Which of the following statements describes a limitation associated with break-even analysis?

Break-even analysis

The break-even analysis model is a deterministic plan that calculates the volume at which the total costs are equal to the total revenue. The model is on the CD accompanying this book under the name breakeven. This level of volume is defined as the break-even point. The break-even point is derived by calculating the contribution per unit sold, which in turn is defined as the unit selling price less the unit variable cost. The unit contribution is then divided into the fixed costs and the result is the number of units that must be sold for the contribution to absorb the total fixed costs.

The break-even point is not a stationary concept. The volume required in order to pay the total cost continually changes over time due to changes in various costs and prices.

The plan shown here is designed to demonstrate the effect of inflation on the break-even point, which is achieved by providing a growth factor for the fixed costs, the variable costs and the price. When these figures have been entered the break-even point will automatically be extrapolated for four years.

The completed model is shown in Figure 11.7.

The formulae required to calculate the break-even point for the plan in Figure 11.7 are not complex and are shown in Figure 11.8.

The break-even analysis shown here assumes a single-product situation and frequently this is not the case. Where multiple products are involved the fixed costs or overheads must first be apportioned and then a break-even point calculated for each product or product category. The result will be a break-even point statement for the firm as a whole, which will include a series of volumes, one for each product.

7.2.2 CVP and Breakeven Analysis

CVP analysis studies the relationship between changes that occur in the output (typically volume, but this may refer to activity levels) and changes in revenues, expenses, and profit. It attempts to define what happens to the financial results if a specified level of activity or volume changes. It is important to keep in mind that the relationship between output, costs, revenues, and profit is studied within a short period of time.

Managers use CVP analysis to help answer questions such as:

How will total revenues and total costs be affected if the output level changes—for example, if we sell and produce 2,000 more units?

If we raise or lower our sales price, how will that affect the output level?

Analytically, the relation between costs, volume, and profit is referred to as the operating margin (EBIT):

EBIT=revenues–costs=(p×V)−[(cv×V)+CF]

where

V=volume or activity level

P=selling price

cv=variable costs

CF=fixed costs

Table 7.1 shows the analysis in a simple case wherein price and costs are kept as fixed while simulating units to be sold (from 0 to 50).

Table 7.1. A Simulation of CVP Analysis

Table 7.1 shows an important value of volume: V at which EBIT is 0—this point is called the breakeven point (BEP). Using analytical formulas, it is possible to calculate the value of single variables (volume, cost, and revenue) by which enterprises reach the BEP.

The following equation provides an example using the volume as reference. To find the BEP volume, EBIT is equal to 0:

EBIT=0→(p×V)−[(cv ×V)+CF]→V(p−cv )=CF

which allows the calculation of the BEP volume:

VBEP= CF(p−cv)

We can also use the equation for introducing a profit element (target EBIT); in this case, the equation becomes:

TargetEBIT=(p×V)−[(cv×V)+CF]→V(p−cv)=CF+targetEBIT

V=CF+targetEBIT(p−cv )

Figure 7.5 shows the graphical representation of CVP analysis and BEP. BEP is calculated in terms of quantity (the same can be done in terms of revenues).

Step 5—computation of the project's break-even point

It is important to know the break-even point for the project. Applying net sales revenue and fixed and variable costs, the lending officer can determine the break-even point for the project. As Table 7.17 shows, the projected sales break-even point for Year 3 is ₦38.26 million.

Table 7.17. Computation and Analysis of Break-Even Point for Year 3

Using information from Table 7.17, and projected sales revenue of ₦64,871.25 for Year 3, the break-even point is calculated as follows:

Breakevenpoint(sales)=FixedCost/[1−[VariableCost/Sales]] =21,755.24/[1−[27,983.49/64,871.25]]=21,755.24/[1−0.4314]=21,755.25/0.5686=荘38,261.06

Anti-Aircraft Measures

The risk reduction furnished by anti-aircraft measures is 1.3%, and the break-even analysis in the right side of Table 4.3 shows that an attack frequency needs to exceed 0.16 hijacking attacks per year in the condition in which the attacker arrives at the airport undeterred and undetected, for anti-aircraft measures to be cost-effective. The actual hijacking attack frequency is expected to be slightly higher than this: some 0.2 attacks per year.

The measure marginally passes a cost-benefit analysis as the benefit- to-cost ratio is 1.2 for hijackings, with a high 20% probability of occurring each year (Table 4.4). However, if the threat likelihood turns out to be a bit lower—for example, if we counted the 9/11 attacks as a single attack (that is, attack probability halves to 10%), anti-aircraft measures then fail to be cost-effective.

Thus, although our analysis shows that the measure barely passes a cost-benefit analysis, there are realistic conditions in which the measure could fail to do so, and probably quite decisively. Consequently, we classify this measure as “marginal” in terms of cost-effectiveness.

Plan for Expansion of Operations

Both Ahmed and Fatima will operate the business as a part-time venture in the first 6–12 months. After the break-even point of the venture, the two founders will be working full time.

As the company grows, the gaps in the experience of the founders will be filled by the board of directors who will come on board to offer mentorship services. We are in the process of seeking advisers with experience in R&D and production planning. This is because the two areas are very critical for the success of XYZ and the company will benefit from the expertise of qualified people.

Despite the fact that the founders have strong managerial skills, maximizing growth will require diverse skills. After the first year of operations, XYZ will pursue a more qualified team who has experience and knowledge of different products. We will also take advantage of interns especially during start-up.

Loans Secured by Inventories

Illustrative Example: Loans Secured by Inventory

Location: Models are available on the Elsevier Website www.ElsevierDirect.com

Brief Description: Illustrates inventory audit worksheets and checklists, inventory break-even analysis, and acceptance/rejection cost modeling.

If a borrower is considered a poor or questionable risk, lenders may insist on a blanket lien against inventory—assuming suppliers have filed no prior liens and will continue to ship behind the bank’s lien. While blanket liens provide security against all inventories, borrowers are free to dispose of inventory as long as funds are earmarked to reduce outstandings. The downside risk of using inventory as collateral includes declining stock values or severe markdowns by borrowers in a panic.

Discussion Questions

1.

Describe the process for assessing costs and benefits of proposed regulations in the United States and the difficulties in applying this process to transportation security programs.

What were the projected costs and “qualitative” benefits in TSA’s 2011 rulemaking on air cargo screening? What was the “break-even” analysis?

What are the Privacy and Civil Liberties Oversight Board and the DHS Privacy Office? Which of these has been more active with respect to transportation security programs?

Describe the major privacy concerns posed by the ATS and how these have been addressed by DHS.

What are some of the cyber threats to transportation systems? (You may refer to threats not included in the text.)

Name factors that may limit future funding of transportation security programs and describe how these limitations may be dealt with by policymakers.

7.5 Capital expenditure – appraisal methods

There are a number of accepted methods available for the comparison and appraisal of the virtues of proposed capital expenditure projects. Those considered here are as follows:

Pay-back period. This consists of calculating how long it will take for the profits generated by the capital outlay to equal the outlay itself, such profits usually being calculated after taking into account tax and any grants receivable. The defects of this method are that it takes no account of the profitability of the schemes after the break-even point is reached and the same value is placed upon each pound of profit, whether it is earned in year 1 or year 10. This latter shortcoming is avoided by the use of Discounted Cash Flow assessment.

Rate of return. A rate of return is calculated on the profits remaining after the initial outlay has been written off. This method suffers from the same defect mentioned in (1) above and also from the use of arbitrary periods for the writing down of the initial expenditure and of arbitrary rates of interest for the calculation of the rate of return.

Discounted cash flow (DCF). This method recognizes that £1000 income in five years' time is worth less than £1000 receivable this year. The use of DCF in appraising two or more competing projects offers two methods of assessment: the Net Present Value (NPV) or DCF Rate of Return.

The principle of NPV is best understood by applying an agreed discounting rate, that is, the best investment rate obtainable by the company, to the sum to be invested. A discounting rate of 10% assumes that £100 invested now will be worth £110 in a year's time. Conversely, it is assumed that £110 in a year's time is, at 10%, worth £100 today. From these assumptions it is possible to construct DCF tables for varying numbers of years and discounting rates (see Table 7.1).

Table 7.1. Application of NPV. To illustrate the uses of the two DCF methods the following example assumes the following data relating to two competing projects

Although Project B shows a greater total of net cash inflows over the whole period, at net present values Project A indicates a more satisfactory return, all other factors being ignored.

To use Table 7.2, which is based on the formula 1/(1 + i)n, where i is the rate of interest and n is the number of years, the relevant factor is found for the rate and number of years and multiplied by the amount for which the NPV is required. Thus to find the NPV for £1500 receivable in 5 years at 10% from the table is found the factor of 0.621 and this, multiplied by £1500, gives an NPV of £931.5. Most spreadsheets used on personal computers include a formula for calculating NPV, so avoiding the need to construct tables.

Table 7.2.

The cash flow expected for each period is discounted by the factor for the rate of interest chosen and the number of periods in which the cash flows will occur. The number of periods is calculated from the commencement of the capital expenditure. The factors are arrived at from the formula 1/(1 + i)n, where i is the rate of interest expressed as a decimal and n is the number of periods. In reality, the factors assume that the cash flow passes on the last day of each period but can be adopted where the flow is roughly even throughout the period.

The use of NPV (or DCF) leaves unresolved an important problem, that of determining the rate of interest or return to be used. Different rates of return could alter the ranking of the projects by changing the point at which the returns shown by the projects are in balance. If the company's own rate of return on capital is higher than that revealed by the NPV calculation then the apparently more viable scheme may not prove to be the more acceptable.

An alternative is therefore to use another method, using the same principles, by calculating a DCF rate of return. This has the advantage of not involving any assumptions as to interest rates, but calculates the effective rate of return on each project. The DCF rate of return is defined as the rate which reduces the NPV to zero. This method is more difficult to calculate in that it necessitates taking several trial values until two are found giving values on either side of zero. A weighted average can then be applied to ‘fine tune’ the result.

Where there are constraints upon the provision of funds then the DCF rate of return method will be the more appropriate. Where the organization has ready access to finance then the NPV method, using the known long-term borrowing rate, should be used.

5.2.2 Start-up financing

Start-up financing (Fig. 5.3) comes in the picture when the legal entity of a start-up company has been already set. In this phase not only is the legal entity founded but also there is a sound business plan. Nonetheless, the risk in investing in a company at this stage is still very high. The risk is based on launching a company built on a well-founded business idea and not on the gamble of discovering a new business idea. Start-up financing is also called “Early-stage Venture Capital."

At this point in the business, risk depends on two variables: the total amount of the net financial requirement and the time necessary to reach the break-even point of the activity financed. The risk is not strongly connected with the entrepreneur or the validity of his business idea, which are preconditions for the participation. What is really important is the potential growth of the industry in terms of capital intensity required and the forecasted trend of the turnover. The high level of risk is due to the investment realized at the time (t0) when it is uncertain whether the business will reach the break-even point.

The performance profile of a private equity in a start-up initiative, in terms of internal rate of return, is connected with the ability and capacity to re-sell the participation on the financial market. The track record and credibility of the private equity investor is a key factor in the success of the exit strategy when obtaining the desired return from the investment realized. The main investor's goal (a good and successful exit from the investment) can be facilitated by drawing up agreements with other private equity funds regarding their availability and commitment to buy the participation after a predefined period of time. Another solution is to sign a buy back agreement with the entrepreneur or other shareholders who agree to repurchase the venture capitalist's participation in the company after a predefined period of time (put option). However, the drawback of this possibility is that it assumes that the entrepreneur will have money enough to buy the stake back once the exit time will come. This is why the entrepreneur may be required to put some money in an escrow account. An alternative to a put option may be the pledge of some collaterals of the entrepreneurs. In the end, to create the right incentive for the entrepreneur to fully exploit the financing given by the investor is to grant him some stock options. In this way the entrepreneur is incentivized to work to enhance the profitability of the company as much as possible.

The rounds of financing received in the start-up phase by the Venture-Backed Company are typically classified as Series A or Series B, where they indicate the first and the second significant rounds of investments. Unlike with Seed or Angel investing, in Start-up financing there is an actual company that is subject of a long scrutiny and due diligence process by the investor.

1 Traditional Welfare-program Design

The design of a traditional cash-benefit program can be seen in Fig. 1, which shows the budget constraint under a typical cash-benefit program. This welfare program pays a benefit (G), often called the guarantee level, to those at the lowest levels of income. In Fig. 1 we show G paid to those who work zero hours, and assume that those who do not work have little other income. Of course, some families might have other income that would make them ineligible for welfare benefits, even if they were not working. As hours of work increase and earnings rise (at a given wage, w), the welfare benefit declines at a rate t, the benefit reduction rate or benefit tax rate, until at some income level (Y* in Fig. 1, at H* hours of work) benefits disappear entirely. This is point A in Fig. 1 and is often referred to as the break-even point.

Several aspects of the design of this welfare program are important. Note first that the maximum benefit payment occurs at the lowest hours of work. On the one hand, this assures that the poorest families receive the most aid. On the other hand, this creates disincentives to work, by increasing the income available to nonworkers from 0 to G. Note second that the rate at which income increases for families below the break-even point is lower than the rate at which earnings rise. For every hour worked between 0 and H*, earnings increase by the hourly wage (w), but income increases only by w(1 − t). This is because public benefits are reduced at a rate t for every hour worked. This is equivalent to a reduction in the hourly wage; for every hour worked, these families earn only w(1 − t) rather than w. Standard analysis of income and substitution effects suggests that wage changes have theoretically ambiguous effects on work incentives, but the empirical literature indicates that wages are positively correlated with labor supply among low-wage workers. This means that a lower wage will lower labor supply.

The enactment of a welfare program similar to that described in Fig. 1 is expected to reduce labor supply, by increasing the number of persons who choose the zero hours point, as well as by reducing hours of work among those who would have worked somewhere between 0 and H* hours in the absence of a welfare program. In addition, because of the ‘kink’ in the budget constraint at point A, some people whose hours would be greater than H* in the absence of the welfare program will find it preferable to drop to a point below H*.

One way to view the trade-offs inherent in this type of welfare program is to realize that this program essentially contains two policy parameters—the maximum level of benefits, G, and the benefit reduction rate, t. But there are often at least three goals for these programs: to provide adequate income support to those who are not expected to work, to provide work incentives for those who can work, and to keep government spending at a reasonable level. If there is an increase in the benefit level G, this improves income support, but reduces work incentives and increases government spending. If the benefit reduction rate t is lowered, this moves the break-even point up the income distribution, to higher levels of income and higher hours of work. The result is an increase in work incentives for those at zero or low hours of work, but this will also induce more welfare participation among those near the new (higher) break-even point. It will also increase government expenditures, by expanding eligibility to more families.

A wide variety of empirical studies have attempted to estimate the impact of benefit levels and benefit reduction rates on labor supply. In fact, in the 1970s, the US government funded a series of randomized experiments known as the negative income tax experiments, which compared the impact of different levels of G and t (Robins 1985, Munnell 1987). (A cash-assistance program as outlined in Fig. 1 that is run through the tax system is known as a negative income tax; in this case one receives a payment if income is below a certain level, and pays taxes if income is above a certain level.) Other researchers have used variation in benefit levels and effective tax rates across states in the USA to look at the impact of these parameters. Moffitt (1992) summarizes this literature. His conclusions are that the primary cash support program in the USA for low-income families (Aid to Families with Dependent Children or AFDC) created nontrivial work disincentives. (AFDC was replaced with a block grant known as Temporary Assistance to Needy Families or TANF in 1996.) A midpoint estimate of the impact of AFDC is that it reduced work by about 5.4 hours per week, a 30 percent reduction in work effort.

There are circumstances under which these tradeoffs between income support and work incentives may be less problematic. For instance, for a population from whom little or no work is possible or expected, it may be easy to set a high G (allowing greater income support), along with a high t (creating a break-even point at a low level of hours). The limited work incentives in this design are unimportant if there is no desire to encourage work among the eligible population. An alternative way to avoid these problems is to institute a mandatory work program for welfare participants who are judged to be able to work. For example, a wide variety of states in the USA have experimented with what are typically called ‘workfare’ programs, which mandate that work-eligible recipients must work a certain number of hours in publicly created jobs in order to maintain eligibility for their benefits. These and other work-incentive programs are discussed below.

Researchers have also noted that these tradeoffs between work and cash support may be less problematic in a situation where there is ‘stigma’ associated with being on welfare. Moffitt (1983) has modeled this situation, showing that if persons believe there is a cost to being on welfare (such as the stigma of being looked down on by one's neighbors), this will make persons less likely to use it, and will shift welfare participation only to the neediest cases. If stigma is greater among those who are more able-bodied and work-ready, and less among needier and less work-able persons, this will reduce the work disincentives of the program, while protecting its income-support aspects. Of course, if stigma is also high among needy persons who are not able to work, this could make the program less effective as a social safety net. It may be difficult to target efforts to increase participation among the neediest without also reducing stigma and increasing participation among the less needy as well.

Stigma is only one reason why participation rates (often called take-up rates) among those eligible for a program are often far below 100 percent. There may be costs associated with participating, related to the regular reporting and certification process. There may also be a lack of information about the program among eligibles. It is not unusual to find that close to half of those eligible for a particular public-assistance program do not participate in it (Blank and Ruggles 1996).

While much of the research literature has focused on the labor supply effects of traditional welfare programs, other concerns have also been raised about such programs. For instance, welfare programs which provide support for mothers with children may increase the incidence of divorce or out-of-wedlock childbearing. The literature on these effects is much more controversial, and also more limited in terms of empirical sophistication. In general, there is little evidence of strong benefit effects on family fertility or female headship, but there are also methodological problems with much of the literature on this topic. (Moffitt 1992 also discusses these issues. A more recent review occurs in Robins and Fronstin 1996.) Disagreement over the impact of the negative income tax experiments on divorce and separation has also resulted in more recent estimates suggesting the impacts were relatively small (Cain and Wissocker 1990).