Social discount rate (SDR) is the discount rate used in computing the value of funds spent on social projects. Discount rates are used to put a present value on costs and benefits that will occur at a later date. Determining this rate is not always easy and can be the subject of discrepancies in the true net benefit to certain projects, plans and policies. The discount rate is considered as a critical element in cost–benefit analysis when the costs and the benefits differ in their distribution over time, this usually occurs when the project that is being studied is over a long period of time.
Use in cost–benefit analysis
It may be used in estimating the value of creating a highway system, schools, or enforcing environmental protection, for example. All of these things require a cost–benefit analysis where policy makers measure the social marginal cost and the social marginal benefit for each project. Almost all new policies will not even be considered until after a cost–benefit analysis has been completed. The social discount rate can appear in both calculations either as future costs such as maintenance or as future benefits such as reduced pollution emissions.
Calculating the true social marginal cost can be a lot easier than measuring the social marginal benefit. Because of the uncertainty involved with calculating benefits, problems may arise e.g., should a dollar amount be put on time based on average wages, contingent valuations or revealed preferences? One of the big problems today is putting a value on a life. While some might say that a life is priceless, economists usually state the value to be somewhere between three and ten million dollars. Another problem is that because the current generation will often be paying for most of the costs while future generations will be reaping most of the benefit, whether current and future benefits ought to be weighed differently.
The proper discount rate should represent the opportunity cost of what else the firm could accomplish with those same funds. If that means that the money could be instead used to invest in the private sector that would yield 5% and that is the next best alternative for using that money then 5% would be the social discount rate
The US government uses a variety of discount rates but something around 7% is what the US Office of Management and Budget (OMB) recommends for a pretax rate of return on private investments. In the United Kingdom, HM Treasury fixes the social discount rate for the public sector at 3.5%.
Calculation
The SDR is directly analogous to concepts found in corporate finance such as the hurdle rate or the project appropriate discount rate; so the mathematics are identical. The benefit or cost per dollar can be calculated by:
where r equals the SDR and t equals time. For benefits or costs that have no end and discount starting tomorrow it is just:
where discounting starts at t=0 it is:
A higher SDR makes it less likely a social project will be funded. A higher SDR implies greater risks to the assumption that the benefits of the project will be reaped. A small increase in the social discount rate can matter enormously for benefits far into the future so it is very important to be as accurate as possible when choosing which rate to use.
Ramsey's social discount rate is calculated as follows:
, where is time preference, is the elasticity of marginal utility of consumption and is the growth rate.
There is a strong case for factoring in the equity issue when discounting benefits and costs of intergenerational projects such as those designed to combat climate change and environmental degradation.
The social discount rate is a reflection of a society's relative valuation on today's well-being versus well-being in the future. The appropriate selection of a social discount rate is crucial for cost–benefit analysis, and has important implications for resource allocations. There is wide diversity in social discount rates, with developed nations typically applying a lower rate (3–7%) than developing nations (8–15%).