NPV – Net Present Value
By James Bell
- Finance ,
- Tags: Finance
- 01 Jul
The Net Present Value is used to show the current value of future cash flows. This simple formula is a good primer for understanding the time value of money. By using a discount rate consistently over many periods, this formula is not only good at capital budgeting analysis, it’s also a great teaching tool. You’ll see that as you calculate periods farther out from your present one, that the present value is reduced ceteris paribus.
Net Present Value
![\[ NPV=\sum_{n=1}^{N} \frac{C_n}{(\{1+r^n)}}- C_0 \]](http://stumptownfin.com/wp-content/ql-cache/quicklatex.com-fa2bf167fd2b07184d15500bff63fff5_l3.png "Rendered by QuickLaTeX.com")
where
Net cash Inflows during period n
Initial Investment at period 0
Discount Rate
Total Number of Periods
Each Period
Net Present Value
We are adding the present values of each period and then subtracting the initial investment from this newly calculated aggregate value.
Net Cash Inflows
Click here to see how to calculate free cash flows. These are the expected cash flows that are generated each period.
Initial Investment
This is the initial outlay of cash, or investment made to generate future cash flows. At the end of the day, you have more or less than this number. Any gains or losses will use this as a basis of measurement and this is why we subtract it at the end.
Discount Rate
The discount rate considers the risk of uncertainty and the time value of money. Weighted Cost of Capital, or WACC is often used as the discount rate when we assume the investment has the same market risk as the firm. Other important risks, such as Enterprise Risk, exists partly in the future cash flows, but also in the cost of capital which is a part of the discount rate.
The higher the discount rate, the greater the uncertainty which lowers our present value of future cash flows. Assuming the discount rate is constant is better for shorter term projects, or for mature companies that are very consistent year over year.
Periods
These are typically years, but it could be quarters or theoretically any unit of time as long as it’s consistently used. If you are doing this in Excel, each year will have a column that you add up to get our NPV. Total years is denoted by the big N, and each year by the lowercase n so you know how many years to include if you choose similar notation for communication.
Other Considerations
NPV is a formula that contains other formulas and assumptions. We compute CAPM in order to compute WACC, then we take WACC as our discount rate to compute NPV. Yet unsystemic risks, such as Enterprise Risk we include in our Cost of Capital. Some have found that adoption of Enterprise Risk Management actually reduces the cost of capital ( Berry-Stolzle & Xu, 2018). At a minimum, 25% of the total increase in value from ERM comes from the reduction in the cost of capital (Hoyt & Liebenberg, 2011).
Citations
Hoyt, R., & Liebenberg, A. (2011). The Value of Enterprise Risk Management. The Journal of Risk and Insurance, 78(4), 795-822.
Berry-Stolzle, T., & Xu, J. (2018). ENTERPRISE RISK MANAGEMENT AND THE COST OF CAPITAL. Journal of Risk and Insurance, 85(1), 159-201.