Equation (15.5) (page 586) shows the net present value of an investment in an electric motor factory. Half of the $10 million cost is paid initially and the other half after a year. The factory is expected to lose money during its first two years of operation. If the discount rate is 4 percent, what is the NPV? Is the investment worthwhile?

The net present value (NPV) shows the difference between the cash inflow and outflow; thus, it considers all the future receives from the investment. It will be attractive only when it has a positive value. Otherwise, it will not be worth taking the investment.

The project cost $10 million; the factory lost $1 million in the first year and $0.5 million in the second year. It also earned $0.96 million until the year 20. The rate of interest is 4%, i.e., 0.04 (=4/100).

The NPV is calculated below:

$$\begin{gathered} NPV=-5-\frac{5}{\left(1+r\right)}-\frac{1}{{\left(1+r\right)}^2}-\frac{0.5}{{\left(1+r\right)}^3}-\frac{0.96}{{\left(1+r\right)}^4}-\frac{0.96}{{\left(1+r\right)}^5}-..................-\frac{0.96}{{\left(1+r\right)}^{20}} \\ =-5-\frac{5}{\left(1+0.04\right)}-\frac{1}{{\left(1+0.04\right)}^2}-\frac{0.5}{{\left(1+0.04\right)}^3}-\frac{0.96}{{\left(1+0.04\right)}^4}-\frac{0.96}{{\left(1+0.04\right)}^5}-..................-\frac{0.96}{{\left(1+0.04\right)}^{20}} \\ =-5-4.808-0.925-0.445+0.821+0.789+0.759+0.730+0.701+0.674+0.649 \\ +\text{0.624 + 0.600 + 0.577 + 0.554 + 0.533 + 0.513 + 0.493 + 0.474 + 0.456 + 0.438 + 0.456} \\ =\$0.338million \\ =\$338,000 \end{gathered}$$

The NPV is negative, i.e., the net loss of the investment will be $338,000. Hence, the investment is not worthwhile.