,000 and a salvage value of
$75,000. Maintenance costs are $7,000 for the first year and increase by $2,000 each year.
Assuming interest at 10%, find the equivalent annual cost of owning and maintaining the
truck. 𝐴=($45,000)(𝐴𝑃
5. A contractor knows that she must replace her forklift in 12 years at an estimated cost of
$195,000. She plans to start making deposits into a bank account at the beginning of the year
3 years from now and continue until the end of the eighth year (7 equal payments). How
much money should she deposit in each of the 7 years at an interest rate of 6% to have the
needed $195,000 at the end of the 12 years?
6. A contractor knows that he must replace a mobile crane in 10 years at an estimated cost of
$600,000. How much should he deposit today and at the beginning of each of the next 7
years (8 equal payments) at an interest rate of 10% to have the needed $600,000 at the end of
the 10 years?
Commented [GM1]: There is a typo in the book. The
salvage value should be $7,500. We used the correct value in
the solution
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7. A contractor has purchased 5 elevating scrapers for $650,000 each and plans to use them for
about 12,500 hours of operation. He expects to be able to sell the used scrapers for 10% of
the purchase price after 12,500 hours of use. Tires cost about $20,000 per set to replace
(estimated to occur after 2,500 hours of use). What is the estimated ownership cost of each
scraper (in $/hour) if its annual usage is estimated to be 1,250 hours per year?
8. A contractor is considering the purchase of a new truck for $40,000 which has an estimated
useful life of 8 years. He believes that he can sell the used truck for $8,000 at the end of the
8 years. Annual operating costs are estimated to be $2,000 per year. As an alternative, the
contractor can purchase a used truck for $20,000 with an estimated useful life of 4 years.
Annual operating costs for the used truck are estimated to be $2,800 per year, and the salvage
value should be $2,000 at the end of the 4 years. At an interest rate of 8%, which alternative
should the contractor select?
9. The question arises whether it is more economical to replace the engine on a tractor with a
new one, or rebore the cylinders of the old engine and thoroughly recondition it. The original
cost of the engine 10 years ago was $7,000. To rebore and recondition it now will extend its
useful life for an estimated 5 years and will cost $2,800. A new engine will have an initial
cost of $6,200 and will have an estimated life of 10 years. It is expected that the annual cost
of fuel and lubricants with the reconditioned engine will be about $2,000 and that this cost
will be 15% less with the new engine. It is also believed that repairs will be about $250 a
year less with the new engine than with the reconditioned one. Assume that neither engine
has any realizable value when retired. At an interest rate of 6%, which alternative should be
selected?
10. A contractor has purchased a small backhoe for $120,000 that he plans to use in excavating
ditches for utilities construction. He plans to use the backhoe for 8 years and sell the used
machine for $40,000. He must replace the tires on the backhoe after each 3,000 hours of use
at a cost of $15,000. Annual operating and labor costs are estimated to be $20,000 per year.
The contractor estimates that the backhoe will be used about 1,000 hours per year. If the
minimum attractive rate of return is 12%; what is the hourly owning and operating cost for
the backhoe?
11. A used tracked dozer costs $135,000. It will be operated for 5 years, when it will be sold for
an estimated value of $65,000. It will cost $80,000 to maintain and operate for the first year.
This will increase by $5,000 per year over the life of the machine. If the prevailing rate for
interest, insurance, taxes, and storage is 14%; what is the equivalent annual cost of owning
and operating the machine?
12. A project has a first cost of $120,000 and an estimated salvage value after 25 years of
$20,000. Estimated average annual receipts are $25,900; estimated average annual
disbursements are $15,060. Assuming that annual receipts and disbursements will be
uniform, compute the prospective rate of return.
$120,000+($15,060)(𝑃𝐴
13. A contractor has purchased a small excavator for $280,000 that she plans to use for 10 years.
She anticipates that the used excavator can be sold for $25,000 after 10 years of use.
Average annual earnings generated by the excavator are estimated to be $125,000, and the
average operating and labor costs are estimated to be $75,000. What is the estimated rate of
return that the excavator will generate for the contractor?
14. A contractor has purchased a wheeled loader for $130,000 and expects to use the loader an
average of 1,500 hours per year. Tires cost $6,000 to replace (estimated to occur after each
4,500 hours of use) and major repairs will be needed every 6,000 hours at a cost of $5,000.
The contractor expects to be able to sell the loader for $10,000 after she has used it for
15,000 operating hours. Fuel, oil, and minor maintenance cost about $19.75 for each hour
the loader is used. Interest, insurance, and taxes total about 16%. How much should the
contractor charge per hour for use of the loader to recover her costs?