Now that you can value benefits and costs, here's a crucial complication: timing and uncertainty matter! A dollar today isn't worth the same as a dollar next year, and future outcomes are often uncertain.

Engagement Message

Why might you prefer $100 today over $100 next year, even with zero inflation?

Discounting converts future values to present values for fair comparison. If you could invest $100 today at 5% interest, you'd have $105 next year - so $105 next year is worth $100 today.

Engagement Message

If the interest rate were 10% instead, would future money be worth more or less in present value?

Present Value = Future Value ÷ (1 + discount rate)^years

So $100 in one year at 5% = $100 ÷ (1.05) = $95.24
$100 in two years at 5% = $100 ÷ (1.05)² = $90.70

Engagement Message

How would you calculate the present value of $100 received in three years at 5%?

The social discount rate for government policy is hotly debated. Higher rates (5-7%) favor present benefits over future costs. Lower rates (2-3%) give more weight to future generations. This matters enormously for long-term policies.

Engagement Message

Which discount rate seems more appropriate for environmental policies with 50-year impacts?

Real policies face unknowns: Will ridership be 1,000 or 5,000 daily? Will costs be $2 million or $3 million? Expected value helps us deal with uncertainty by considering multiple scenarios with their probabilities.

Engagement Message

If there's a 30% chance of 1,000 riders and 70% chance of 3,000 riders, what's the expected ridership?

Expected value = (Probability₁ × Outcome₁) + (Probability₂ × Outcome₂)

For our ridership: (0.30 × 1,000) + (0.70 × 3,000) = 300 + 2,100 = 2,400 expected riders