Question

You can purchase an oil pipeline for $3 million today. It is forecasted to generate $2 million a year, with the first payment one year from today. The pipeline’s operating costs are negligible, and it is expected to last for a very long time. Unfortunately, the volume of oil shipped through this pipeline is expected to decline, and the cash flows are expected to decline by 4% per year. Further, to comply with environmental regulations, it will need a $1.2 million investment after 10 years from its purchase (today). Assuming the projects discount rate is 10%… a. What is the NPV of the pipeline’s cash flows if its cash flows are assumed to last forever? b. What is the NPV of the cash flows if the pipeline is scrapped after 20 years?

Answer 1

A: Initial outlay = 3000,000

PV of cash inflows = CF1/(r-g)

= 2000000/(10%+4%)

=14285714.29

PV of investment after 10 years = Fv/(1+r)^n

= 1200,000/1.1^10

=462651.95

Net present value = -3000000+ 14285714.29 -462651.9473

= 10,823,062.34

B: Initial outlay = 3000,000

PV of cash inflows = (P/(r-g))*(1-((1+g)/(1+r))^n)

= (2000000/(10%+4%))*(1-((1-0.04)/(1.1))^20)

= 13347130.8

PV of investment after 10 years = Fv/(1+r)^n

= 1200,000/1.1^10

=462651.95

Net present value = -3000000+ 13347130.8 -462651.9473

=9884478.85