Net Present Value (NPV)

Part of the decision making process is comparing the estimated cash flows from the available opportunities.  NPV uses the time value of money to summarize a cash flow forecast to a single value.  The concept is that the value of cash far in the future is lower than the value of cash in the short term.  This is expressed in the discount rate used in the calculation.  The discount rate is analogous to the interest rate the investor would like for cash deposited at a secure bank.

Within the investment process, NPV is used to determine the magnitude of an investment.  For example, a major energy company may only be interested in projects with an NPV greater than $100m as anything smaller will have no impact on the balance sheet, whilst a small property company may not want anything greater than $10m in order to mitigate risk.

Profitability is indicated by the Internal Rate of Return (IRR) of a project.  The basis of decision making in many organizations is that the NPV is within defined limits and that the IRR is greater than a "hurdle rate".  The selection of NPV thresholds, discount and hurdle rates is a feature of the organization culture.

Sample Data

The examples are based on two hypothetical projects.

Project A takes place over five years, it starts with an initial outlay incurred over the first year, followed by three years of positive cash-flow and some post-project expenditure during the final year.

This project is typical of a mineral extraction project where there is a front end investment in facilities (e.g. processing plant, transportation infrastructure etc.), a period of positive cash flow as the mineral is sold and finally an environmental clean-up (e.g. removal of spoil heaps etc.).

Project B is a simple asset purchase followed by ten years of positive cash flow.

Project B is typical of a real estate venture or lease finance deal.

Calculation

The calculation of an NPV, once a discount rate has been set is three stage process:

Step 1 - Calculate Discount Factors

The discount factor (DF) for a given year end (Y) where the discount rate is expressed as a %age is derived from the formula

Discount Factor = (1+Discount_Rate/100)^-Y

Cash flows occurring "now", i.e. Y=0 are undiscounted.

Typically, this calculation is performed using a spreadsheet (e.g. Excel, Google Docs etc.),  The table below shows the discount factors from "now" to the end of Year 5 for discount rates of 5%, 10% and 15%.

Year	Discount Rate (%)
	5	10	15
0	1.000	1.000	1.000
1	0.952	0.909	0.870
2	0.907	0.826	0.756
3	0.864	0.751	0.658
4	0.823	0.683	0.572
5	0.784	0.621	0.497

The table is based on the assumption that the cash flow occurs at the year end.  If the cash flows are more complex, then discount factors can be calculated for actual time they occur. Also if the cash flows are continuous, then assuming that they occur at mid-year may be prefereable.

Step 2 - Discount the Cash flow

The calculations are based on a discount rate of 10%.  The discounted cash flow for a given year is calculated by multiplying the undiscounted cash flow for that year by the appropriate discount factor.

Year	DF	Undiscounted		Discounted
		A	B	A	B
0	1.000	-10.0	-50.0	-10.0	-50.0
1	0.909	-40.0	10.0	-36.4	9.1
2	0.826	35.0	10.0	28.9	8.3
3	0.751	30.0	10.0	22.5	7.5
4	0.683	25.0	10.0	17.1	6.8
5	0.621	-17.0	10.0	-10.6	6.2
6	0.564	0.0	10.0	0.0	5.6
7	0.513	0.0	10.0	0.0	5.1
8	0.467	0.0	10.0	0.0	4.7
9	0.424	0.0	10.0	0.0	4.2
10	0.386	0.0	10.0	0.0	3.9
Totals		23.0	50.0	11.6	11.4

 Step 3 - Sum the Discounted Cash Flows

The final stage is to sum the discounted cash flows to form the NPV.  It can be seen from the above examples, that whilst there is a significant difference in the total cash flows, the NPVs are similar.

Sensitivity Analysis

Part of the appraisal process is to determine what factors influence the outcome, one aspect of this is to perform a sensitivity analysis.  Typically, variations in the NPV are potted for a base case, with variations in a single parameter.  In the case of a mineral extraction project, the cost of site restoration maybe a critical factor.  As this topic is related to NPV, we'll look at the discount rate itself.  A project which relies on cash flows far into the future will be more sensitive to the choice of discount rate.  The table below shows the NPV of the example projects at different discount rates:

Project	Discount Rate
	5%	10%	15%
A	16.8	11.6	7.2
B	27.2	11.4	0.2

The effect of choice of discount rate is clearer when displayed on a graph.

Footnote

Investment appraisal is a complex task.  The maths and stats element can be one of the easier elements, the social, cultural and environmental elements may be harder to assess.

Page Updated: 01-Nov-2007

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