Program Background: Corporate Average Fuel Economy $($CAFE$)$ standards regulate the average fuel economy of all the cars that a car manufacturing sells into a given model year. Originally enacted in $1975$ in response to the energy crisis, CAFE standards were meant to reduce oil imports. In addition to reducing U$.$S$.$ dependence on foreign oil, improvements in CAFE standards have been linked to reductions in greenhouse gas emissions. Currently, CAFE standards require cars to achieve $30$ miles per gallon; the proposed program would raise the standard to $40$ miles per gallon.

Program Issues: In order to evaluate the costs and benefits of CAFE standards of $40$ mpg$,$ the following data are relevant:

The program will require $$4$ billion in R&D and other initial investment expenditures per year over the next $10$ years.

The program is expected to increase R&D and unit cost manufacturing costs by $$1,000$ per vehicle.

Annual vehicle sales are estimated at $16$ million vehicles.

Annual reduction in gasoline use will be $120$ billion gallons during the first year and will remain constant.

The average cost of gasoline is $$3\mathrm{.}50$ per gallon.

Annual carbon emissions reductions are estimated at $600$ million tons annually. The social cost of carbon $($a measure of the global damage caused by each ton of CO$2$ emitted$)$ is $$40$ per ton.

Assume all cash flows are realized at the end of each year and that the time horizon is $10$ years. Unless otherwise noted, assume a $5\%$ discount rate.