Discounted Cash Flow in Financial Management

Discounted Cash Flow

Discounted Cash flow is an approach aimed at evaluating the financial aspects of a project, a company or its assets, and it uses the concepts of Time Value of Money. All future cash flows are discounted and estimated to their present values. The discounting methodology is employed in determining the economic attractiveness of capital investment projects, which reduces the value of future cash receipts or payments.

Net Present Value (NPV)

The net present value, in simple words, can be described as the present value of cash flows minus the investments.

The NPV of an investment in a particular project is the present value of expected cash inflows less the present value of the project’s expected cash outflows, discounted at the appropriate cost of capital.

The following procedure is used to compute the NPV of a project, as described by Brealey, Myers and Marcus (2001):

• Identifying all the costs (outflows) and benefits (inflows) that are associated with an investment
• Determining the appropriate discount rate or opportunity cost for the investment
• Using the appropriate discount rate to find the present value of each cash flow
• Computing the NPV, as the sum of all the DCF

Mathematically, it may be expressed as:

where:

• Ct = the expected net cash flow at time t
• Co = the initial cash outlay
• T= the estimated life of the investment
• r = the discount rate or the opportunity cost of capital

The basic idea behind NPV analysis is that if a project has a positive NPV, this amount goes to the firm’s shareholders.

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As such, if a firm undertakes a project with a positive NPV, shareholder wealth is increased.

The NPV decision rules, as described by Brealey, Myers and Marcus (2001), may be summarized as follows:

• Accept projects with a positive NPV. Positive NPV projects will increase shareholder wealth
• Reject with a negative NPV. Negative NPV projects will decrease shareholder wealth
• When two projects are mutually exclusive, the project with the higher positive NPV should be accepted
• Internal Rate of Return (IRR, Yield)

IRR is defined as the rate of return that equates the Present value of an investment’s expected benefits (inflows) with the present value of its costs (outflows), as expressed by Mathur (2002). Equivalently, the internal rate of return may be defined as the discount rate for which the NPV of an investment is zero.

Calculating IRR requires only that we identify the relevant cash flows for the investment opportunity being evaluated. Market-determined discount rates, or any other external (market-driven) data, are not necessary with the IRR procedure. The general formula for the IRR is:

Source: Keown (2004). P 266

Analyzing an investment (project) using the IRR method provides the analyst with a are result in terms of a rate of return. The following are the decision rules of IRR analysis, as discussed by Helfert (2001):

Accept projects with an IRR that is greater than the firm’s (investors) required rate of return
Reject projects with an IRR that is less than the firm’s (investor’s) required rate of return
NPV and IRR

According to Helfert (2000), for a single project, the IRR and NPV rules lead to exactly the same accept/reject decision. If the IRR is greater than the required rate of return, the NPV is positive, and if the IRR is less than the required rate of return, the NPV is negative.

When the acceptance or rejection of one project has no effect on the acceptance and rejection of another, the two projects are considered to be independent projects. When only one of two projects may be accepted, the projects are considered to be mutually exclusive. According to Helfert (2000), for mutually exclusive projects, the NPV and IRR methods can give conflicting project rankings. This can happen when the projects’ initial costs are of different sizes or when the timing of the cash flow is different.

Let us consider an example where NPV and IRR give conflicting decisions. Assume NPV and IRR analysis of two mutually exclusive projects produced the results shown in the following figure.

Source: Myers, Brealey and Marcus (2001) p. 185

As indicated, the IRR criteria recommends that Project A should be accepted. On the other hand, the NPV criteria indicates the acceptance of project B.

Now investment in Project A increases shareholder wealth by $2272.72, while investing in Project B increases shareholder wealth by $6363.64. Now, in this case the rule states that, given that shareholder wealth maximization is the ultimate goal of the firm, we should always select the project with the greatest NPV when the IRR and NPV rules provide conflicting decisions. Therefore, Project B will be selected as it adds most value to the firm.

Mathematically speaking, the NPV method assumes the reinvestment of a project’s cash flows at the opportunity cost of the capital, while the IRR method assumes that the reinvestment rate is the IRR. The discount rate used with the NPV approach represents the market-based opportunity cost of capital and is the required rate of return for the shareholders and the firm.

Time weighted rate of return and the money weighted rate of return

In investment management applications, the internal rate of return is called the money weighted rate of return because it accounts for the timing and amount of all dollar flows into and out of the portfolio. The beginning value of the account is an inflow as are all the deposits into the account. All withdrawals, on the contrary, from the account are outflows, as is the ending value.

An investment measure that is not sensitive to the additions and withdrawals of funds is the time-weighted rate of return. In the investment management industry, the time-weighted rate of return is the preferred performance measure. Keown (2004) explains that the time weighted rate of return measures the compound rate of growth of $1 initially invested in the portfolio over a stated measurement period. In contrast to the money-weighted rate of return, the time weighted rate of return is not affected by cash withdrawals or additions to the portfolio. The term ‘time-weighted’ refers to the fact that returns are averaged over time.

In comparison, money-weighted rate of return signifies the average growth rate of all the money invested, while time-weighted return depicts the growth of a single unit invested. Money-weighted return is also sensitive to the timing of external cash flows, whereas Time-weighted return is not affected by it. Time-weighted return is considered a superior measure for evaluating managers who do not have control over the size or timing of cash flows. E.g. According to Keown (2004), a mutual fund manager has no control over the withdrawal or depositing of funds by the customer on any particular day. Therefore, in order to comply with Global Investment Performance Standards (GIPS) returns must be presented on a time-weighted basis.

However, there can be certain situations when money-weighted return is considered to be a more appropriate measure. Consider the example of private equity managers, who typically receive commitments from investors but are not supposed to accept the funds until an appropriate investment is available. Now, since the size and timing of cash flows can be controlled here by the manager, it would be more appropriate to evaluate them on bases of the money-weighted return.

Payback period

These days almost every large corporation calculates the NPV of proposed investments, but the management may also take account of other criteria when making investment decisions. Most often, it may look at the project’s payback period. Payback is the same as a very rough guide to an investment’s worth.

Payback period is another method of investment appraisal which is measured in terms of time. It describes the amount of time required until cash flows recover the initial investment of the project. The payback rule states that a project should be accepted if its payback period is less than a specified cut-off period.

Mathematically;

Payback Period = Cost of project / Annual cash inflows

As a rough rule of thumb the payback rule may be adequate, but it is easy to see that it can lead to nonsensical decisions. Myers, Brealey and Marcus (2001) have described an example, comparing projects A and B. Project A has a 2 year payback and a large positive NPV. Project B also has a 2-year payback but a negative NPV.

Source: Myers, Brealey and Marcus (2001) p. 190

Project A is clearly superior, but the payback rule ranks both equally. This is because payback does not consider any cash flows that arrive after the payback period. A firm that uses the payback criterion with a cut-off of two or more years would accept both A and B despite the fact that only A would increase shareholder wealth.

A second problem with payback is that it gives equal weight to all cash flows arriving before the cut-off period, despite the fact that the more distant flows are less valuable. For example, look at project C. It also has a payback period of 2 years but it has an even lower NPV than project B. This is because its cash flows arrive later within the payback period.

To use the payback rule a firm has to decide on an appropriate cut-off period. If it uses the same cut-off regardless of project life, it will tend to accept too many short-lived projects and reject too many long-lived ones. The payback rule will bias the firm against accepting long-term projects because cash flows that arrive after the payback period are ignored.

Which method or methods would be most appropriate to an unquoted United Kingdom public limited company which manufactures parts for the automotive industry?

In case of a company that manufactures parts for the automotive industry, the most obvious investment would be new and better functioning machinery, i.e. improvement in infrastructure. These machinery would be expected to generate future cash flows. Now, according to my understanding NPV should be the ideal investment appraisal technique for such a firm. As the firm would be interested in knowing whether the new machine will generate positive net cash flows in future, thereby maximizing shareholder wealth.

References

1. Brealey, Richard A., Myers, Stewart C. & Marcus, Alan J. (2001). Corporate Finance. McGraw-Hill.
2. Brigham, Joel, Houston, Eugene Brigham (2001). Fundamentals of Financial Management.  Harcourt College Publishers.
3. Helfert, Erich A. (2001). Financial Analysis Tools And Techniques: A Guide For Managers. McGraw-Hill.
4. Mathur, Iqbal (2002). Introduction to financial management. Collier Macmillan.
5. Keown, Arthur J. (2004). Financial Management: Principles & Applications. Collier Macmillan.
6. Jorion, P. (2000). Value at Risk: The Benchmark for Controlling Market Risk. 2nd ed. McGraw Hill.
7. Sagner, James, Allman-Ward, Michele (2003). Essentials of Managing Corporate Cash. Collier Macmillan.