lecture 8 9

© Faculty of Mechanical Engineering, GIKI

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ME 291Engineering

Economy

Lecture 8

Chapter 3

Combining Factors

Faculty of Mechanical EngineeringGhulam Ishaq Khan Institute, Topi, Swabi


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Calculations for Uniform Series that are shifted

• When a uniform series begins at a time other than at the end of period 1, it is called a shifted series.

• The present worth is always located one period prior to the first uniform series amount when using the P / A factor.

• The future worth is always located in the same period as the last uniform series amount when using the F / A factor.

• Steps to solve a shifted series– Draw a diagram of the positive and negative cash flows.– Locate the present worth or future worth of each series

on the cash flow diagram.– Determine n for each series by renumbering the cash

flow diagram.– Draw another cash flow diagram representing the

desired equivalent cash flow.– Setup and solve the equations.


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Example 3.1

• An Engineering technology group just purchased new CAD software for $5000 now and annual payments of $500 per year for 6 years starting 3 years from now for annual upgrades. What is the present worth of the payments if the interest rate is 8% per year?


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Example 3.2

• Recalibration of sensitive devices cost $8000 per year. If the machine will be recalibrated for each 6 years starting 3 years after purchase, calculate the 8-year equivalent uniform series at 16% per year.


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Calculations involving uniform-series and randomly placed single amounts

• When a cash flow includes both a uniform series and randomly placed amounts, both are handled separately.

• Total is then calculated, by summing them.


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Example 3.3

• An engineering company in Quetta that owns 50 hectares of valuable land has decided to lease the mineral rights to a mining company., the primary objective is to obtain long term income to finance ongoing projects 6 and 16 years from the present time. The engineering company makes a proposal to the mining company that it pay $20,000 per year for 20 years beginning 1 year from now, plus $10,000 six years from now and $15,000 sixteen years from now. If the mining company wants to pay off its lease immediately, how much it should pay if the investment should make 16% per year?


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Example 3.4

• Assume similar cash flow estimate to those projected in the previous example for the engineering company planning to lease its mineral rights. However, move the beginning year for the $20,000 per year series forward 2 years to start in year 3. it will now continue through year 22. Utilize engineering economy relations to determine the five equivalent values listed below at 16% per year.

– Total present worth PT in year 0

– Future worth F in year 22

– Annual series over all 22 years

– Annual series over the first 10 years

– Annual series over the last 12 years


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Example 3.4 (Cash Flow Diagram)


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Calculations for Shifted Gradients

• The present worth of an arithmetic gradient will always be located two periods before the gradient starts.

• To find the equivalent A series of a shifted gradient through all the periods, first find the present worth of the gradient at actual time 0, then apply the (A / P, i , n) factor.


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Example 3.5

• Gerri, an engineer at Fujitsu, has tracked the average inspection cost on a robotics manufacturing line for 8 years. Cost averages were steady at $100 per completed unit for the first 4 years, but have increased consistently by $50 per unit for each of the last 4 years. Gerri plans to analyze the gradient increase using the P/G factor. Where is the present worth located for the gradient? What is the general relation used to calculate total present worth in year 0?


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Example 3.6

• Setup the engineering economy relations to compute the equivalent annual series in year 1 through 7 for the cash flow estimate in figure below.


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Example 3.7

• Chemical engineers at a Coleman Industries plant in the Midwest have determined that a small amount of a newly available chemical additive will increase the water repellency of Coleman’s tent fabrics by 20%. The plant superintendent has arranged to purchase the additive through 5-year contract at $7000 per year, starting 1 year from now. He expects the annual price to increase by 12% per year thereafter for the next 8 years. Additionally, an initial investment of $35,000 was made now to prepare a site suitable for the contractor to deliver the additive. Use i=15% to determine the equivalent total present worth for all these cash flows.


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Figure Example 3.7


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Example 3.8

Assume that you are planning to invest money at 7% per year as shown by the increasing gradient of figure below. Further, you expect to withdraw according to the decreasing gradient shown. Find the net present worth and equivalent annual series for the entire cash flow sequence and interpret the results.


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Example 3.10

• Present worth by combining factors

– Calculate the total present worth of the following series of cash flows at i = 18% per year.

lecture 8 9

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