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)

The net present value of benefits is the present value of those net benefits.

Net benefit is simply the sum of benefits minus the sum of costs.

NPV is the current value of all net benefits associated with a project

The net benefits are converted to present value by discounting.

NPV Formula

Tt

tt

tt

r

CostBenefitNPV

1 1

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

Tt

tt

t

Tt

tt

t

r

Costr

Benefit

BCR

1

1

1

1

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