Jordan is considering building a nuclear power plant, which will be ready for production in 2030. The country's governing body is also considering a decommissioning liability law for the operator to put aside $1 million every month towards decommissioning cost, when the plant is producing electricity. During the 60 years of production life of the plant, the operator will put $1 million at the end of the month in a savings account, earning 7.25% compounded semi-annually. At the end of the production life of the plant, there are no more contributions and the money is expected to grow at the rate of 6% compounded quarterly for the next 30 years. What will be the value of the decommissioning fund in 2120?

Question

Quizplus · Accepted Answer

To calculate the value of the decommissioning fund, we need to use the formula for the future value of an annuity due and the future value of a lump sum.

First, we need to calculate the future value of the monthly contributions for 60 years, which is an annuity due. We have:

PMT = $1 million
n = 60 x 12 = 720 months
i = 7.25%/2 = 3.625% per six months
We need to use the formula for the future value of an annuity due with semi-annual compounding:

FV = PMT x [((1 + i)^n - 1) / i] x (1 + i)
FV = $1 million x [((1 + 3.625%)^720 - 1) / 3.625%] x (1 + 3.625%)
FV = $181,878,436

This means that by the end of the production life of the plant, the operator will have saved $181,878,436 for decommissioning.

Now, we need to calculate the future value of this lump sum for 30 years after the end of production, with quarterly compounding:

PV = $181,878,436
n = 30 x 4 = 120 quarters
i = 6%/4 = 1.5% per quarter
We need to use the formula for the future value of a lump sum:

FV = PV x (1 + i)^n
FV = $181,878,436 x (1 + 1.5%)^120
FV = $70,936,508,221

Therefore, the value of the decommissioning fund in 2120 will be $70.94 billion, which is option D.

Jordan Is Considering Building a Nuclear Power Plant, Which Will