Engineering Economy

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Engineering Economy Practice Problems for Exam
5 By Douglas Rittmann, Ph.D., P.E
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1. The cost of a machine for producing a certain
part is 40,000. The machine is expected to have
a maintenance cost of 14,000 and an 8,000
salvage value after its 5-year economic life. If
the variable cost for producing the part is 1.50
per unit and the part can be sold for 4.00 per
unit, how many parts per year must the company
sell in order to breakeven at an interest rate of
12 per year?
Solution - Let x represent the number of parts
per year required for breakeven. The annual worth
equation is        0 -40,000 (A/P, 12, 5) -
14,000 8000 (A/F, 12, 5) - 1.50x
4.00x        0 -40,000 (0.27741) - 14,000
8000 (0.15741) 2.50x  -2.50x
-23,837        x 9,534 parts/yrThus, if the
company expects to sell more than 9,534 parts per
year, it should produce the part. At any sales
level below 9,534 parts per year, the company
would lose money and, therefore, should not
invest in the machine.
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2. A company can purchase a certain machine or
rent one. If purchased, the machine will cost
15,000 and will have a 5-year life with a 10
salvage value. Its operating cost will be 8000
per year. If the machine is rented, it will cost
400 per day. At an interest rate of 10 per
year, the minimum number of days the machine must
be needed to justify its purchase is
Solution -15,000 (A/P, 10, 5) - 8,000
1,500 (A/F, 10, 5) -400x                  
-15,000 ( 0.2638 ) - 8,000 1,500 (0.1638) 
-400x                                            
                                             x
29.2
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Present Worth Computations with
Inflation Inflation is an increase in the amount
of money necessary to obtain the same amount of
goods. This occurs when the value of the currency
goes down from one time period to the next.
Different-valued currencies (in different time
periods) must be accounted-for, because economic
calculations span many time periods. That is to
say, we must account for not only for money's
time value, but also its actual value. Up to now,
we assumed that the value (i.e. worth) of the
currency was the same from one time period to the
next.
There are two ways to make meaningful economic
calculations when the value of the currency is
changing (1) Convert the amounts that occur in
the different time periods into amounts that make
the currencies have the same value before time
value calculations are made, or (2) change the
interest rate that is used in the economic
equations in such a way that it accounts for the
different valued currencies as well as the time
value of money.
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The first case is called making calculations in
constant-value dollars (also known as today's
dollars). Money in one period of time, t1, will
have the same value as money in another period of
time, t2, when the t2 amount is divided by the
inflation that occurred between the two time
periods. The general equation is       Eq
14.1  Dollars in period  t1     dollars in
period t2                                      
                         
Inflation between t1 and t2
Let dollars in period t1 be called today's
dollars and dollars in period t2 be called future
dollars or then-current dollars. If f represents
the inflation rate per period and n is the number
of periods between t1 and t2, Equation 14.1
becomes        Today's dollars   then-current
dollars                                         
   (1 f)n
Once this conversion has been made, then the
interest rate that must be used in the economic
equations is the real interest rate. The real
interest rate, i, is the rate that represents
time-value-of-money-only considerations when
money is moved from one time period to another.
This is the rate that was used in all
calculations up to this point. The market
interest rate (or inflated interest rate) is a
combination of the real interest rate, i, and the
inflation rate, f. In equation form, the inflated
interest rate, if, is    if i f ( i f )
,  where i real interest rate f inflation
rate if inflated interest rate
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Cost Indexes A cost index is a ratio of the cost
of something today to its cost at some time in
the past. As such, it is a tool which can be used
to estimate the cost of things today based on
their cost some time ago. This endeavor is
especially important to engineers who are
involved in design because cost is probably the
single most important factor in the design of
anything.Many of the indexes that are
frequently used by engineers are updated monthly
and published in professional journals like
Engineering News Record (ENR) and Chemical
Engineering. Table 15-1 shows the values for
three of the most common indexes for the years
1985 thru 1999.
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News Record (ENR) and Chemical Engineering. Table
15-1 shows the values for three of the most
common indexes for the years 1985 thru
1999.                                            
                                                  
                                      
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The general equation for updating costs through
the use of a cost index is                      
  Ct Co (It)   /   Io                          
                  1    
           where Ct estimated cost at present
time t                         Co cost at
previous time to                         It
Index value at time t                         Io
Index value at time to The next example
illustrates its use Example 15.1 An engineer
involved in a major construction project
discovered that a similar project had been
completed in 1990.  If the previous project had a
construction cost of 1.545 million, what would
the estimated construction cost be in 1999 based
on the ENR construction cost index?
Solution From Table 15.1, the ENR construction
cost index rose from a value of 4770.03 in 1990
to 6059.47 in 1999.  Therefore, the estimated
construction cost in 1999 would be              
          C1999 1.545 (6059.47)  / 4770.03    
                             1,963,000
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A 20 HP centrifugal pump (with motor) can be
purchased for 1500. For an exponent value of
0.46 in the cost-capacity equation, the cost of a
100 HP pump would be estimated to be(A)
1,653      (B) 2,295      (C) 2,835     (D)
3,145
Solution C100 1500 (100/20)0.46
3,145 Answer is (D)
The ENR Construction Cost Index values for 1990
and 1997 are 4770.03 and 5851.80, respectively.
If the index is changed so that 1990 is to have a
base value of 100, the value in 1997 would be
closest to(A) 115.21      (B) 122.68       (C)
1250.03     (D) over 126
Solution Divide 1997 value by the 1990 value and
multiply by 100 1997 value (5851.80) (100) /
4770.03 122.68 Answer is (B)
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Depreciation and Depletion One definition of the
word depreciation is to lessen in estimated
value  lower the worth of. In general, the
value of an asset decreases with time because of
age, wear, or obsolescence. A number of methods
for systematically expressing the decreasing
value of assets with time have been developed
over the years. These so-called depreciation
models result in values which (1) affect income
taxes, and (2) provide information to investors
about the worth of the assets of public
companies. Depreciation affects income taxes
because it is one of the deductions (from income)
that businesses can take before calculating the
amount of taxes they owe per the following
equation Taxes (income deductions) (tax rate)
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Since depreciation is a deduction (just as labor
costs, rent, and other expenses are for
businesses), the taxes owed are reduced by an
amount equal to the depreciation times the tax
rate (assuming income stays the same).  For
example, a business that has a depreciation
deduction of 5000 in a year when its tax rate is
40 would have its tax bill reduced by 2000 that
year (i.e. 5000 0.40). The depreciation
calculated for this purpose is called tax
depreciation and must be determined using only
IRS-approved models. Book depreciation refers to
the depreciation procedures used by corporations
to more accurately reflect to shareholders the
value of their assets.  Two of the models used
for depreciating assets are discussed below. The
modified accelerated cost recovery system (MACRS)
is the only currently-approved depreciation model
allowed for tax depreciation in the United
States.  According to this model, the
depreciation charge for a given year is
calculated by multiplying the assets depreciable
amount (known as its basis, B, which is usually
its first cost) by a depreciation rate. In
equation form, MACRS depreciation is Dt
dtB where dt depreciation rate,
                       B Assets
basis,
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Thus, the depreciation charge in year 3 for a
10,000 asset which has a 5-year recovery would
be 1,920 (i.e. 10,000 0.1920)
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The book value of an asset refers to its
undepreciated amount and is represented as the
difference between the first cost, B, and the sum
of the depreciation that has been charged up to
that time. In equation form, BVt B - ?D
          (B - Sums of D's )
For example, an asset that costs 10,000 and has
a 5-year recovery period would have a book value
at the end of year 3 equal to BV3 10,000
10,000 (0.20) 10,000 (0.32) 10,000 (0.1920)  
         10,000 10,000 (0.20 0.32
0.1920)                    2,880
While the MACRS model is the only one approved
for tax depreciation, a model frequently used by
corporations for book depreciation is the
straight line model. Under this model, the
depreciation charge is the same each year per the
following equation D (B SV) / n
where B Asset first cost                
               SV Asset salvage value          
                        n Asset life
Thus, an asset which has a first cost of 10,000
with an expected salvage value of 2000 after a
5-year useful life would have a depreciation
charge of 1,600 each year ?i.e.(10,0002000)/5?.
The book value of an asset depreciated by the
straight line method would be BVt B tD
where t no. of years asset has been depreciated
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The depreciation models discussed up to this
point apply to assets that can be replaced. For
assets that cannot be replaced, like natural
resources, different procedures are used for tax
accounting purposes. There are two methods which
can be used to account for this so-called
depletion cost depletion and percentage
depletion. Cost depletion involves the
multiplication of a cost factor, pt, by the
amount of resource removed in a given year. The
factor, Pt, is equal to the first cost of the
resource divided by the total amount of
recoverable resource            Pt (first
cost)  / resource capacity
The annual depletion deduction is Pt times the
amount of resource harvested in that year. For
example, if a gold mine which cost 1,000,000 had
an estimated 4000 ounces of gold, the depletion
factor would be 250 per ounce (i.e.
1,000,000/4000). The depletion charge in a year
when 1,000 ounces is removed would be 250,000
(i.e. 250 1000). Percentage depletion is a
procedure wherein a certain percentage of the
income from harvesting the resource is taken as
the deduction. The percentage that is taken is a
function of the type of resource involved as
shown in the table below
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Thus, if 10,000 ounces of gold are harvested in a
year when gold is selling for 270 per ounce, the
depletion allowance deduction would be (0.15)
(10,000) (270) 405,000 (subject to certain tax
law restrictions).
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Questions?