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WHAT TO DISCOUNT
1.Only cash flow is relevant.
2. Estimate incremental (after tax) cash flows.
3. Be consistent in treatment of inflation.
4. Recognize project interactions.
1
I.
Basic Data
Expected Net Cash Flow
Year
Project L
Project S
0
($100)
($100)
1
10
70
2
60
50
3
80
20
II.
Evaluation Techniques
A. Payback period
B. Discounted payback period
C. Net present value (NPV)
D. Internal rate of return (IRR)
E. Modified internal rate of
return (MIRR)
2
Payback period = Expected number of years
required to recover a project's cost
Year
0
1
2
3
Project L
Expected Net Cash Fl ow
Annual
Cumul ati ve
($100)
($100)
10
(90)
60
(30)
80
50
PaybackL = 2 + $30/$80 years
= 2.4 years
PaybackS = 1.6 years
Weaknesses of Payback:
1
Ignores the time value of money. This
weakness is eliminated with the discounted
payback method
2
Ignores cash flows ocurring after the
payback period
3
n
NPV 

t0
CF
(1  K )
t
t
Project L:
0
|
-100
10%
1
|
10
2
|
60
3
|
80
9.09
49.59
60.11
NPVL= $ 18.79
NPVS = $19.98
If the projects are independent, accept both.
If the projects are mutually exclusive, accept Project S
since NPVS > NPVL.
Note:
NPV declines as K increases and NPV rises as K
decreases.
4
n
IRR :

t0
CF
(1  IRR )
t
t
 $ 0  NPV
Project L:
0
|
-100
8.47
43.02
48.57
$ 0.06
1
|
10
=
2
|
60
3
|
80
$0
IRRL = 18.1%
IRRS = 23.6%
If the Projects are independent, accept both because IRR > k.
If the projects are mutually exclusive, accept Project S
since IRRS > IRRL.
Note:
IRR is independent of the cost of capital.
5
Project L:
0
|
-100.00
100.00
$ 0.00
1
|
10
2
|
60
MIRR =16.5%
3
|
80
66.00
12.10
158.10 = TV of inflows
= NPV
PV outflows = $100
TV inflows = $158.10
$100 = $158.10(PVIFMIRRL,3)
MIRRL = 16.5%
MIRRs = 16.9%
MIRR is better than IRR because
1 MIRR correctly assumes reinvestment at project's
cost of capital
2 MIRR avoids the problems of multiple IRRs.
6
K
0 %
5
10
15
20
50 _
40 _
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
30 _
Crossover Point = 8.7%
20 _
10 _
0
IRRS = 23.6%
|
5
|
10
|
15
|
20
|
25
|
k(%)
IRRL = 18.1%
7
500
_
375
_
250
_
125
_
0
-125
_
-250
_
-375
_
-500
_
|
|
|
|
|
100
200
300
400
500
Year
0
1
2
|
600
Cash Flow
(in Thousands)
(800)
5000
(5000)
[email protected] 10% =-$386,777. Do not accept; NPV<0,
IRR= 25% and 400%
MIRR= 5.6%. Do not accept: MIRR< K.
8
1. Estimate the Cash flows.
2. Assess the riskiness of the cash flows.
3. Determine the appropriate discount rate.
4. Find the PV of the expected cash flows.
5. Accept the project if PV of inflows > costs
Definitions:
Independent versus mutually exclusive projects.
Normal versus nonnormal projects.
9
I.
Two mutually exclusive projects
Year
0
1
2
3
4
NPV (10%)
II.
Project S
($100,000)
60,000
60,000
$4,132
Net Cash Flow
Project L
($100,000)
33,500
33,500
33,500
33,500
$6,190
Ignoring the difference in lives,
ProjectL should be chosen. But
since Project S will be replicated, the
analysis should be modified by
using either:
A. Replacement chain approach
B. Equivalent annual annuity approach.
10
I.
Replacement chain approach
Project S:
0
|
4,132
1
|
3,415
7,547
2
|
4,132
3
|
4
|
3
|
4
|
= Extended NPVS
Project L:
0
|
6,190
II.
1
|
2
|
Equi val ent annui ty approach
EAA
is the equal
PV  $ 4,132
EAA
s
annual
payment
, n  2 , i  10%
 PMT
 $ 2 , 381
Infinite
horizon

Find
$2,381
over the
payments
life.
PMT
 $ 23 ,810
0.10
PV  $ 6 ,190 , n  4 , i  10%
EAA
L
 PMT
Infinite
Find
PMT
 $ 1, 953
horizon

$1,953
0.10
 $ 19 , 530
11
n
CIF
(1  K )
COF

(1  K)

PI

t
t
t0
n
t
t
t0
Project L:
PI
L

$ 9 . 09  $ 49 . 59  $ 60 . 11
$ 100
 1.19
If the projects are independent, accept
both projects.
If the projects are mutually exclusive,
accept Project S since PIS>PIL.
12
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