Biomass Economics -- Unit 5
Capital Investment Decision Rules:
•
•
•
Payback Period
Net Present Value (from last time)
Internal Rate of Return
Payback Period:
How many years to recuperate initial investment?
Decision rule:
 invest
If (payback) < x years ?
Weakness:
1) ignores time value of money
2) “x” is chosen arbitrarily
These can lead to the wrong rankings of different projects, or even to the adoption of
negative NPV projects:
Project 1
Project 2
Project 3
Year 0
-100
-100
-100
Year 1
60
40
0
Year 2
39
60
0
Year 3
1
0
80
Year 4
0
0
80
Payback Period;
(rank)
3 years ;
(2nd)
2 years;
(1st)
4 years;
(3rd)
NPV (@ i=10%);
(rank)
-12.47 ;
(2nd)
-14.05 ;
(3rd)
14.75;
(1st)
Result: Rank order completely reversed when NPV criterion is applied
Biomass Economics -- Unit 5
NPV: ... (see notes from last time)
Apply NPV with caution: discount rate used must reflect opportunity cost of capital
in an equally risky investment
Internal Rate of Return (IRR):
The discount rate at which the project’s NPV is exactly zero
Note: If IRR > (actual opportunity cost of capital) then NPV > 0
(for well-behaved cash flows)
Decision rule: If our opportunity cost of capital is less than the IRR, ==> invest
A sample well-behaved cash flow:
$
NPV
0
discount rate
IRR
Biomass Economics -- Unit 5
IRR Continued:
For well-behaved cash flows, the IRR and NPV decision rules will agree on which projects
should be financed
What’s the difference?
NPV is in terms of dollars
IRR is in terms of rate-of-return
Note: NPV and IRR won’t necessarily agree on the rankings; NPV is the better measure if
projects are mutually exclusive
$
0
NPV - Project 1
io
i1
discount rate
NPV - Project 2
Biomass Economics -- Unit 5
Example:
What is the IRR of a project 1 above?
Cash flow:
Year 0
-100
Year 1
60
Year 2
39
Year 3
1
Year 4
0
PV(Costs) = 100
PV (Benefits) = 60/(1+i) + 39/(1+i)^2 + 1/(1+i)^3
NPV = PV(Benefits) - PV(Costs) = 0
(to calculate IRR)
i.e. solve (for i):
100 = 60/(1+i) + 39/(1+i)^2 + 1/(1+i)^3
How?
•
•
Method 1: Trial and error (plug in various values of “i”, and compute)
Method 2: Use “goal seek” in Excel 2007. (In older versions I think this was called
“Solver”)
<Computer demo>
Biomass Economics -- Unit 5
A
1
i
2
0.1
3
Year
0
1
2
3
4
4
5
6
7
8
9
...and the answer is ....
IRR= 14.45%
B

C
Placeholder for i
Cash Flow
-100
0
0
80
80
PV
=B4/(1+$A$2)^A4
=B5/(1+$A$2)^A5
=B6/(1+$A$2)^A6
=B7/(1+$A$2)^A7
=B8/(1+$A$2)^A8
=SUM(C4:C8)
Biomass Economics -- Unit 5
Problem:
1. Compute the IRRs on the following cash flows, in order to rank the projects from most to
least profitable:
Project 1
Project 2
Project 3
Project 4
Year 0
-750
-750
-750
-750
Year 1
0
200
300
100
Year 2
0
200
300
150
Year 3
0
200
300
200
Year 4
0
200
300
250
Year 5
0
200
300
300
Year 6
0
200
300
350
Year 7
0
200
300
400
Year 8
1700
200
-750
-200
2. Compute the NPV and NPV-based rankings for the cash flows above, assuming discount
rates of
a) 2%
b) 9%