EE 200: Engineering Economics 2 Time Value of Money
2
2
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
2
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 + ?? )
§ ?? = $3,500 § ?? = 0.03 = 3% annual
inflation
§ ?? = 40 years
Effective Umich Inflation rate Given ??, ??, ??; Find ?? Rearranging: ?? = ?? 1 + ?? )
o ?? = 2 3
4 5 ? 1
o ?? = 0.0055 = 5.5%
4
Probably a bit high ee200.m Part A
4
Fred Wilma Barney Betty Dino Description
Age 35 30 25 20 20 Age starting retirement savings
n yrs 20 20 15 10 45 Years making deposit of A k$
N yrs 30 35 40 45 45 Years of investing (65 Age)
A k$ 10 7.5 5 5 2 Annual lump sum deposit
Retirement Savings Analysis Drives Strategy You Should Adopt Upon Graduation
5 Cases shown below Assumptions
o Stock market average annual rate of return is 10%
o Contribute same annual amount for ?? years starting at ??????
Assumptions (cont.) o Investments compound after that
for N ? ?? years to Age 65 o Determine projected retirement
account value at Age 65
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7
10/31/19
3
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
