# The net present value investment rule

Net present value is the difference between a project's value and its costs. The net present value investment rule states that firms should only invest in projects with positive net present value.

When calculating the net present value of a project the appropriate discount rate is the opportunity cost of capital, which is the rate of return demanded by investors for an equally risky project. Thus, the net present value rule recognizes the time value of money principle.

To find the net present value of a project involves several steps:

**How to find the net present value of a project**

1. Forecast cash flows

2. Determinate the appropriate opportunity cost of capital, which takes into account the principle of time value of money and the risk-return trade-off

3. Use the discounted cash flow formula and the opportunity cost of capital to calculate the present value of the future cash flows

4. Find the net present value by taking the difference between the present value of future cash flows and the project's costs

There exist several other investment rules:

- Book rate of return

- Payback rule

- Internal rate of return

To understand why the net present value rule leads to better investment decisions than the alternatives it is worth considering the desirable attributes for investment decision rules. The goal of the corporation is to maximize firm value. A shareholder value maximizing investment rule is:

- Based on cash flows

- Taking into account time value of money

- Taking into account differences in risk

The net present value rule meets all these requirements and directly measures the value for shareholders created by a project. This is fare from the case for several of the alternative rules.

The book rate of return is based on accounting returns rather than cash flows:

**Book rate of return**

Average income divided by average book value over project life

The main problem with the book rate of return is that it only includes the annual depreciation charge and not the full investment. Due to time value of money this provides a negative bias to the cost of the investment and, hence, makes the return appear higher. In addition no account is taken for risk. Due to the risk return trade-off we might accept poor high risk projects and reject good low risk projects.

**Payback rule**

The payback period of a project is the number of years it takes before the cumulative forecasted cash flow equals the initial outlay.

The payback rule only accepts projects that "payback" in the desired time frame.

This method is flawed, primarily because it ignores later year cash flows and the present value of future cash flows. The latter problem can be solved by using a payback rule based on discounted cash flows.

**Internal rate of return (IRR)**

Defined as the rate of return which makes NPV=0. We find IRR for an investment project lasting T years by solving:

The IRR investment rule accepts projects if the project's IRR exceeds the opportunity cost of capital, i.e. when IRR > r.

Finding a project's IRR by solving for NPV equal to zero can be done using a financial calculator, spreadsheet or trial and error calculation by hand.

Mathematically, the IRR. investment rule is equivalent to the NPV investment rule. Despite this the IRR investment rule faces a number of pitfalls when applied to projects with special cash flow characteristics.

1. Lending or borrowing?

- With certain cash flows the NPV of the project * increases *if the discount rate

*This is contrary to the normal relationship between NPV and discount rates.*

**increases.**2. Multiple rates of return

- Certain cash flows can generate NPV=0 at multiple discount rates. This will happen when the cash flow stream changes sign. Example: Maintenance costs. In addition, it is possible to have projects with * no *IRR and a

*NPV.*

**positive**3. Mutually exclusive projects

- Firms often have to choose between mutually exclusive projects. IRR sometimes ignores the magnitude of the project. Large projects with a lower IRR might be preferred to small projects with larger IRR.

4. Term structure assumption

- We assume that discount rates are constant for the term of the project. What do we compare the IRR with, if we have different rates for each period, * rl, r2, r3, *...? It is not easy to find a traded security with equivalent risk and the same time pattern of cash flows.

Finally, note that both the IRR and the NPV investment rule are discounted cash flow methods. Thus, both methods possess the desirable attributes for an investment rule, since they are based on cash flows and allows for risk and time value of money. Under careful use both methods give the same investment decisions (whether to accept or reject a project). However, they may not give the same ranking of projects, which is a problem in case of mutually exclusive projects.