Gitman 10th: Ch. 4 46 slides n

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Chapter 4Time Value of Money

• Principles of Managerial Finance
• Gitman 10th edition
• Finance 330--Wolfe

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Time Value of Money (TVM)

• 1 today vs. 1 in the future

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Time lines
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4 calculation methods

• 1. formulas
• 2. formulas with tables
• 3. spreadsheets
• 4. financial calculator

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Financial calculator
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Cash Flows (CFs)

• CFs are assumed to occur at the end of the period
• this is the default setting on our calculator
• today time zero (0)

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CF patterns

• single amounts
• annuities
• mixed streams

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FV of a single amount

• Prob. 4-4 case D
• deposit 25,000 today _at_ 10 for 12 yrs.
• value _at_ EOY 12?

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FV of a single amount (cont.)

• Formulas 4.4 4.6
• FVn PV0(1i)n
• FVn PV0(FVIFi,n)

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Using the calculator
CLR TVM P/Y 1
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PV of a single amount

• Prob. 4-11 Case A
• What is PV of 7,000 recd 4 yrs. from now, if
  the discount rate 12?

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PV of a single amount (cont.)

• Formulas 4.9 4.11
• PV0 FVn1/(1i)n
• PV0 FVn(PVIFi,n)

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Using the calculator
CLR TVM P/Y 1
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Annuities

• a series of equal payments (CFs) recd. or paid
  in the future

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Annuities (cont.)

• Ordinary annuity
• CFs at end of periods
• Annuity due
• CFs at beginning of periods

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Ordinary Annuity

• PVA one period before 1st CF
• FVA as of last CF

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Annuity due

• PVA as of 1st CF
• FVA one period after last CF

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Annuity calculations

• can solve using formulas, formulas with tables,
  spreadsheets, or fin. calculator

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FV of an (ordinary) annuity

• Prob. 4-41(b)
• If you deposit 600/yr. for 42 yrs. beginning 1
  yr. from today, how much will you accumulate?
  I/Y 8

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FV (cont.)

• can find the FV of each separate CF add the 42
  FVs

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Using the calculator
CLR TVM P/Y 1
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PV of an (ordinary) annuity

• most amortized loan problems are PVA problems
• PVA loan principal
• usually solving for PMT

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PV (cont.)

• Problem if your loan payment 2,000/yr. on a
  10 yr. 6 loan, how much did you borrow?

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Using the calculator
CLR TVM P/Y 1
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PV of perpetuity

• perpetuity an annuity forever
• PV Payment / interest rate
• interest rate discount rate

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Mixed Streams
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FV PV of mixed streams
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Nominal Effective Rates

• 12 compounded quarterly results in you earning
  more than 12/yr.
• 12 is the nominal rate

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Nom. Effective Rates (cont.)

• to calculate effective rate
• 2nd IConv

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Nom. Effective Rates (cont.)

• Arrow down through 3 cells
• NOM 12 ENTER
• C/Y 4 ENTER
• EFF CPT
• EFF 12.5509

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Loan Amortization

• installment loans are PV of annuity probs.
• pmts. include princ. interest

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Loan Amortization (cont.)

• What is the annual pmt. on a 5 yr. 15, 10,000
  loan?

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Loan Amortization (cont.)

• How much interest in the 3rd pmt.?
• go to amortization worksheet
• 2nd Amort
• arrow down through the 5 cells

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Loan Amortization (cont.)

• P1 3 ENTER
• P2 3 ENTER
• should now see
• BAL -4,849.7426
• PRN 1,961.4731
• INT 1,021.6824

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Loan Amortization (cont.)

• amortizing a range of PMTS, say all 5 PMTS
• P1 1 ENTER
• P2 5 ENTER
• arrow down through BAL, PRN, INT

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Loan Amortization (cont.)

• What if this loan were a monthly pmt. loan?

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Loan Amortization (cont.)

• if this loan were a monthly pmt. loan,
• set I/Y to 15/12 1.25
• change N to 5 x 12 60
• CPT PMT
• PMT 237.8993

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Non-annual Compounding

• for calculator entries need to adjust the N I/Y
• e.g., monthly payment problem
• N 12 x no. of yrs.
• I/Y annual int. rate/12

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Mortgage loan

• 100,000 home, borrow 80
• loan amount 80,000

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Mortgage loan (cont.)

• 30 yr., 6, 80,000 loan
• what is PMT?

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How much interest in

• 1st PMT?
• P1 1 P2 1
• 360th PMT?
• P1 360 P2 360
• whole loan?
• P1 1 P2 360

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Loan balance after

• 15 yrs. through the loan?
• P1 1 P2 180
• 20 yrs. through the loan?
• P1 1 P2 300

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Paying off early?

• How long will it take to pay off the loan if you
  add 100 each month to your PMT?

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Loan Amortization (cont.)

• to get out of the Amort Worksheet
• 2nd QUIT