$1.50 back at the end of the class period.Option #2: You give me $10 now and I’ll give you $11 back at the end of the class period. You can choose only one of two options. Assume a zero rate of interest because our class lasts only 2 hours. Which option would you choose?
34Example 4: NPV vs. IRR (Mutually Exclusive Projects)Project0123IRRIRRNPV NPV @5%@5%Long10010608018.1%18.1%$33$33HigherHigherShort10070502023.6%23.6%HigherHigher$29$29Which one should we take?Suppose r = 5%.
35Construct NPV ProfilesEnter CFs in CFjand find NPVLandNPVSat different discount rates: r05101520NPVL50 33197NPVS402920125
(4)
36
NPV ($)
Discount Rate (%)
IRR
L
= 18.1%
IRR
S
= 23.6%
Crossover
Point
=
8.7%
Microsoft Excel
Worksheet
Double click on the icon
37
To Find the Crossover Rate
1.
Find cash flow differences between the
projects.
See data at beginning of the
case.
2.
Enter these differences in CF
j
register,
then press IRR.
Crossover rate = 8.68%,
rounded to 8.7%.
3.
Can subtract S from L or vice versa, but
better to have first CF negative.
4.
If profiles don’t cross, one project
dominates the other.
38
Which project(s) should be
accepted at r=5%?
If S and L are
independent
, accept both. NPV >
0. IRR
S
and IRR
L
> r = 5%.
If Projects S and L are
mutually exclusive
, accept
L because NPV
S
< NPV
L
at r = 5%, although
IRR
S
> IRR
L
.
Conflict!!!
Choose between mutually exclusive projects on
basis of
higher NPV
.
Adds most value in dollar.
39
NPV and IRR always lead to the same
accept/reject decision for independent
projects:
r > IRR
and NPV < 0.
Reject.
NPV ($)
r (%)
IRR
IRR > r
and NPV > 0
Accept.
40
Mutually Exclusive Projects
r
8.7
r
NPV
%
IRR
S
IRR
L
L
S
r < 8.7: NPV
L
> NPV
S
, IRR
S
> IRR
L
CONFLICT
r> 8.7: NPV
S
> NPV
L
, IRR
S
> IRR
L
NO CONFLICT
41
Reinvestment Rate Assumptions
NPV assumes reinvest at r (opportunity cost of
capital).
IRR assumes reinvest at IRR.
Reinvest at opportunity cost, r, is more realistic,
so NPV method is best.
NPV should be used to
choose between mutually exclusive projects.
reinvestment
assumption
42
42
Another Problem with IRR
Another Problem with IRR
IRR has another problem socalled
IRR has another problem socalled
“Multiple IRRs.”
“Multiple IRRs.”
43
Normal Cash Flow Project:
Cost (negative CF) followed by a
series of positive cash inflows.
One
change of signs.
Nonnormal Cash Flow Project:
Two
or more changes of signs.
Most common:
Cost (negative
CF), then string of positive CFs,
then cost to close project.
Nuclear power plant, strip mine.
Two kinds of Cash Flows
44
Inflow (+) or Outflow () in Year
0
1
2
3
4
5
N
NN

+
+
+
+
+
N

+
+
+
+

NN



+
+
+
N
+
+
+



N

+
+

+

NN
45
Example 5: NPV vs. IRR (Multiple IRRs)
0
1
2
3
4
5
NPV
@5.62%
NPV
@27.78%
NPV
@10%
22 15
15
15
15
40
?
?
$0.7M
Greenspan Mining Co. is considering a project to strip
mine coal.
The project requires an investment of $22
million and is expected to produce a cash inflow of
$15 million in each Year 1 through 4. However, the
Company is obligated to
pay
$40 million in Year 5 to
restore the terrain.
The Company’s opportunity cost
of capital is 10%.
What are the IRR(s) and NPV?
46
Multiple IRRs
47
Could find IRR with calculator:
1.
Enter CFs as before.
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