G- Capital budgeting

Capital budgeting is the planning of major projects which require large capital outlays. A significant proportion of financial analysis within a firm is conducted on such individual projects. Each such project can be looked upon as an investment in the same light as an investment in a share of stock. Moreover, an entire company is the sum of its projects (with due recognition for a possible synergy between projects). The valuation of individual projects bears much similarity with valuation of other financial assets.

1)- Calculation of NPV

Any financial decision can be looked upon as a determination of whether what is put in today (i.e. purchase price of a stock, amount of loan applied for or initial outlay of a project) is greater or smaller than what is received back (i.e. discounted value of future benefits). This approach is also known as net present value (or NPV) calculation. The net present value approach is generally studied in the context of investment projects which a firm contemplates to undertake, which is known as capital budgeting. The format NPV is a mere extension of the general formula, and its logic is appropriate to all financial decisions. The NPV of a project is given by the formula

NPV = SPV(Ct) - I₀

where Ct = cash flows in period t
I0 = initial outlay in period 0

A positive decision will be made (to undertake a project, or to buy a stock or a bond, to issue the loan or to acquire a company) if the NVP is greater than zero. Cash flows are calculated taking the incremental revenues, minus all incremental costs, plus the cash saving from non-cash expenses as specified in the previous chapter. When using a presentation in the format of a projected income statement, the calculation of cash flow is nothing more than adding back depreciation to operating profit after tax. Naturally, the difficulty resides in making accurate projections for revenues andcosts, and choosing an appropriate discount rate. There are cases where there is no incremental revenue, but a saving in expenses which constitute the beneficial cash flow. The initial outlay is usually the purchase price, but other auxiliary uses of funds must not be omitted, such as additional inventory that may have to be carried, as well as advertisement campaign (to generate the additional revenues), increased bad debt provision, training and installation expenses.

Example of NPV calculation:

A publishing company considers the purchase of an additional printing press that will allow it to sell more books. Over the three years of the life of the press the additional sales are projected to be $50,000, 60,000 and 80,000 and necessitate incremental expenses of $30,000 each year. The purchase price of the press is 120,000 and there will be an increase in inventory of 20,000. The company uses straight line depreciation and has a marginal tax rate of 30%. An appropriate required rate of return for this type of project is assumed to be 10%.

NPV = 47,000 x (1+.1)-1 + 54,000 x (1+.1)-2 + 75,000 x (1+.1)-3 - 120,000 - 20,000

= 47,000 x .90909 + 54,000 x .82644+ 75,000 x .75131 - 120,000 - 20,000

= 42,727 + 44,627 + 56,348 - 120,000 - 20,000

= 3,702

2)- Calculation of IRR

An alternative approach is to calculate what rate of return is earned. This return is called the internal rate of return (or IRR), and it is the same concept as the yield to maturity of bonds. IRR is that specific discount rate for which the combined discounted benefits equal the initial outlay (i.e. NPV = 0). The internal rate of return is then compared to the required rate of return (or RRR) for this particular type of investment. A positive decision will be made if IRR is greater than RRR.

Example of calculation of IRR:

3)- Cost of capital

The cost of capital to be used is an opportunity rate of return for the firm. There are two general ways of looking at it. The first is to turn to the sources of funds, under the assumption that the cost of capital for any individual project should be the same as the cost of capital for the entire company. In this case, management can choose either the average cost of capital or the marginal cost of capital which have been presented in the case of mergers and acquisitions of the entire firm for the acquiring firm (i.e. not the company that is to be acquired). In the average cost of capital, the proportions of debt and equity may be modified to reflect the anticipated capital structure after the new project(s) are funded.

The second method looks at the projects as competing in their respective markets and assigns to each project the level of BETA for that particular industry. Here the cost of capital is a risk adjusted average cost of capital.

4)- Comparison between NPV and IRR

The two methods, NPV and IRR, are identical, with the exception of a very few special cases discussed in most corporate finance textbooks and briefly in the appendix to this chapet, in which multiple outlays cause the IRR calculation to yield more than one solution. Otherwise, essentially, in both theory and practice, the two methods are used interchangeably. But there are occasions for one method to be more useful than the other. This is especially true when not jus one but several projects are considered.

When comparing several opportunities the decision should be to choose all projects with positive NPV, or equivalently IRR greater than RRR. There is no problem until the projects are looked upon as mutually exclusive. In the case where all the projects cannot be accepted because of a capital constraint (i.e. maximum sum of all outlays in a given time period), the rule is to choose the combination of projects that yields the largest total NPV. Here, starting by accepting the project with the largest NPV is not always the right first step because it depends on the size of outlays for each respective project. Whereas, accepting the project with the highest IRR is the correct first step. Then choosing all subsequent IRR in descending order seems to lead to the optimal solution. But it is not necessarily so, if for instance, the last project chosen prevents accepting a lower IRR project that generates nevertheless a larger NPV because of its bigger size. It is indeed the total increase in value that the decision must maximize, not the rate of return. Another difficulty appears to exist when projects have different lives (i.e. one project generates benefits over a longer period of time than another project). Here also, IRR does not have superiority over NPV because the method is to calculate an annualized NPV.

-- examples of NPV IRR conflict --

NPV is recognized in financial circles as the measure that must be maximized. It is the most common method. IRR is appealing because it is a relative measure, and is easily compared (just as the yield of a bond). It suffers from the difficulty of calculation, even with the availability of specialized calculators and computer programs. In addition, using only IRR does not guarantee that wealth will be maximized as illustrated above by the case under capital constraint. Yet, NPV is not an infallible method either. Thus, older methods that were used before NPV became the recommended method, and are still occasionally found more appropriate. In addition, there are circumstances where discounting cash flows is not feasible.

4)- Other financial decision methods

a)- Profitability index

The profitability index PI is calculated as a ratio

PI = SPV(Ct) / I0

where Ct = cash flows in period t
I0 = initial outlay in period 0

Example of calculation:

In the previous example of the purchase of a printing press the PI is

PI = (42,727 + 44,627 + 56,348) / (120,000 - 20,000)

= 143,702 / 140,000

= 1.02644

The decision rule is to choose all the projects that have a profitability index greater than one. Or when there are conflicting projects choose the project with the highest profitability index. Conceptually, PI is very similar to NPV, and in practice, it is much easier to calculate than IRR. Most notably, it allows to reach an optimal combination of projects when a capital constraint exists.

b)- Cost-benefit analysis

A cost-benefit analysis is simply a ratio of cost to benefits (i.e. it is the inverse of the profitability index). The traditional cost-benefit analysis does not involve discounting, and it used to be the most common method for capital budgeting. Nowadays, it is still used in cases where the real discount rate is very close to zero, where it is not possible to determine a discount rate or when the future benefits to be so uncertain that discounting would be a needless complication. The method is most popular in public finance because of a combination of the above reasons:
a- real rates of return on government securities approach zero;
b- with short term spikes in inflation, rates of return on government securities can turn negative, which clearly would not be reasonable for a discount rate;
c- many financial decision in public works have political and social dimensions that are more important than the monetary ones.

Take for instance, the case of building a highway. The benefits are lower travelling time and fewer road accidents, which are very difficult to quantify but are even more important than the additional economic activity where the highway passes. On the costs side, construction costs may be smaller than the cost of relocation and possibly retraining of the inhabitants of the houses that must be demolished. In addition, the displaced households make up a political vote that may be damaging to the government official making the decision. That is why considering alternative locations of the highway is imperative. A cost-benefit analysis is quite sufficient for the purpose.

c) Payback period

The payback period is calculated as the number of years (or fraction thereof), that it takes to get back in cash flows the initial outlay put into a project. The method is to choose all projects whose payback period is less that a given payback cut-off, and when comparing projects, those that have the shortest payback periods.

For example: A mining company has located a significant reserve of a precious metal. The potential mine is located in a politically unstable country where other mining companies have been reluctant in enter because of periodic social strife and the likelihood of expropriation of foreign businesses within two years if they show profits. The initial investment is $5,000,000 and net after tax incremental cash flows of 1m, 2m, 2m, 5m, 8m over the next five years.

Solution: the payback period PBP is 3 years since it takes the cash flows of the first three years (1m+2m+2m) to cover the initial investment of 5m. But the potential of expropriation within 2 year is the payback cut-off. The payback period of the project is longer than the payback cu-off. The project should be rejected.

The method is fundamentally defective because it ignores the cash flows beyond the payback period (which would the additional wealth for the owner). The lack of discounting is also theoretically questionable. But, as the example illustrates, in all situations where an external threat may have an overwhelming influence, these drawbacks are minor, and the method has its usefulness.

Recently, a discounted payback method has started to appear in finance textbooks. It is calculated as the number of years it takes for the discounted cash flow to be equal to the initial outlay. When studying the concept of duration of bonds, one will recognize that it is the same concept.

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