Question

1. Consider an environmental policy that promises to yield the following stream of benefits and costs: $1 million of costs immediately and $500,000 of benefits immediately, along with a one- time benefit of $250,000 after 5 years, and another one-time benefit of $250,000 after 10 years. Write an expression for the present value net benefits (PNV) of the policy, assuming r is the discount rate. Would you recommend this policy? Briefly explain.

Answer 1

Cost today= 1000000

Benefit today = 500000

Benefit after 5 yrs= 250000

Benefit after 10 yrs = 250000

let interest rate be r, then

Present value of benefits = 500000 + 250000 / (1+r)^5 + 250000 / (1+r)^10

= 500000 + 250000[ 1/(1+r)^5 + 1/(1+r)^10]

We will not recommend this policy as NPV will be negative at any given r

We have net cost of 500000 in first yr (1000000-500000)

Future benefit of 250000 at the end of yr 5 and yr 10 will be discounted at the given r and will always be less than 500000 so NPV will always be negative.