Engineering economic analysis involves present and future economic factors; thus, it is critical to obtain reliable estimates of future costs, benefits and other economic parameters. Several methods to do so are discussed here.

Estimates can be rough estimates, semi detailed estimates, or detailed estimates, depending on the needs for the estimates.

A characteristic of cost estimates is that errors in estimating are typically nonsymmetric because costs are more likely to be underestimated than overestimated.

Difficulties in developing cost estimates arise from such conditions as one-of-a-kind estimates, resource availability, and estimator expertise. Generally the quality of a cost estimate increases as the resources allocated to developing the estimate increase. The benefits expected from improving a cost estimate should outweigh the cost of devoting additional resources to the estimate improvement.

Several models are available for developing cost (or benefit) estimates.

The **per-unit model** is
a simple but useful model in which a cost estimate is made for a single unit,
then the total cost estimate results from multiplying the estimated cost per
unit times the number of units.

The **segmenting model**
partitions the total estimation task into segments. Each segment is
estimated, then the segment estimates are combined for the total cost estimate.

**Cost indexes** can be used to account for historical
changes in costs. The widely reported Consumer Price Index (CPI) is an
example. Cost index data are available from a variety of sources. Suppose
A is a time point in the past and B is the current time. Let IV_{A}
denote the index value at time A and IV_{B} denote the current index
value for the cost estimate of interest. To estimate the current cost
based on the cost at time A, use the equation:

Cost at time B = (Cost at
time A) (IV_{B} / IV_{A}).

The **power-sizing model**
accounts explicitly for economies of scale. For example, the cost of
constructing a six-story building will typically be less than double the
construction cost of a comparable three-story building. To estimate the cost of
B based on the cost of comparable item A, use the equation

Cost of B = (Cost of A) [ ("Size" of B) /
("Size" of A) ] ^{x}

where x is the appropriate power-sizing exponent, available from a variety of sources. An economy of scale is indicated by an exponent less than 1.0 An exponent of 1.0 indicates no economy of scale, and an exponent greater than 1.0 indicates a diseconomy of scale.

"Size" is used here in a general sense to indicate physical size, capacity, or some other appropriate comparison unit.

**Learning curve** cost estimating is based on the
assumption that as a particular task is repeated, the operator systematically
becomes quicker at performing the task. In particular, the model is based
on the assumption that the time required to complete the task for production
unit 2x is a fixed percentage of the time required for production unit x for
all positive, integer x. The learning curve slope indicates "how
fast" learning occurs. For example, a learning curve rate of 70%
represents much faster learning than a rate of 90%. If an operator
exhibits learning on a certain task at a rate of 70%, the time required to
complete production unit 50, for example, is only 70% of the time required to
complete unit 25.

Let b = learning curve
exponent

= log (learning curve rate in decimal form) / log 2.0

Then T_{N} = time estimate
for unit N (N = 1, 2, ...)

= (T_{1}) (N)^{b}

where T_{1} is the
time required for unit 1.

As an example: A learning
curve rate is 70%, the operator’s time for the first^{t} unit is 65 seconds.
What is the operator’s time for the 50^{th} unit?

T_{100} = T_{1}
* (50) ^ b = 65 * (50) ^ -0.5145 = 8.68 min

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Question 1.

The cost to provide workplace safety training to a new employee is estimated at $600 for a particular manufacturer. Use the per-unit cost estimating model to estimate the annual workplace safety training cost if an estimated 30 new employees are hired annually.

Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed.

A $600

B $1,800

C $6,000

D $18,000

Question 2.

Given the data below, use the segmenting model to estimate a manufacturer's total annual cost.

Estimated annual production volume = 400,000 units

Estimated direct labor cost per unit = $3.75

Estimated indirect labor cost per unit = $0.92

Estimated raw material and purchased part cost per unit = $32.50

All other costs are independent of production volume and are estimated at $800,000 per year.

Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed.

A $2,668,000

B $15,668,000

C $14,868,000

D $15,300,000

Question 3.

Given the data below, use the
segmenting model to estimate a manufacturer's ** average cost per unit**
produced. Note that this is different from the previous question.

Estimated annual production volume = 400,000 units

Estimated direct labor cost per unit = $3.75

Estimated indirect labor cost per unit = $0.92

Estimated raw material and purchased part cost per unit = $32.50

All other costs are independent of production volume and are estimated at $800,000 per year.

Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed.

A $37.17

B $34.50

C $39.17

D $6.67

Question 4.

Use the cost index method to estimate the current construction cost for a building equivalent to one constructed in 1980 at a cost of $2.7 million. According to the Engineering News-Record, the 1980 average Building Cost Index was 1941. Suppose that the current year Building Cost Index has been estimated at 3620.

(Source: http://enr.construction.com/features/conEco/costIndexes/bldIndexHist.asp)

Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed.

A $5.400 million

B $5.036 million

C $5.170 million

D $3.620 million

Question 5.

Use the power-sizing model to estimate the cost of a piece of equipment that has 75% more capacity than a similar piece of equipment that cost $1,000. The appropriate power sizing exponent for this type of equipment is 0.725.

Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed.

A $1,750

B $725

C $750

D $1,500

Question 6.

Use a combined cost index and the power-sizing cost estimating model to estimate the current cost of a piece of equipment that has 50% more capacity than a similar piece of equipment that cost $30,000 five years ago. The appropriate power-sizing exponent for this type of equipment is 0.8, and the ratio of the cost indexes (current to 5 years ago) is 1.24. (Note that this is more complex than the previous questions.)

Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed.

A $29,760

B $51,454

C $55,800

D $44,640

Question 7.

At a learning curve rate of 80%, estimate the time in minutes required to assemble production unit number 100 given that the first production unit required 74.8 minutes to assemble.

Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed.

A 17.0

B 47.9

C 59.8

D 74.8

Question 8.

At a learning curve rate of 80%, estimate the time in minutes required to assemble production unit number 100 given that unit number 50 required 20.0 minutes to assemble.

Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed.

A 10.0

B 11.5

C 16.0

D 20.0