Question

Suppose analysts agree that the losses resulting from climate change will reach x dollars 100 years from now. Use the concept of present value to explain why estimates of what needs to be spent today to combat those losses may vary widely. Would you expect the variation to narrow or get wider if the relevant losses were 200, rather than 100, years into the future?

Complete the following using a principle amount = $100.

Instructions: Enter your responses rounded to two decimal places.

Discount rate / years 20 yrs 50 yrs 100 yrs
2%
5%

Is there greater volatility with a lower discount rate or higher discount rate?

The higher rate
The lower rate

Answer 1

We are given the principle amount = $100. For a discount rate of 2%, the value of $100 will turn out to be $100*(1 + 2%)^20, = 148.59, 20 years from now, $100*(1 + 2%)^50 = 269.16, 50 years from now and similarly $100*(1 + 2%)^100 = 724.46, 100 years from now.

For a discount rate of 5%, the value of $100 will turn out to be $100*(1 + 5%)^20, = 265.33, 20 years from now, $100*(1 + 5%)^50 = 1146.74, 50 years from now and similarly $100*(1 + 5%)^100 = 13150.13, 100 years from now.

There is a greater volatility with a higher discount rate.

The estimates of what needs to be spent today to combat those losses may vary widely because of risk factors associated with the market for which expected discount value is taken to care off. We can expect the variation to get wider if the relevant losses were 200, rather than 100, years into the future because then the amoun will be multiplied / compounded for a larger period of time.