Question

Suppose the costs of an environmental pollution-control program are $35 million in year 0 (the start of the program), $55 million in year 1, and $35 million in year 2. Suppose the benefits of the program are $20 million in year 1, $45 million in year 2, and $70 million in year 3.  In this problem, t is defined as the year (so t = 0 for year 0, etc.). The regulatory authority requires the use of a discount rate of 5%.  Use all decimal places in the denominator - round the resulting values to two (2) decimal places and express in dollars ($).

a. Calculate the present value of costs (PVC).

b. Calculate the present value of benefits (PVB).

c. Calculate the present value of net benefits (PVNB).

d. Given your response to part c., should the environmental pollution-control program be implemented? Briefly explain.

Answer 1

Ans:

a)

Present value of costs = $119.10 million

Explanation

Present value = Cash flow * 1/(1+r)^n

= $35 million * 1/(1+0.05)^0 + $55 million * 1/(1+0.05)^1 + $35 million * 1/(1+0.05)^2

= $35 million * 1 + $55 million * 0.952 + $35 million * 0.907

= $35 million + $52.36 million + $31.74 million

= $119.10 million

b)

Present value of benefits = $120.33 million

Explanation

Present value = Cash flow * 1/(1+r)^n

= $20 million * 1/(1+0.05)^1 + $45 million * 1/(1+0.05)^2 + $70 million * 1/(1+0.05)^3

= $20 million * 0.952 + $45 million * 0.907 + $70 million * 0.864

= $19.04 million + $40.81 million + $60.48 million

= $120.33 million  

c)

Present value of net benefits = $1.23 million

Explanation

present value of net benefits = present value of benefits - present value of costs

= $120.33 million - $119.10 million

= $1.23 million

d)

Yes, environmental pollution-control program should be implemented.

Explanation

Since the present value of net benefits is positive, environmental pollution-control program should be implemented.