You own a gas pipeline that requires no maintenance and will produce $2 million of revenue next year. Unfortunately, the volume of gas is expected to decline by 4.0% per year.
a.If the discount rate is 11.0% and the pipeline lasts forever, what is it worth today?
b.If the pipeline is to be abandoned at the end of 20 years, what is it worth today?
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a. To calculate the present value of the gas pipeline when it lasts forever with a declining volume, we can use the formula for the present value of a perpetuity with a constant growth rate:
Present Value = Annual Revenue / (Discount Rate - Growth Rate)
Given:
Annual revenue = $2,000,000
Discount rate = 11.0%
Growth rate = 4.0%
Plugging in these values into the formula:
Present Value = $2,000,000 / (0.11 - 0.04)
Present Value = $2,000,000 / 0.07
Present Value = $28,571,428.57
Therefore, the gas pipeline is worth approximately $28,571,428.57 today.
b. If the pipeline is to be abandoned after 20 years, we need to calculate the present value of the cash flows for the next 20 years. The declining volume each year will affect the cash flows.
The formula to calculate the present value of cash flows is:
Present Value = Sum of (Annual Revenue / (1 + Discount Rate)^n) for n = 1 to 20
Given:
Annual revenue = $2,000,000
Discount rate = 11.0%
Number of years = 20
Calculating the present value of cash flows for the next 20 years:
Present Value = ($2,000,000 / (1 + 0.11)^1) + ($2,000,000 / (1 + 0.11)^2) + ... + ($2,000,000 / (1 + 0.11)^20)
Using a financial calculator or spreadsheet software, the present value is approximately $19,388,075.75.
Therefore, if the gas pipeline is to be abandoned after 20 years, it is worth approximately $19,388,075.75 today.
To determine the present value of the gas pipeline, we need to calculate the net present value (NPV) of its future cash flows. NPV calculates the current value of future cash flows by discounting them back to present value using a given discount rate.
a. To calculate the present value of the gas pipeline when it lasts forever, we can use the perpetuity formula. The equation for the NPV of a perpetuity is as follows:
NPV = Cash Flow / Discount Rate
In this case, the cash flow represents the revenue generated by the gas pipeline, which is $2 million per year. The discount rate is 11.0%. Using these values, we can calculate the NPV:
NPV = $2,000,000 / 0.11
= $18,181,818.18
Therefore, the value of the gas pipeline today, assuming it lasts forever, is approximately $18,181,818.18.
b. When the pipeline is to be abandoned in 20 years, we need to determine the present value of its cash flows for those 20 years. The volume decline of 4.0% per year also needs to be accounted for.
To calculate the present value of the cash flows for each year, we can use the formula for the sum of a geometric series. The equation for the NPV of a geometric series is as follows:
NPV = Cash Flow * (1 - (1 + Discount Rate)^(-n)) / Discount Rate
In this case, the cash flow is $2 million per year, the discount rate is 11.0%, and the number of years (n) is 20. Using these values, we can calculate the NPV:
NPV = $2,000,000 * (1 - (1 + 0.11)^(-20)) / 0.11
= $16,076,899.36
Therefore, the value of the gas pipeline today, considering it will be abandoned in 20 years, is approximately $16,076,899.36.