Declining perpetuities and annuities. You own an oil pipeline that will generate a $2 million cash...
Declining perpetuities and annuities. You own an oil pipeline that will generate a $2 million cash return over the coming year. The pipeline’s operating costs are negligible, and it is expected to last for a very long time. Unfortunately, the volume of oil shipped is declining, and cash flows are expected to decline by 4% per year. The discount rate is 10%.
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What is the PV of the pipeline’s cash flows if its cash flows are assumed to last forever?
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What is the PV of the cash flows if the pipeline is scrapped after 20 years?
Homework Answers
1.
Present valuenof perpetuity=Cas flow next year/(discount rate-growth rate)=2/(10%-(-4%))=14.29
2.
Present value of annuity with growth rate g=Cash flow next year/(1+discount rate)*(1-((1+g)/(1+discount rate))^n)/(1-(1+g)/(1+discount rate))=2/1.1*(1-(0.96/1.1)^20)/(1-0.96/1.1)=13.35
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