Chapter 5 Powerpoint

# Chapter 5 Powerpoint - CHAPTER 5 Time Value of Money F IN 3...

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Time Value of Money CHAPTER 5

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T i m e V a l u e o f M o n e y F I N 3 4 0 3 - B u s i n e s s F i n a n c e O t h e r T o p i c s S i n g l e C a s h F l o w O t h e r C a s h F l o w s F u t u r e V a l u e P r e s e n t V a l u e C o m p l e x C a s h F l o w s A n n u i t i e s I n t e r e s t R a t e s C a l c u l a t i n g O t h e r V a l u e s L o a n A m o r t i z a t i o n P e r p e t u i t i e s
Time Value of Money Definitions : PV = Present value FV = Future vale i = Interest rate i = Compounding rate i = Discount rate N = Number of time periods

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Time Value of Money PMT = Annuity or perpetuity payment CF t = Cash flow (period t) FVIF i,N Interest factors PVIF i,N for single values FVIFA i,N Interest factors PVIFA for regular annuities
Future Value - Single Cash Flow FV N = [PV] [(1 + i) N ] FVIF i,N = (1 + i) N FV N = [PV] [FVIF i,N ]

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1,000.00 1,120.00 1,254.40 1,404.93 1,573.52 1,762.34 1 2 3 4 5 Deposit at t = 0 i = 12% Future Value - Single Cash Flow
Future Value - Single Cash Flow FV 5 = (\$1,000)(1.12) 5 FVIF 12%,5 = (1.12) 5 = 1.76234 FV 5 = (\$1,000)(1.76234) FV 5 = \$1,762.34

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Interest on Interest 0 \$1,000.00 --- 1 \$1,120.00 \$120.00 2 \$1,254.40 \$254.40 \$14.40 3 \$1,404.93 \$404.93 \$30.53 4 \$1,573.52 \$573.52 \$48.59 5 \$1,762.34 \$762.34 \$68.82 i = 12% \$162.34 Year Future Value Interest Interest on
Set payments to 1 per year (1 period) Clear All 1 P/YR 1 Now : N = number of periods (can be years) I/YR = interest rate per period Calculation Using the 10B

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Inputs 5 12 -1,000 0 Outputs 1,762.34 N I/YR PV PMT FV Calculation Using the 10B Clear All One of the cash flows (either input or output) will be negative. In this example we are depositing money (a negative or outflow) versus the ending value when we would get cash back (a positive or inflow).
\$0.00 \$1.00 \$2.00 \$3.00 \$4.00 \$5.00 0 1 2 3 4 5 6 7 8 9 10 Number of Compounding Periods F u t u r e V a l u e 0% 5% 10% 15% Future Value of One Dollar

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Present Value - Single Cash Flow PV N = [FV] PVIF i,N = PV N = [FV] [PVIF i,N ] 1 (1+i) N 1 (1+i) N _______ _______
1,000.00 892.86 797.19 711.78 635.52 567.43 Value at t = 5 i = 12% 4 3 2 1 0 Present Value - Single Cash Flow

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Present Value - Single Cash Flow PV 5 = (\$1,000) PVIF 12%,5 = = 0.56743 PV 5 = (\$1,000)(0.56743) 1 (1.12) 5 _________ 1 (1.12) 5 _________
Inputs 5 12 0 -1,000 Outputs 567.43 N I/YR PV PMT FV Calculation Using the 10B Clear All

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\$0.00 \$0.20 \$0.40 \$0.60 \$0.80 \$1.00 \$1.20 0 1 2 3 4 5 6 7 8 9 10 Number of Discounting Periods P r e s e n t V a l u e 15% 10% 5% 0% Present Value of One Dollar
1 (1+i) N = 1 (1+i) N Present versus Future Value PVIF = 1/FVIF FVIF = 1/PVIF _________ _________

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Time Lines 0 1 2 3 4 CF 0 CF 1 CF 2 CF 3 CF 4 Tick marks are at the end of periods. Time 0 is today; Time 1 is the end of Period 1 or the beginning of Period 2. i% is the interest rate per period. i%
Time Lines 0 1 2 3 4 100 Time line for \$100 single (also called lump sum) cash flow received at Time Period 3. i%

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Time Lines 0 1 2 3 4 100 100 100 100 Time line for a \$100, 4-year, regular (ordinary) annuity. i%
Time Lines 0 1 2 3 4 100 100 100 100 Time line for a \$100, 4-year, annuity due. i%

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Time Lines 0 1 2 3 4 -50 100 75 50 60 Time line for a complex (uneven) cash flow with an outflow of \$50 at Time 0, followed by inflows of \$100, \$75, \$50, and \$60 at Time Periods 1-4.
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## Chapter 5 Powerpoint - CHAPTER 5 Time Value of Money F IN 3...

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