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# Net present value

Net present value is a form of calculating discounted cash flow. It is merely the process of calculating the discount of a series of amounts of cash at future dates, and adding them all up. It is a time consuming process, but not difficult at all.

For example: X corporation during capital budgeting is trying to decide whether or not to proceed with a new product line. The new product will have startup costs, operational costs, and incoming cash flows increasing over time.

X corporation's CFO has declared that all new projects must have an NPV of more than zero and an internal rate of return of more than the weighted average cost of capital. Which just means that the project must pay the company back within five years, and must return more than its normal short-term (money market) rate of return. The weighted average cost of capital is 10% per annum (year).

This project will have a cash outlay (up-front cost to purchase machinery and train employees) of \$100,000, and the personnel and maintenance costs will be \$5,000 per year. It will return nothing the first year, but is projected to earn \$31,250 per year after that.

The NPV is calculated for each cash flow:

``` \$-100,000 today = \$-100,000 / 1.10^0 = \$-100,000.
\$-5,000 today = \$-5,000 / 1.10^0 = \$-5,000.
\$-5,000 in 1 yr = \$-5000 / 1.10^1 = \$-4,545.45
\$-5,000 in 2 yr = \$-5000 / 1.10^2 = \$-4,132.23
\$-5,000 in 3 yr = \$-5000 / 1.10^3 = \$-3,756.57
\$-5,000 in 4 yr = \$-5000 / 1.10^4 = \$-3,415.07
\$31,250 in 1 yr = \$31,250 / 1.10^1 = \$28,409.09
\$31,250 in 2 yr = \$31,250 / 1.10^2 = \$25,826.45
\$31,250 in 3 yr = \$31,250 / 1.10^3 = \$23,478.59
\$31,250 in 4 yr = \$31,250 / 1.10^4 = \$21,344.17
```
Then all of the discounted (current) values are added together to find the NPV:

``` -100,000.00
-  5,000.00
-  4,545.45
-  4,132.23
-  3,756.57
-  3,415.07
28,409.09
25,826.45
23,478.59
21,344.17
-----------
-21,791.02
```