Question

A proposed nuclear power plant will cost $1.9 billion to build and then will produce cash flows of $270 million a year for 15 years. After that period (in year 15), it must be decommissioned at a cost of $870 million. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers in billions rounded to 3 decimal places.)

a. What is project NPV if the discount rate is 4%?

b. What if the discount rate is 18%?

Answer 1

a.

NPV at 4% discount rate

0.619

billion

Working:

# 1

Present value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.04)^-15)/0.04

i

4%

=

11.11839

n

15

# 2

Present value of 1

=

(1+i)^-n

=

(1+0.04)^-15

=

0.555265

# 3

Present value of annual cash flows

=

0.2700

billion

*

11.11839

=

3.001965

Less:

Present value of cash outflow:

Present value of initial cost

1.900

Present value of cost in 15 years

0.8700

billion

*

0.555265

=

0.4831

2.383

NPV

0.619

b.

NPV at 18% discount rate

-0.598

billion

Working:

# 1

Present value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.18)^-15)/0.18

i

18%

=

5.091578

n

15

# 2

Present value of 1

=

(1+i)^-n

=

(1+0.18)^-15

=

0.083516

# 3

Present value of annual cash flows

=

0.2700

billion

*

5.091578

=

1.374726

Less:

Present value of cash outflow:

Present value of initial cost

1.900

Present value of cost in 15 years

0.8700

billion

*

0.083516

=

0.0727

1.973

NPV

-0.598