 APR
= Annual Percentage Rate, stated annual
interest rate

1+nominal interest rate
real interest rate =
1
1 inflation rate

+

(1
)
1
m
r
EAY
m
=
+

effective annual yield or interest rate; is the
annual value gained with or without
compounding
EAY = APR (annual Compounding)
EAY > APR (More Freq. Compounding)

Continuous Compounding
=
0
rT
C
e
•

PV of Perpetuity
=
C
r

PV of Growing Perpetuity
=
C
r
g

R must be greater than g for formula
to
work

PV
0
of an Annuity
=
1
(1
)
(1
)
T
C
r
r

+

PV
0
of a Growing Annuity
1
1 (
)
1
T
g
C
r
g
r
+


+
Mortgage Payments (Monthly)
Term = 20 yrs * 12 = 240 Pds
APR = 12% / 12 = 1%
r
=
1%
Each Payment:
Balance x r = Interest Payment
Monthly Payment – Interest Payment =
Principle Reduction
Balance A  Principle Reduction=Balance B
Comparing
Assets w/ Unequal Lives
1. Find NPV for 1 life cycle
2. Find Cost / yr
PV = x * A
3. Compare Ax and Bx
Determining Cash Flow
Cash = (Revenue – Cash Costs)(1  .34) + .
34(Depreciation)
What happens to Cash Flow…
1. Sales rise by $1? Down .34 tax Up .66
2. Materials costs rise by $1?
Pay $1
Retain .40
Down .60
Depreciation expense rises by $1?
Income Down $1
Tax down .34
Cash up .34
Calculate:
NPV of Project: 30 + 21/1.12 + 21/1.12^2
IRR
: 30 + 21 / (1+r) + 21 / (1+r) ^2 = 0
Cash Effects of Purchase and Sale of Assets
1. Initial cash outlay:
1000 @ C 0
(Cannot be expensed)
2. Depreciation Expense = 1000
Depreciation expense each Year:
D1 = .200 (1000) = 200
C1 = 68
D2 = .320 (1000) = 320
C2 = 108.8
D3 = .192 (1000) = 192
C3 = 65.28
D4 = .115 (1000) = 115
C4 = 39.10
D5 = .115 (1000) = 115
C5 = 39.10
D6 = .058 (1000) = 58
C6 = 19.72
A.
D * T (.34)
= C
B.
Discount All Cash Flows
C. Sum to Get NPV of
Depreciation Tax Shield
* For ever 1$ Depreciation…
Pre Tax Income Down 1$
3. Resale of Used Asset
Resale Price
500K
Book Value

0

Taxable gain
500K
1
1
0
1
1
1
1
1
(
)
Div
EPS
P
NPVGO
r
g
r
EPS
RE
Div
EPS POR
Div
=
=
+

=
+
→
=
NVPGO EXAMPLE
1.
Earnings constant
2.
EPS = Div (Cash Cow
Value of a share = EPS / r
=
Div / r
Now Firm retains entire dividend @ Date 1 to
invest in a single project
Date 0:
NPV of Project
= NPVGO
# of Shares
Thus,
Value of a Share after commit to Project:
EPS / r
+ NPVGO
Earnings / yr = 1M
Stock: 100k outstanding
EPS = 10
A. @ Date 1 Firm can spend 1M on a Mktg
Campaign which will increase subsequent
earnings by 210, 000 or increase EPS by 21%
1. Cash Cow (Pays out all Earnings)
P = EPS / r = 10 / .10 = $100
Value of MKTG campaign @ Date 1:
1M
+
210,000 / .10
=
1.1M
@ Date 1
@ Date 2
Value of MKT campaign @ Date 0: = Discount
1 Period:
1.1M / 1.1 = 1M
Thus NVPGO = 1M / 100k = $10
Now EPS = EPS / r
+
NPVGO
$100
+
$10
=
$110
OR METHOD 2
Value created b/c:
Rate of Return (21%) >
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 Spring '10
 jaffe
 Annual Percentage Rate, Interest, Interest Rate, Net Present Value, Nominal Interest Rate, Spot rate, Forward rate, EAY

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