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FM8e- ch28

# FM8e- ch28 - 28 1 WEB CHAPTER 28 Basic Financial Tools A...

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28 - 1 Time Value of Money Bond Valuation Risk and Return Stock Valuation WEB CHAPTER 28 Basic Financial Tools: A Review

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28 - 2 Time lines show timing of cash flows. CF 0 CF 1 CF 3 CF 2 0 1 2 3 i% Tick marks at ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2.
28 - 3 Time line for a \$100 lump sum due at the end of Year 2. 100 0 1 2 Year i%

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28 - 4 Time line for an ordinary annuity of \$100 for 3 years. 100 100 100 0 1 2 3 i%
28 - 5 What’s the FV of an initial \$100 after 1, 2, and 3 years if i = 10%? FV = ? 0 1 2 3 10% Finding FVs (moving to the right on a time line) is called compounding. 100 FV = ? FV = ?

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28 - 6 After 1 year: FV 1 = PV + INT 1 = PV + PV (i) = PV(1 + i) = \$100(1.10) = \$110.00. After 2 years: FV 2 = PV(1 + i) 2 = \$100(1.10) 2 = \$121.00.
28 - 7 After 3 years: FV 3 = PV(1 + i) 3 = \$100(1.10) 3 = \$133.10. In general, FV n = PV(1 + i) n .

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28 - 8 What’s the FV in 3 years of \$100 received in Year 2 at 10%? 100 0 1 2 3 10% 110
28 - 9 What’s the FV of a 3-year ordinary annuity of \$100 at 10%? 100 100 100 0 1 2 3 10% 110 121 FV = 331

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28 - 10 3 10 0 -100 331.00 N I/YR PV PMT FV Financial Calculator Solution Have payments but no lump sum PV, so enter 0 for present value. INPUTS OUTPUT
28 - 11 10% What’s the PV of \$100 due in 2 years if i = 10%? Finding PVs is discounting, and it’s the reverse of compounding. 100 0 1 2 PV = ?

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28 - 12 Solve FV n = PV(1 + i ) n for PV: ( 29 PV = FV 1+i = FV 1 1+i n n n n ( 29 ( 29 PV = \$100 1 1.10 = \$100 PVIF = \$100 0.8264 = \$82.64. i,n 2
28 - 13 What’s the PV of this ordinary annuity? 100 100 100 0 1 2 3 10% 90.91 82.64 75.13 248.69 = PV

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28 - 14 Have payments but no lump sum FV, so enter 0 for future value. 3 10 100 0 N I/YR PV PMT FV -248.69 INPUTS OUTPUT
28 - 15 How much do you need to save each month for 30 years in order to retire on \$145,000 a year for 20 years, i = 10%? 0 360 2 20 1 2 PMT PMT PMT ... 1 19 months before retirement years after retirement -145k -145k -145k -145k ...

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28 - 16 How much must you have in your account on the day you retire if i = 10%? How much do you need on this date? 2 20 ... 1 19 years after retirement -145k -145k -145k -145k ... 0
28 - 17 You need the present value of a 20- year 145k annuity--or \$1,234,467. 20 10 -145000 0 N I/YR PV FV PMT 1,234,467 INPUTS OUTPUT

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28 - 18 How much do you need to save each month for 30 years in order to have the \$1,234,467 in your account? You need \$1,234,467 on this date. 0 360 1 2 PMT PMT PMT ... months before retirement ...
28 - 19 You need a payment such that the future value of a 360-period annuity earning 10%/12 per period is \$1,234,467. 360 10/12 0 1234467 N I/YR PV FV PMT 546.11 INPUTS OUTPUT It will take an investment of \$546.11 per month to fund your retirement.

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28 - 20 Key Features of a Bond 1. Par value: Face amount; paid at maturity. Assume \$1,000. 2. Coupon interest rate: Stated interest rate. Multiply by par value to get dollars of interest. Generally fixed. (More…)
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