Question

In 200 years an asteroid will destroy Florida. Our only chance to stop the destruction is to launch a missile today to intercept the asteroid. Assume that the nominal value of Florida in 200 years will be $2 trillion. Assume a discount rate of 7%. Let the cost of the missile today be $X . Write a mathematical equation that if true would mean that launching the missile passes a cost-benefit test. (Do not calculate $X explicitly.) Explain each part of your equation in a few words.

Answer 1

[ $2 trillion / ( 1.07 )^200 ) - $X ] >= 0

Step-by-step explanation:

First, we need to determine the equation that determines the present value of Florida

Present value of Florida = Nominal value of Florida in 200 years / ( 1 + discount rate )^numbers of years = $2 trillion / ( 1 + 7% )^200 = $2 trillion / (1.07)^200

Now determine the present value of Missile

Present value of Missile = $X

Hence, the equation for cost-benefit test should be as follow

Present value of Florida - Present value of Missile >= 0

[ $2 trillion / ( 1.07 )^200 ) - $X ] >= 0