10.3 Discounting and Net Present Value

Cost-benefit analysis is crucial for evaluating public policies. Discounting and net present value help compare costs and benefits occurring at different times. These techniques account for the time value of money, allowing policymakers to make informed decisions about long-term projects.

Discounting converts future values to present values using a discount rate. Net present value (NPV) sums discounted cash flows to assess project viability. Understanding these concepts is essential for analyzing policies with impacts spanning multiple years or generations.

Discounting Fundamentals

Discount Rate and Time Preference

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• Discount rate represents the opportunity cost of capital or the rate of return that could be earned on an investment in the financial markets with similar risk
• Reflects the time value of money, which suggests that a dollar today is worth more than a dollar in the future due to its potential earning capacity
• Time preference refers to the preference for consumption now rather than later, influencing the choice of discount rate
• Higher time preference indicates a greater preference for present consumption over future consumption, resulting in a higher discount rate

Social Discount Rate and Intergenerational Equity

• Social discount rate is used to compare costs and benefits that occur at different points in time from the perspective of society as a whole
• Differs from individual discount rates as it considers the well-being of both current and future generations
• Intergenerational equity concerns the fairness of the distribution of costs and benefits across different generations
• Lower social discount rates place greater weight on the welfare of future generations, promoting intergenerational equity
• Choosing an appropriate social discount rate is crucial for long-term public projects (infrastructure investments, environmental policies) that impact multiple generations

Evaluating Projects

Net Present Value (NPV)

• NPV is a method used to determine the present value of all future cash flows generated by a project, discounted at the appropriate discount rate
• Calculated by summing the present values of all expected cash inflows and outflows over the life of the project
• Formula: $NPV = \sum_{t=0}^{n} \frac{C_t}{(1+r)^t}$, where $C_t$ is the net cash flow at time $t$, $r$ is the discount rate, and $n$ is the number of periods
• A positive NPV indicates that the project is expected to generate a return greater than the discount rate and should be accepted
• A negative NPV suggests that the project is not economically viable and should be rejected

Benefit-Cost Ratio and Internal Rate of Return (IRR)

• Benefit-Cost Ratio (BCR) is the ratio of the present value of benefits to the present value of costs
• Calculated by dividing the sum of discounted benefits by the sum of discounted costs
• A BCR greater than 1 indicates that the project's benefits outweigh its costs, making it economically feasible
• Internal Rate of Return (IRR) is the discount rate that makes the NPV of a project equal to zero
• Represents the highest rate of return that a project can generate without incurring losses
• To calculate IRR, set the NPV formula to zero and solve for the discount rate $r$
• A project is considered acceptable if its IRR is higher than the required rate of return or the cost of capital
• When comparing mutually exclusive projects, the one with the highest IRR is generally preferred, assuming all other factors are equal