Transcript AGEC/FNR 406 LECTURE 10 Rice drying on the Philippine National Highway Benefit-Cost Measures Lecture Goals: 1.

AGEC/FNR 406
LECTURE 10
Rice drying on the Philippine National Highway
Benefit-Cost Measures
Lecture Goals:
1. Present three tools of benefit-cost analysis
2. Discuss advantages and disadvantages of BCA
Don’t neglect to review the BCA packet!
Three BCA tools:
1. Net Present Value (NPV)
2. Benefit-Cost Ratio (BCR)
3. Net Present Value (NPV)
Net Present Value (NPV)
NPV is the current value of all net benefits
associated with a project
Net benefit is simply the sum of benefits minus
the sum of costs.
The net present value of benefits is the present
value of those net benefits.
The net benefits are converted to present value
by discounting.
NPV Formula
t T
NPV  
t 1
 Benefit
t
 Cost
1  r 
t
t

Key Point
If the project has a NPV > 0, then it is
worth considering on its economic merits.
If the project has a NPV < 0, then it fails
to return benefits greater than the value of
the resources used.
NPV Example
Time
Benefit
Cost
Net Benefit
0
100
150
-50
1
100
100
0
2
100
50
50
all
300
300
0
-50/(1+.1)0 + 0/(1+.1)1 + 50/(1+.1)2 = -8.68
Benefit Cost Ratio (BCR)
BCR is computed as the PV of Benefits divided
by the present value of Costs.
Discounted benefits and discounted costs are
calculated and summed separately, then divided.
BCR Formula
Benefitt 

t

1 r
t 1
BCR  t T
Costt 

t
t 1 1  r 
t T
Key Point
If the project has a BCR > 1, then it is
worth considering on its economic merits.
If the project has a BCR < 1, then it fails
to return benefits larger than its costs.
BCR Example
Num. = 100/(1.1)0 + 100/(1.1)1 +100/(1.1)2 = 273.54
Den. = 150/(1.1)0 + 100/(1.1)1 +50/(1.1)2 = 282.22
BCR = 273.54/282.22 = 0.97 < 1
Internal Rate of Return (IRR)
The IRR is the maximum interest rate that could
be paid for the project resources that would leave
enough money to cover investment costs and still
allow society to break even.
The IRR is the discount rate at which the PVof
benefits equals the present value of costs.
IRR Formula
Solve for the IRR by finding i that solves:
PV(Benefits) = PV(Costs)
Use algebra or a spreadsheet
Key Point
The IRR must exceed the chosen
discount rate for the project to be
accepted.
IRR Example
100/(1 + i)0 + 100/(1 + i)1 +100/(1 + i)2 =
150/(1 + i)0 + 100/(1 + i)1 +50/(1 + i)2
i=0
Advantages of BCA
1. Provides a framework
2. BCA is quantitative
3. BCA is based on facts
4. The methods provide clarity
5. Results allow comparability
Disadvantages of BCA
1. Requires valuation
2. Discount rate sensitivity
3. Plagued by uncertainty
4. Silent on equity
5. BCA is anthropocentric