Financial Analysis Of Nuclear Plant Project

Problem:

A proposed nuclear power plant will cost $2.2 billion to build and then will produce cash flows of $300 million a year for 15 years. After that period (in year 15), it must be decommissioned at a cost of $900 million. a. What is project NPV if the discount rate is 5%?  b. What if the discount rate is 18%?

Solution:

To calculate the Net Present Value (NPV) of the nuclear power plant project, we follow these steps:

1. Cash inflows:

   • The plant produces cash flows of $300 million per year for 15 years.

2. Cash outflows:

   • The initial cost of building the plant is $2.2 billion (incurred at time $t = 0$).

   • The decommissioning cost of $900 million is incurred in year 15.

3. Discount rate:

   • We calculate the NPV for two discount rates: 5% and 18%.

Formula:

The NPV formula is:

$$NPV = \sum \left( \frac{C_t}{(1 + r)^t} \right) - C_0$$

Where:

• $C_t$ = Cash flow at time $t$(inflows and outflows)

• $r$ = Discount rate

• $C_0$ = Initial cost (at time $t = 0$)

• $t$ = Time period

Step-by-Step Calculation:

• Initial Cost $C_0 = -2.2$ billion (outflow)

• Annual Cash Flow $C_1$ to $C_{15} = 300$ million

• Decommissioning Cost in Year 15 = $-900$ million

Let's compute the NPV using both discount rates.

The Net Present Value (NPV) of the nuclear power plant project is:

• At a 5% discount rate: $480.98 million

• At an 18% discount rate: -$747.69 million

This means that the project is financially viable at a 5% discount rate but results in a negative NPV at an 18% discount rate, indicating it would not be profitable at the higher rate.