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1
Last Class
0T
Prof. Q. Ma
HADM 2222: DCF Valuation
1
FV = PV (1+r)
T
Time Line
PV
FV
Discounted Cash Flow Valuation
±
Be able to compute
²
The FV (PV) of multiple cash flows
²
FV, PV, r, C, and T of level cash flows
²
APR, EAR
Prof. Q. Ma
HADM 2222: DCF Valuation
2
²
Loan payments
±
Understand
²
How loans are amortized or paid off
²
How interest rates are quoted
±
Use
time line
and financial calculator
Multiple Cash Flows – FV
T1
T
Time Line
CF
1
FV=?
CF
2
CF
3
T2
T3
Prof. Q. Ma
HADM 2222: DCF Valuation
3
FV
1
= CF
1
(1+r)
T-T1
FV
3
FV
2
FV
1
FV
2
= CF
2
(1+r)
T-T2
FV
3
= CF
3
(1+r)
T-T3
FV= FV
1
+ FV
2
+ FV
3
Example – FV
You will be able to deposit $4,000 at the end of
each of the next three years in a bank account
paying 8 percent interest. You currently have
$7,000 in the account.
How much will you have in four years?
Prof. Q. Ma
HADM 2222: DCF Valuation
4
±
How much will you have in four years?
Example – FV
04
Time Line
$7,000
FV=?
12
3
$4,000
$4,000
$4,000
Prof. Q. Ma
HADM 2222: DCF Valuation
5
FV
3
=4,000 (1.08)
2
FV
2
=4,000 (1.08)
3
FV
1
=7,000 (1.08)
4
FV= FV
1
+ FV
2
+ FV
3
+ FV
4
= $ 23,547.87
FV
4
=4,000 (1.08)
1
General Approach
±
Analysis
²
Time line with relevant time points
²
Cash flow stream
±
Execution
Fl
&
i
l
l
t
Prof. Q. Ma
HADM 2222: DCF Valuation
6
²
Formula & generic calculator
±
Summation of all cash flows’ FV
²
Financial calculator
²
Spreadsheet

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Multiple Cash Flows – PV
T
T
3
PV=?
CF
3
CF
1
CF
2
Time Line
T
1
T
2
Prof. Q. Ma
HADM 2222: DCF Valuation
7
PV= PV
1
+ PV
2
+ PV
3
PV
1
=CF
1
/(1+r)
T1-T
PV
2
=CF
2
/(1+r)
T2-T
PV
3
=CF
3
/(1+r)
T3-T
General Approach
±
Analysis
²
Time line with relevant time points
²
Cash flow stream
±
Execution
Prof. Q. Ma
HADM 2222: DCF Valuation
8
²
Formula & generic calculator
±
Summation of all cash flows’ PV
²
Financial calculator
²
Spreadsheet
Applications of DCF
±
FV of multiple cash flows (EQ 1,2)
±
PV of multiple cash flows (EQ 3,4)
±
Simple investment decisions (EQ 5)
Prof. Q. Ma
HADM 2222: DCF Valuation
9
²
Concept of net present value (NPV)
±
Saving for retirement (EQ 6)
±
PV and FV “hybrid” (EQ 7)
A Note on Cash Flow Timing
±
Cash flow of period t means cash flow at
the
end
of period t
²
Example: you earn $1,000 every month on
your part-time job. Cash flows are paid at the
Prof. Q. Ma
HADM 2222: DCF Valuation
10
end of each month.
²
How about your monthly rent?
±
The end of period t = beginning of period
t+1?
Level Cash Flows – Perpetuity
±
Perpetuity –
infinite
series of equal
payments
±
Cash flow pattern
Prof. Q. Ma
HADM 2222: DCF Valuation
11
±
PV = C / r
±
Example (Preferred stocks)
Perpetuity – Example
±
Suppose your company wants to sell preferred
stock at $100 per share. A very similar issue of
preferred stock already outstanding has a price
of $40 per share and offers a dividend of $1
every quarter. What dividend will your
company have to offer if the preferred stock is
Prof. Q. Ma
HADM 2222: DCF Valuation
12
company have to offer if the preferred stock is
going to sell?

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