Question

You own an oil pipeline that will generate a $2 million cash return over the coming year. The pipelines operating costs are negligible, It is expected to last for a very long time. Unfortunately the volume of oil ship is declining and cash flows are expected to decline by 4% per year. The discount rate is 10%. What is the PV of the pipelines cash flows if its cash flows are assumed to last for ever? don round intermediate calculations. round your answer to the nearest while dollar amount. what is the pv of the cashflows if the pipeline is scrapped after 20 years? do not round intermediate calculations. round your answer to the Hearst whole dollar amout.

Answer 1

The pipeline project is expected to generate $2 mn in the first year.

Cashflows are expected to decline at a rate of 4% each year.

Discount rate is 10%

• In the first scenario we expect the pipeline to run for ever or perpetuity.

For this condition the discounted agggregate cashflow would look like such:

C (individual cashflow) = $2 mn, r=10%, g= -4%

PV = C/(1+r) + C/(1+r)^2 + C/(1+r)^3 + ............

or PV = C/r ( Simple derivation from above formula. Known as Present value of perpetuity formula)  

For growing or decreasing perpetuity the formula would be:

PV = C/(r-g) (g:- growth rate)

Ans: PV = 2/(0.1+0.04) (as growth would be -4%)

= 2/0.14 = $14.286 mn

• In the second scenario we consider the project to run for 20 years

Using the formula for growing annuity formula we get:

PV = C/(r-g) * [1- ((1+g)/(1+r))^t] ( t:- age of project or no of times cashflows)

PV = 2/(0.1+0.04) * [1-(0.96/1.1)^20]

PV = 14.286 * [1- 0.0657] = 14.286 * 0.9343 = $13.347 mn.