EE 200: Engineering Economics 2 Time Value of Money

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136 ENGINEERING ECONOMICS

ENGINEERING ECONOMICS

Factor Name Converts Symbol Formula Single Payment Compound Amount to F given P (F/P, i%, n) (1 + i)

n

Single Payment Present Worth to P given F (P/F, i%, n) (1 + i)

–n

Uniform Series Sinking Fund to A given F (A/F, i%, n) ( ) 11+ ni

i

Capital Recovery to A given P (A/P, i%, n) ( )

( ) 11 1 +

+ n

n

i ii

Uniform Series Compound Amount to F given A (F/A, i%, n)

( ) i i n 11+

Uniform Series Present Worth to P given A (P/A, i%, n)

( ) ( )n

n

ii i +

+ 1

11

Uniform Gradient Present Worth to P given G (P/G, i%, n)

( ) ( ) ( )nn

n

ii n

ii i

++ +

11 11

2

Uniform Gradient † Future Worth to F given G (F/G, i%, n)

( ) i n

i i n+

2 11

Uniform Gradient Uniform Series to A given G (A/G, i%, n) ( ) 11

1 + ni n

i

NOMENCLATURE AND DEFINITIONS A ?????????????Uniform amount per interest period B ?????????????Benefit BV ???????????Book value C ?????????????Cost d??????????????In ation ad usted interest rate per interest period Dj ????????????Depreciation in year j EV ???????????Expected value F ?????????????Future worth, value, or amount f ?????????????? eneral in ation rate per interest period G ?????????????Uniform gradient amount per interest period i ??????????????Interest rate per interest period ie ?????????????Annual effective interest rate MARR ????Minimum acceptable/attractive rate of return m ?????????????Number of compounding periods per year n??????????????Number of compounding periods; or the expected

life of an asset P ?????????????Present worth, value, or amount r ??????????????Nominal annual interest rate Sn ????????????Expected salvage value in year n

Subscripts j ??????????? at time j n??????????? at time n †??????????? F/G = (F/A – n)/i = (F/A) × (A/G)

Risk Risk is the chance of an outcome other than what is planned to occur or expected in the analysis?

NON-ANNUAL COMPOUNDING

i m r1 1e m

= + -b l

BREAK-EVEN ANALYSIS By altering the value of any one of the variables in a situation, holding all of the other values constant, it is possible to find a value for that variable that makes the two alternatives equally economical? This value is the break-even point? Break-even analysis is used to describe the percentage of capacity of operation for a manufacturing plant at which income will ust cover expenses. The payback period is the period of time required for the profit or other benefits of an investment to equal the cost of the investment?

Time Value of Money Relating Future and Present Worth Shows Unreasonable Costs

3 ?? is Future Worth ?? is Present Worth ?? is the number of compounding periods ?? is Uniform Amount per interest period (Payment) ?? is the interest rate per period

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10/31/19

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College Costs Have Historically Increased Faster than Inflation: Compound Interest Model

• Umich: Total Annual Cost o 1980: $3,500 o 2020: $30,000 o At 3% annual inflation o Should be: $11,417 o From ?? = ?? 1 + ?? )

§ ?? = $3,500 § ?? = 0.03 = 3% annual

inflation

§ ?? = 40 years

• Effective Umich Inflation rate • Given ??, ??, ??; Find ?? • Rearranging: ?? = ?? 1 + ?? )

o ?? = 2 3Write a artical about the material on engineering economics presented in the pdf

1.part 1: Write a summary at least 250 words as counted by Microsoft Word of the material presented in the pdf. The summary should be written as if summarizing material succinctly for a superior. It should not contain your opinions or reflections, just the key points.

2.part 2: Personal Reflection. At least 250 words as counted by Microsoft Word. Write a response to the material presented in the pdf. The reflection can include your opinions on the material, ideas with which you agreed, ideas with which you disagreed, ideas you found interesting, and any personal life experiences related to the ideas raised.

3.part3: Write 2-3 questions about the material presented and/or read that you have after the presentation/reading (without answer)

4. part4: For part 4, focus your action plan on how you can use tonights material to change your personal behavior about money. (about 100 word).