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Chapter 6
Discounted Cash Flow Valuation
Slide 6  1
Chapter Outline
±
Future and Present Values of Multiple Cash Flows
±
Valuing Level Cash Flows: Annuities and Perpetuities
±
Comparing Rates: The Effect of Compounding
±
Loan Types
Slide 6  2
±
Future Value of Multiple Cash Flows
●
We have discussed: for a single cash flow:
FV = PV (1+r)
t
Where, PV = Value of original investment
FV = Future value of investment
t = Number of periods
r = Interest rate per period
●
FV for Multiple Cash Flows
We convert multiple cash flows to the same time point.
Then, the future value of a stream of cash flows is the sum of the
FV of each cash flow.
Multiple Cash Flows: FV
Slide 6  3
±
Future Value:
Example
Consider the following uneven cash flow stream with r = 10%:
Find FV at year 3 of each cash flow and add them together.
(PV is to be discussed)
t=0
1
2
3
$700
(PV)
$400
$400
$400
FV?
Multiple Cash Flows: FV
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●
Value at year 3
Year 0 (today):
FV = 700(1.08)
3
= 881.80
Year 1:
FV = 400(1.08)
2
= 466.56
Year 2:
FV = 400(1.08) = 432.00
Year 3:
Value = 400
Total FV = 881.80 + 466.56 + 432 + 400 = 2,180.36
●
Further, what will be the value at year 4?
2,180.36(1.08) = 2,354.79
Multiple Cash Flows: FV
Slide 6  5
±
Another Example
Suppose you invest $500 in a mutual fund today and further
invest $600 in one year. The fund pays 9% annually.
●
How much will you have in two years?
FV = 500(1.09)
2
+ 600(1.09) = 1248.05
●
How much will you have in 5 years if you make no further
deposits?
First way:
FV = 500(1.09)
5
+
600(1.09)
4
= 1616.26
Second way:
Use year2 value:
FV=1248.05(1.09)
3
= 1616.26
Multiple Cash Flows: FV
Slide 6  6
Multiple Cash Flows: PV
±
Present Value of Multiple Cash Flows
We first calculate the PV for each cash flow, then add them
together.
±
The Link between PV and FV
If we want to find the FV at time
t
for the same stream of
cash flows, we can use the basic formula after finding PV.
t
r
PV
FV
)
1
(
+
=
()
()
()
t
t
r
C
r
C
r
C
PV
+
+
+
+
+
+
=
1
...
1
1
2
2
1
1
Slide 6  7
±
Example
Find PV of each of the following cash flows and then add them
together: $200 in one year, $400 in two years, $600 in three
years, and $800 in four years.
Year 1 CF: 200 / (1.12)
1
= 178.57
Year 2 CF: 400 / (1.12)
2
= 318.88
Year 3 CF: 600 / (1.12)
3
= 427.07
Year 4 CF: 800 / (1.12)
4
= 508.41
Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93
Multiple Cash Flows: PV
Slide 6  8
±
Another Example
You are considering an investment that will pay you $1,000 in
one year, $2,000 in two years and $3000 in three years.
If you
want to earn 10% on your money, how much would you be
willing to pay?
Year 1 CF:
PV = 1000 / (1.1)
1
= 909.09
Year 2 CF:
PV = 2000 / (1.1)
2
= 1,652.89
Year 3 CF:
PV = 3000 / (1.1)
3
= 2,253.94
Total PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.92
Total FV in three years: 4,815.92(1.1)
3
= 6,409.99
Multiple Cash Flows: PV
Slide 6  9
Multiple Cash Flows: Use the Calculator
±
Use N, I/Y, PV, and FV for each cash flow then add up
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This note was uploaded on 04/18/2011 for the course FINA 1003 taught by Professor Lin during the Fall '11 term at HKU.
 Fall '11
 Lin
 Compounding, Valuation

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