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%.

(a) What is the PV of the pipeline’s cash flows if its cash flows are assumed to last forever?
(b) What is the PV of the cash flows if the pipeline is scrapped after 20 years?

The present value of the cash flow in perpetuity is $14,285,714.29

The present of the cash flow for 20 years is $13347130.72

Explanation:

The present value of a cash flow growing in perpetuity is given as:

Cashflow/rate of return-growth rate

Cash flow $2 million per year

rate of return 10%

growth rate is -4%

Present value of cash flow in perpetuity is =$2000000/(0.10-(-0.04)

                                                                        =$14,285,714.29

However, the formula present value of cash flow for  given number of years is as follows:

PV= cash flow*1/(rate-growth rate)*1-(1+growth rate)^time/(1+rate)^time

PV=2000000*1/(0.10-(-0.04))*1-(1+(-0.04)^20/(1+0.10)^20=

Time is the number of years -20 years

PV=(2000000*7.142857143 )*1-(0.442002434 /6.727499949)

PV=$13347130.72

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