ctc 475 review cost estimates job quotes (distributing overhead) – rate per direct labor hour –...
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CTC 475 Review
Cost Estimates• Job Quotes (distributing overhead)– Rate per Direct Labor Hour– Percentage of Direct Labor Cost– Percentage of Prime (Labor+Matl) Cost
• Present Economy Problems– No capital investment– Long-term costs are same– Alternatives have identical results
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CTC 475
Interest and Single Sums of Money
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Objectives
• Know the difference between simple and compound interest
• Know how to find the future worth of a single sum
• Know how to find the present worth of a single sum
• Know how to solve for i or n
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Time Value of Money
• Value of a given sum of money depends on when the money is received
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Which would you prefer?
EOY Cash Flow
0 (100,000)
1 70,000
2 50,000
3 30,000
4 10,000
Total + 160,000
EOY Cash Flow
0 (100,000)
1 10,000
2 30,000
3 50,000
4 70,000
Total + 160,000
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Which Would you Prefer?
EOY Cash Flow
0 (5,000)
1 1,500
2 1,500
3 1,500
4 1,500
5 0
Total + 6,000
EOY Cash Flow
0 (5,000)
1 0
2 1,500
3 1,500
4 1,500
5 1,500
Total + 6,000
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Money Has a Time Value
• Money at different time intervals is worth different amounts
• Time (or year at which cash flow occurs) must be taken into account
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Simple vs Compound Interest
• If $1,000 is deposited in a bank account, how much is the account worth after 5 years, if the bank pays
• 3% per year ---simple interest?• 3% per year ---compound interest?
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Simple vs Compound Interest
EOY Cash Flow-Simple
0 $1,000
1 $1,030
2 $1,060
3 $1,090
4 $1,120
5 $1,150
EOY Cash Flow-Compound
0 $1,000.00
1 $1,030.00
2 $1,060.90
3 $1,092,73
4 $1,125, 51
5 $1,159.27
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Simple Interest Equation
• Simple—every year you earn 3% ($30) on the original $1000 deposited in the account at year 0
Fn=P(1+i*n)Where: F=Future amount at year nP=Present amount deposited at year 0i=interest rate
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Compound Interest Equation
• Compound—every year you earn 3% on whatever is in the account at the end of the previous year
Fn=P(1+i)n
Where: F=Future amount at year nP=Present amount deposited at year 0i=interest rate
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Example-Simple vs Compound
An individual borrows $1,000. The principal plus interest is to be repaid after 2 years. An interest rate of 7% per year is agreed on. How much should be repaid using simple and compound interest?
Simple: F=P(1+i*n)=1000(1+.07*2)=$1,140
Compound: F=P(1+i)n=1000(1.07)2=$1,144.90
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Simple or Compound?
• In practice, banks usually pay compound interest
• Unless otherwise stated assume compound interest is used
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Factor Form
• Previous slide shows equation form for compound interest
• The factor form is a shortcut used to find answers faster from tables in the book
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Factor Form
• F=P(F/Pi,n)
Find the future worth (F) given the present worth (P) at interest rate (i) at number of interest periods (n)
Future worth=Present worth * factor Note that the factor=(1+i)n
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Example of Find F given P problem-Equation vs Factor
An individual borrows $1,000 at 6% per year compounded annually. If the loan is to be repaid after 5 years, how much will be owed?
Equation: F=P(1+i)n=1000(1.06)5=$1,338.20
Factor: F= P(F/P6,5)=1000(1.3382)=$1,338.20
Note that the factor comes from Appendix C, Table C-9, from your book. Also note that the factor = (1.06)5 =1.3382
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Find P given F
Can rewrite F=P(1+i)n equation to find P given F:
Equation Form: P=F/(1+i)n =F*(1+i)-n
OR
Factor Form: P=F(P/Fi,n)
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Example of Find P given F problem-Equation vs Factor
What single sum of money does an investor need to put away today to have $10,000 5 years from now if the investor can earn 6% per year compounded yearly?
Equation: P=F*(1+i)-n=10,000(1.06)-5 =$7,473
Factor: P=F(P/Fi,n)=1000(0.7473)=$7,473
Note that the factor comes from appendix C out of your book. Also note that the factor = (1.06)-5 =0.7473. Also note that the F/P factor is the reciprocal of the P/F factor
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Example of Find P given F
If you wish to accumulate $2,000 in a savings account in 2 years and the account pays interest at a rate of 6% per year compounded annually, how much must be deposited today?
F=$2,000P=?i=6% per year compounded yearlyn=2 years
Answer: $1,780
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Relationship between P and F
• F occurs n periods after P• P occurs n periods before F
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Find i given P/F/n
Can rewrite F=P(1+i)n equation and solve for i
15 years ago a textbook costs $25.00. Today it costs $50.00. What is the inflation rate per year compounded yearly?
Answer: 4.73%
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Find n given P/F/i
Can rewrite F=P(1+i)n equation and solve for n
How long (to the nearest year) does it take to double your money at 7% per year compounded yearly?
Answer: 10 years
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Solve for NMethod 1-Solve directly
• F=P(1+i)n
• 2D=D(1.07) n
• 2=1.07 n
• log 2 = n*log(1.07)• n=10.2 years
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Solve for nMethod 2-Trial & Error
2=1.07nn
n Value1 1.075 1.40
10 1.9715 2.76
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Solve for NMethod 3-Use factors in back of book• F/P=2 • @ n=10; F/P=1.9727• @ n=11; F/P=2.1049• To the nearest year; n=10• Interpolate to get n=10.2
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Series of single sum cash flows
How much must be deposited at year 0 to withdraw the following cash amounts? (i=2% per year compounded yearly)
EOY Cash Flow
0 P=?
1 $1,000
2 $3,000
3 $2,000
4 $3,000
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Cash Flow Series (Present Worth)
P(at year 0)=:1000(P/F2,1)+
3000(P/F2,2)+
2000(P/F2,3)+
3000(P/F2,4)
EOY Cash Flow
0 P
1 $1,000
2 $3,000
3 $2,000
4 $3,000
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Series of single sum cash flows
How much would an account be worth if the following cash flows were deposited? (i=2% per year compounded yearly)
EOY Cash Flow
0 0
1 $1,000
2 $3,000
3 $2,000
4 $3,000
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Cash Flow Series (Future worth)
F(at year 4)=:1000(F/P2,3)+
3000(F/P2,2)+
2000(F/P2,1)+
3000(F/P2,0)
EOY Cash Flow
0 0
1 $1,000
2 $3,000
3 $2,000
4 $3,000
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Next lecture
• Uniform Series