**The NPV of an investment is the present value of the series of cash flows generated by the investment minus the cost of the initial investment**

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### 1. Net Present Value (*NPV*) explained

THE net present value (** NPV**) of an investment is the present value of the series of cash flows generated by the investment minus the cost of the initial investment. Each cash inflow/outflow is discounted back to its present value and then summed together:

Where *t* is the time of the cash flow; *r* is the discount rate (see below for further explanation); *Ct* is the net cash flow (cash inflow minus cash outflow) at time *t*; and *Co* is the cost of the initial investment made at time zero.

NPV is used to analyse the profitability of an investment. As a general rule, assuming you have selected an appropriate discount rate, only those investments that yield a positive NPV should be considered for investment.

### 2. The discount rate

The rate used to discount future cash flows to their present value is an important variable in the net present value calculation. To some extent, the selection of the discount rate depends on the use to which the NPV calculation will be put.

**2.1 Option 1 – cost of capital:**

One option that is often used is to use a firm’s weighted average cost of capital.

There are two problems with using the cost of capital for the discount rate. Firstly, it may not be possible to know what the cost of capital will be in the future. One solution to this problem is to use a variable discount rate that increases over time to reflect the yield curve premium for long-term debt. A yield curve is the relation between the interest rate (or cost of borrowing) and the time to maturity and is usually upward sloping asymptotically. There are two common explanations for why the yield curve is upward sloping. Firstly, it might be that rising interest rates are expected in the future and investors who are willing to lock their money in now therefore need to receive a higher rate of interest. Secondly, even if interest rates are not expected to rise, longer maturities involve greater risks to an investor and so, to compensate for these inherent uncertainties about the future, a risk premium should be paid.

The second problem with using the cost of capital for the discount rate is that it does not take into account opportunity costs. A positive NPV calculation would tell us that the investment is profitable, but would not tell us whether the investment should be undertaken because there may be more profitable investment opportunities.

**2.2 Option 2 – opportunity cost:**

A second option is to use a discount rate that reflects the opportunity cost of capital. The opportunity cost of capital is the rate which the capital needed for the project could return if invested in an alternative venture. Obviously, where there is more than one alternative investment opportunity, the opportunity cost of capital is the expected rate of return of the most profitable alternative.

For example, assume that a firm has two investment options, investing in Project A (its existing line of business) or Project B (a new line of business). Based on past experience, the firm knows that it can obtain a 15% return from investing in Project A. This means that the opportunity cost of capital for investing in Project B is 15%. Thus, an NPV calculation for Project B will use a discount rate of 15%.

### 3. Common pitfalls

**3.1 Negative future cash flows:**

One potential problem with NPV is that if, for example, the future cash flows are negative (for example, a mining project might have large clean-up costs towards the end of a project) then a high discount rate is not cautious but too optimistic. A way to avoid this problem is to explicitly calculate the cost of financing any losses after the initial investment.

**3.2 Adjusting for risk:**

Another common pitfall is to adjust for risk by adding a premium to the discount rate. Whilst a bank might charge a higher rate of interest for a risky project, that does not necessarily mean that this is a valid way to adjust a net present value calculation. One reason for this is that where a risky investment results in losses, a higher discount rate in the NPV calculation will reduce the impact of such losses below their true financial cost.

**3.3 Dealing with negative NPV:**

The general rule is that only those investments that yield a positive NPV should be considered for investment. However, this will only be true if we have selected an appropriate discount rate. For example, in the example in section 2.2, if we used a discount rate higher than 15% in the NPV calculation for Project B then obtaining a negative NPV calculation does not necessarily mean that we should reject Project B. Unless we have intellionally chosen a higher discount rate to adjust for the risk of the project, the negative NPV result does give us any useful information.

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