Net Present Value (NPV)

Revision as of 22:16, 10 February 2022

Abstract

Big Idea

Project business case development is a critical point in a project where it gives a justification for undertaking a project, in terms of evaluating the benefits, cost, and risk of alternative options and the rationale for the preferred solution. Its purpose is to obtain management commitment and approval for investment in the project. In a business case, financial appraisal plays a key role to answer the fundamental economic questions of whether an investment should be made and which project should be chosen among a selection of different alternatives. The task of financial appraisal is to forecast the financial effects of a planned investment and to present the data in such a way that a a reasoned investment decision can be reached.

The net present value (NPV) method is the most frequently used approach in the financial appraisal of a project.

What is NPV?

The net present value (NPV) is the difference between the present value of all future incoming cash flows and the present value of all future outgoing cash flows. NPV is a widely used method in the financial appraisal that considers the time value of money by applying discounting and compounding of all payment series during the investment period. Time value of money is that money you have in hand now is more valuable than the money you collect later on. That is because you can use it to make more money by running a business, buying something now and selling it later for more, or simply putting it in the bank and earning interest. Future money is also less valuable because inflation erodes its buying power.

Assumptions of NPV

The NPV of a project is calculated based on the following assumptions:

• All the future cash flows are translated to present value by discounting them at the.
• The inflow or outflow of cash other than the initial investment occur at the end of each period.
• The discount rate or cost of capital remains same throughout the life of the project.
• The cash generated by a project is immediately reinvested at the cost of capital.

Formula

As a summary, the following steps are recommended for the calculation of the Net present value:

1. Determination of the initial outflow for the investment.
2. Estimate the expected net cash flows from the investment for each period of the planning horizon.
3. Determination of the discount uniform rate (it is assumed that the discount rate remains unchanged over the life of the investment), in other words, the rate of return required by the investor.
4. Discounting of the expected net cash flows with the discount rate to the time period when the investment is made (determination of the present value).
5. Subtraction of the initial outflow for the investment from the present value. This yields the net present value (NPV).

Discount Factor

The discount rate will be company-specific as it’s related to how the company gets its funds. It’s the rate of return that the investors expect or the cost of borrowing money. If shareholders expect a 12% return, that is the discount rate the company will use to calculate NPV. If the firm pays 4% interest on its debt, then it may use that figure as the discount rate. Typically the CFO’s office sets the rate. In applied work, the assumption of a perfect capital market is not defendable. Investments are financed using equity and/or debt and different costs of capital exist. If an investment is financed exclusively with equity, the discount rate can be derived from an alternative return available in the capital markets (cost of equity) or the average return of a similar investment object. Investments that are exclusively debt-financed can be assessed using the cost of debt to discount the net cash flows. If an investment relies on both equity and debt financing, the discount rate can be calculated as the weighted average of the cost of equity and cost of debt. In this respect, the discount rate can be interpreted as the minimum rate of return that the investor demands for his activities.

The NPV depends on the choice about the discount rate, and on the time span considered by the analysis. Regarding the choice of the discount rate, it is important to consider that the NPV is an inverse function of the discount rate i used in Eq. (5.1), as shown in Fig. 5.2 illustrating that the higher the interest rate, the smaller the net present value.

Graph 1

Moreover, in the case of comparison among several mutually exclusive investment alternatives, the NPV gives a precise rank order only if the discount rate is univocally determined. Otherwise, the analysis may fall into one of the three cases shown in Fig. 5.3 where the relationship between NPV and the discount rate (i) is compared for two alternatives (labeled I and II, respectively).\

Graph 2

Time period

The time period of analysis influences the NPV because as the projects, in general, impose a negative cash flow in the first years and positive cash flows only sometime after its entering into operation, a longer period of analysis includes a bigger number of fiscal years with a positive cash flows than a shorter period of analysis.

Decision rule

• If NPV > 0, the investment should be made. It promises an increase in wealth (profit) in the amount of the net present value.

• If NPV = 0, the investment just returns the cost of capital (opportunity cost). No increase in wealth results.

• If NPV < 0, the investment should be turned down. An implementation would destroy wealth in an amount equal to the negative NPV.

The following two profitability criteria must be met for economic viability of an investment:

Absolute profitability: The Net Present Value of an investment option must be positive or at least zero (NPV≥ 0). Discounting is done with the minimum acceptable rate of return (WACC = hurdle rate)

Relative profitability: The option with the highest positive NPV is the most profitable and usually the preferred option, provided that the investment risk is the same.

Note that the Net Present Values (NPVs) of different options can only be compared if their lifetime is the same.

Applications

Limitations

Annotated Bibliography

Reference Example: According to scientists, the Sun is pretty big.^[1] The Moon, however, is not so big.^[2]

References

1. ↑ E. Miller, The Sun, (New York: Academic Press, 2005), 23–25.
2. ↑ R. Smith, "Size of the Moon", Scientific American, 46 (April 1978): 44–46.

Actual Reference: According to scientists, the Sun is pretty big.^[1] The Moon, however, is not so big.^[2]

References

1. ↑ Häcker J., Ernst D. Investment Appraisal. In: Financial Modeling. Global Financial Markets., (Palgrave Macmillan, London, 2017), https://doi.org/10.1057/978-1-137-42658-1_8
2. ↑ R. Smith, "Size of the Moon", Scientific American, 46 (April 1978): 44–46.