This question involves what economists call the "discount rate," which expresses how much future benefits should be "discounted" compared to present benefits of the same size. If your answer to the hypothetical question is that saving the 100 lives 50 years from now has the same value as saving 100 lives right now, you are applying a discount rate of 0%--that is, benefits in the future are not discounted relative to benefits in the present. If your answer is that saving 100 lives now is a greater benefit than saving 100 lives 50 years from now, you are applying a positive discount rate.
Almost all economists argue that a positive discount rate is appropriate. At an intuitive level, having a benefit happen sooner is worth something. Also, there is a level of certainty in saving 100 lives right now, while saving 100 lives in 50 years has some degree of uncertainty as to whether that will happen. In addition, say that the hypothetical example would cost $1 billion in the present. If you invested that money in a safe financial that pays 3% per year, then after 50 years of compound interest it would add up to $4.38 billion--which makes the cost-benefit tradeoff 50 years from now look less attractive. A discount rate of zero would mean that we treat all costs and benefits as equivalent, no matter whether they occur in the present, the near-future, the middle-future, or the unimaginably distant future. Thus, the near-certainty of a large asteroid hitting the earth in the next few million years would be treated as of equal concern to if we could see the asteroid coming and the event was 10 years away--because the future isn't discounted.
But what should the discount rate be? And should the discount rate be a constant value over time, or a declining value over time? Consider what's at stake here. A higher discount rate means that we have more of an orientation to the present, and in particular will treat future benefits as much less important. A lower discount rate means that while we still have an orientation to the present, we are giving greater weight to what happens in the future. For public policy issues that involve spending resources now for a benefit that would occur (at least partly) in the distant future, like some of the risks of climate change, or the chance of an asteroid hitting the earth, it turns out that the choice of discount rate is extremely important.
An all-star list of environmental and welfare economists tackle this issue in "Should Governments Use a Declining Discount Rate in Project Analysis?" which appeared in the Summer 2014 issue of the Review of Environmental Economics and Policy (8:2, pp. 145–163). The list of authors is
Kenneth J. Arrow, Maureen L. Croppery, Christian Gollierz, Ben Groom, Geoffrey M. Heal , Richard G. Newell, William D. Nordhaus, Robert S. Pindyck, William A. Pizer, Paul R. Portney, Thomas Sterner, Richard S. J. Tol , and Martin L. Weitzman. Here's how the authors describe the curent US policy with regard to discount rates:
"In the United States, however, the Office of Management and Budget (OMB) recommends that project costs and benefits be discounted at a constant exponential rate (which, other things equal, assigns a lower weight to future benefits and costs than a declining rate), although a lower constant rate may be used for projects that affect future generations. ... For intragenerational projects, the OMB (2003) recommends that benefit-cost analyses be performed using a discount rate of 7 percent, representing the pretax real return on private investments, and also a discount rate of 3 percent, representing the “social rate of time preference.”Two points are worth noticing here. First, the U.S. policy has a fixed discount rate over time. Second, the difference between a 7% rate and a 3% discount rate over a long period of time like a century is enormous. Consider a policy that has a benefit of $100 billion that occurrs 100 years in the future. At a discount rate of 7%, it is worth spending $115 million or less in the present to achieve that benefit. (Sometimes it's useful to think of this calculation in reverse: If you invested $115 million at a 7% annual interest rate, you would have approximately $100 billion at the end of a century.) At an annual discount rate of 3% of annual rate it would be worth spending up to $5.2 billion in the present to achieve that benefit. Thus, one of the differences between those who would spend many billions of dollars in the present to reduce the risks of climate change in the decades and centuries ahead, and those who would spend only millions of dollars, can be traced to different discount rates.
But what about other countries? The authors write (citations omitted):
"In evaluating public projects, France and the United Kingdom use discount rate schedules in which the discount rate applied today to benefits and costs occurring in the future declines over time. That is, the rate used today to discount benefits from year 200 to year 100 is lower than the rate used to discount benefits in year 100 to the present."They argue that after taking issues into account like uncertainty about the future, and the fact that the path of benefits recognized in the future will tend to follow a correlated pattern (rather than being random from year to year), a declining discount rate makes sense. You can check the articles for some ways in which such a rate could be estimated from data, but in practice, the decision of what rate to use may be guided by such studies, while ultimately being chosen by a regulator. They conclude:
"We have argued that theory provides compelling arguments for using a declining certainty equivalent discount rate. ... Clearly, policymakers should use careful judgment in estimating a DDR [declining discount rate] schedule, whichever approach is used. Moreover, as emphasized earlier, the DDR schedule should be updated as time passes and more data become available. Establishing a procedure for estimating a DDR for project analysis would be an improvement over the OMB’s current practice of recommending fixed discount rates that are rarely updated."