CTC 475 Review

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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 (LaborMatl) 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?
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Which Would you Prefer?
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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
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Simple Interest Equation

• Simpleevery year you earn 3 (30) on the
  original 1000 deposited in the account at year 0
• FnP(1in)
• Where
• FFuture amount at year n
• PPresent amount deposited at year 0
• iinterest rate

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Compound Interest Equation

• Compoundevery year you earn 3 on whatever is in
  the account at the end of the previous year
• FnP(1i)n
• Where
• FFuture amount at year n
• PPresent amount deposited at year 0
• iinterest 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 FP(1in)1000(1.072)1,140
• Compound FP(1i)n1000(1.07)21,144.90

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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

• FP(F/Pi,n)
• Find the future worth (F) given the present
  worth (P) at interest rate (i) at number of
  interest periods (n)
• Future worthPresent worth factor
• Note that the factor(1i)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
• FP(1i)n1000(1.06)51,338.20
• 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 FP(1i)n equation to find P given
  F
• Equation Form PF/(1i)n F(1i)-n
• OR
• Factor Form PF(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
• PF(1i)-n10,000(1.06)-5 7,473
• Factor
• PF(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?
• F2,000
• P?
• i6 per year compounded yearly
• n2 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 FP(1i)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 FP(1i)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

• FP(1i)n
• 2DD(1.07) n
• 21.07 n
• log 2 nlog(1.07)
• n10.2 years

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Solve for nMethod 2-Trial Error
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Solve for NMethod 3-Use factors in back of book

• F/P2
• _at_ n10 F/P1.9727
• _at_ n11 F/P2.1049
• To the nearest year n10
• Interpolate to get n10.2

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Series of single sum cash flows

• How much must be deposited at year 0 to
  withdraw the following cash amounts? (i2 per
  year compounded yearly)

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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)

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Series of single sum cash flows

• How much would an account be worth if the
  following cash flows were deposited? (i2 per
  year compounded yearly)

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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)

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Next lecture

• Uniform Series