Question

The Environmental Protection Agency (EPA) is deciding whether to undertake two different environmental protection programs. You have been hired to advise the EPA and are presented with the following information:

Program A: Spend $10 million today to reduce children’s exposure to lead in schools, which is expected to save 5 children from getting cancer in 9 years and 10 children from getting cancer in 10 years.

Program B: Spend $5 million each year for the next 3 years to reduce ozone air pollution, which is expected to save two people from premature death each year over the next 4 years.

Additional information: The value of a statistic life is estimated at $3 million. The EPA employs a discount rate of 6%. There are no other relevant costs and benefits.

If the EPA can choose at most one of these programs, should it undertake Program A only, Program B only, or neither project? Explain the reason for your recommendation and clearly show any calculations you make.

Answer 1

We need to calculate Annual Worth of each option here.
PW = Cash Flow / (1+Interest Rate) ^ Duration
AW = NPW / PW Annuity Factor

Program A
PW of initial cost = $10 million

If the project life is 9 years then it has benefits of $15 million
(3 million * 5) / (1.06 ^ 9) = 8.88 million
NPW
8.88 - 10 = -1.12 million

This is negative so we will consider 10 year duration
(3 million * 10) / (1.06 ^ 10) = 16.75 million

NPW
16.75 - 10 = 6.75 million

EAW = 6.75 / 7.3601
= 0.9171 million

Program B
PW of Cost
=PV(6%,3,-5) = 13.37 million

PW of benefits
=PV(6%,4,-6) = 20.79 million

NPW = 20.79 - 13.37 = 7.42 million

EAW = 7.42 / 3.4651
= 2.14 million

Program A has higher benefits but time value of money indicates that the Program B has higher benefits because its realization period is relatively shorter than that of Program A.