422.3
3.Your firm is considering a project with the
following cash flows: an immediate investment of $100 million,
cash inflows of $40 million for 5 years (starting next year), and
a shut-down expense of $20 million in year 5. If your discount
rate for this project is 10%, what is the project's NPV? (2 pts)
First, draw the cash flow diagram for this project:
0 1 2 3 4 5 -100 40 40 40 40 +40-20
The immediate investment of $100 million is already a present value. The 5 cash flows of $40 million can be treated as an annuity and the shut-down expense can be handled separately. The NPV is just the sum of all of the (positive and negative) discounted incremental cash flows associated with the project:
\( \Large NPV = -100 + \frac{40}{.1} \left [ 1 - \frac{1}{\left(1+.10 \right )^{5} } \right ] - \frac{20}{\left(1+.10 \right )^{5} }= 39.213 \).
So, $39.213 million