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11ComparisonMethods2PDF.pdf
11ComparisonMethods2PDF.pdf
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11ComparisonMethods2PDF.pdf-Centre for Management ...
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Page 18
18
IRR of a Project Example 1
•
What is the IRR to buy a bike which costs $500
and would save $160 per year in rental
charges over fiveyears?
–
PW=500 + 160(P/A,r,5)
–
Try r = 10% → PW = 106.52
–
Try r = 20% → PW = 21.50
–
Interpolate: r = 18.3%
–
Actual r = 18.03%
Page 19
19
Graphical Solu8on
•
Use the investment from before:
$90K
1
2
4
3
5
$180K
$120K
$80K
$90K
$150K
6
7
PW in Thousands
IRR
0%
5%
10%
15%
20%
Interest Rate
$250K
$200K
$150K
$100K
$50K
0
-50K
-100K
Page 20
20
IRR of a Project Example 1
•
Con8nuing with the investment example from before,
we calculate the IRR using EE factors:
•
PW = 90K 180K(P/F,i,1)90K(P/F,i,2)+80K(P/F,i,3)+
120K(P/A,i,3)(P/F,i,3) + 150K(P/F,i,7)
•
PW(12%) = $7,479
•
PW(13%) = $4202
•
Now interpolate:
•
IRR = 0.12 + 0.01*7479/(7479+4204) = 0.1264 = 12.6%
$90K
1
2
4
3
5
$180K
$120K
$80K
$90K
$150K
6
7
Page 21
21
Mul8ple IRR
•
One problem with using IRR is that there may
be more than one internal rate of return.
•
0=$1,000$5,000(P/F,i*,1) + $6,000(P/F,i*,2)
Page 22
22
IRR 2 Sign Changes Example
•
One of the alterna8ves for improving an
opera8on is do nothing for 2 years and then
spend $10,000 on improvements. The immediate
gain is $3000, annual income should be $2000
per year for 4 years. What rate of return can be
expected?
PW = 3000 10,000 (P/F,i,2) + 2000 (P/A,i,4) (P/
F,i,2)
PW = 0
→
i = 51%, i = 9.4%
2000
10,000
3000
0
6
Page 23
23
Tests for Mul8ple IRR
•
If the investment is not a
simple investment
•
The present worth of the project is zero for
several interest rates
-50.0
0.0
50.0
100.0
150.0
200.0
250.0
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
i
- interest rate
Present Worth
Page 24
24
External Rate of Return
•
We can test for mul8ple IRRs:
–
If the investment is not a
simple investment
–
The present worth of the project is zero for several
interest rates
•
But the best way is to calculate the External Rate of
Return (ERR)
•
ERR is the Rate of return of the money associated with
a project but is invested outside of the project at the
same interest MARR because we assume that money
not used now can be invested at the same rate.
•
For a given, explicit interest rate, a project can have
only one ERR
•
Must be used when there are mul8ple IRRs
•
A project is acceptable if ERR ≥ MARR
Page 25
25
Approximate ERR calcula8on
•
Since the exact ERR it is usually a very complex
calcula8on, we can use the "approximate"
ERR calc'n.
–
FW(inflows at MARR) = FW(ouqlows at ERR
approx
)
•
Note: the approximate ERR is always between
actual ERR and MARR
•
ERR Calcula8on.xls
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