BUS 320 Lecture Notes - Lecture 5: Amortization Schedule, Tetrafluoromethane, Cash Flow
Chapter Five Study Guide The Value of Money
Times Lines
• Show the timing of cash flows
• Tick marks occur at the end of periods, to Time 0 is today; Time 1 is at the end of the
first period (year, month, etc.) or the beginning of the second period
Drawing Time Lines
$100 lump sum due in 2 years
3-year $100 ordinary annuity
Uneven cash flow stream
Future Value
• What is the future value (FV) of an initial $100 after 3 years, if I/YR = 4%?
o Finding FV of a cash flow or series of a cash flow is called compounding
o FV can be solved by using the step-by-step, financial calculator and spreadsheet
methods
• Step-by-step and formula methods
o Formula: FVN = PV(1+I)N
o After 1 year: FV1 = $100(1.04)1= $104.00
o 2 years: : FV2 = $100(1.04)2= $108.16
o 3 years: : FV3 = $100(1.04)3= $112.49
o After N years: FVN = PV(1+I)N
• Calculator: Set P/YR = 1 and put in END mode
Present Value
• What is the present value (PV) of $100 due in 3 years, if I/YR = 4%?
CF0CF1CF3
CF2
0 1 2 3
I%
100
0 1 2
I%
100 100100
0 1 2 3
I%
100 5075
0 1 2 3
I%
-50
FV = ?
0 1 2 3
4%
100
INPUTS
OUTPUT
N I/YR PMTPV FV
3 04 -100
112.49
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o Finding the PV of a cash flow or series of cash flows is called discounting
(the reverse of compounding)
o The PV shows the value of cash flows in terms of today’s purchasing power
• Solving for PV
o Formula: PV = FVN / (1+I)N
o $100 / (1+I)3
o $88.90
• Calculator, exactly like solving for FV, except we have different input information and
are solving for a different variable
Solving for I
• What annual interest rate would cause $100 to grow to $119.10 in 3 years
• Use calculator
Solving for N
• Also use calculator
What is the difference between an ordinary annuity and an annuity due
Solving for FV: 3-year ordinary annuity of $100 at 4%
• $100 payments occur at the end of each period, but there is no PV
PV = ? 100
0 1 2 3
4%
INPUTS
OUTPUT
N I/YR PMTPV FV
3 04
-88.90
100
INPUTS
OUTPUT
N I/YR PMTPV FV
3 0
6
-100 119.10
INPUTS
OUTPUT
N I/YR PMTPV FV
7.3
010 -1 2
Ordinary Annuity
PMT PMTPMT
0 1 2 3
I%
PMT PMT
0 1 2 3
I%
PMT
Annuity Due
INPUTS
OUTPUT
N I/YR PMTPV FV
3 -1004 0
312.16
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