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

CTC 475

Interest and Single Sums of Money

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

Time Value of Money

• Value of a given sum of money depends on when the money is received

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

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

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

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?

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

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

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

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

Simple or Compound?

• In practice, banks usually pay compound interest

• Unless otherwise stated assume compound interest is used

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

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

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

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)

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

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

Relationship between P and F

• F occurs n periods after P• P occurs n periods before F

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%

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

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

Solve for nMethod 2-Trial & Error

2=1.07nn

n Value1 1.075 1.40

10 1.9715 2.76

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

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

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

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

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

Next lecture

• Uniform Series