Question

(Adapted from Chapter 14, Exercise 1, Berck and Helfand 2011) An activity to improve the well-being of some impoverished people will provide benefits of $1 million right now, but will obliterate the Earth in 200 years. The world’s value in 200 years is projected at $1 trillion ($10^12). There are no costs or benefits between those two dates.

Rounded to the nearest dollar, what is the net present value of avoiding the world's destruction in 200 years at a 10 percent discount rate?

Answer 1

We have the following information

Value of World in 200 years = $1 trillion or $1,000,000,000,000

Discount rate = 10% or 0.1 per annum

P = F(P/F, i, n)

F = Future amount at the end of year n

P = Principal amount

n = Number of interest periods

i = Interest rate

F = $1,000,000,000,000

n = 200

i = 10% or 0.1

P = 1,000,000,000,000/(1 + 0.1)²⁰⁰

P = 1,000,000,000,000(P/F, 10%, 200)

P = 1,000,000,000,000/(1.1)²⁰⁰

P = $5,265.78

So, the net present value of avoiding the World’s destruction in 200 years at a discount rate of 10% is $5,265.78