Question

Pacific Gas \& Electric wants to build a new power plant that will generate $800 million in ten years. The plant costs $400 million to build. Should PG\&E build the plant if:

a) Interest rate is 4% ? Why?
b) Interest rate is 8% ? Why?

Answer 1

If the interest rate is 4%, PG&E should build the power plant as the present value of future cash flows is greater than the cost of building. If the interest rate is 8%, PG&E should not build the plant as the present value is less than the cost of building.

Step-by-step explanation:

If the interest rate is 4%, the cost of financial capital, and the firm can capture a return of 5%, PG&E should consider building the power plant. This is because the present value of the future cash flows from the plant is greater than the cost of building it. To determine the present value, we can use the formula:

Present Value = Cash Flow / (1 + Interest Rate)^Number of Years

Based on the given information, the present value of the future cash flows from the plant would be:

Present Value = $800 million / (1 + 0.04)^10 = $580.82 million

Since the present value is greater than the cost of building the plant ($580.82 million > $400 million), PG&E should build the plant if the interest rate is 4%.

If the interest rate is 8%, the present value of the future cash flows would be:

Present Value = $800 million / (1 + 0.08)^10 = $386.97 million

In this case, the present value is less than the cost of building the plant ($386.97 million < $400 million), so PG&E should not build the plant if the interest rate is 8%.