respond in one paragraph to main question and respond to students

Respond to this main question

After reviewing breakeven analysis and payback periods, describe at least two examples of each. Why are these analyses important? Explain.

Now respond to this student

Break even is where basically you have the same amount with a minor plus or minus. Two examples of this would be when one goes to a casino and they play twenty dollars at the slot machine and when they cash in their winnings, they receive nineteen fifty back. They really didn’t gain or lose anything. Another example would be my commute. Roughly it takes me forty five minutes to get to work but on some days it make take me a little longer or a little shorter depending on traffic. Break even to me is basically the average of whatever it is that you are doing.

Payback is soemthing completely different. Whereas with break even you may or may not see the big picture, with payback you can see okay this is there it is beneficial to me. An example would be investing in a house that you know within a certain amount of time you can sell it and receive some of the money that you invested into the house. Another example would be investing in stocks. If you watch the stock markert carefully, and if you have a major stock that is slow to rise, wait a while for it will be that one day where the stock wilt take a major hike upwards and you will reap the benefits of investing in that stock.

Both of these are important because one needs to know how to plan their monthly budgets and how to allocate what funds to where and how minimize when their business is not going so well.

And respond to this one

Break-even analysis determines the level of sales that generates neither profits nor losses and hence causes the firm to “break even.” Break-even analysis also permits management to see the effects on the level of profits of (1) fluctuations in sales, (2) fluctuations in costs, and (3) changes in fixed costs relative to variable costs. Break-even analysis is based on the following three mathematical relationships: the relationship between (1) output and total revenues (sales), (2) output and variable costs of production, and (3) output and fixed costs of production.

The payback period determines how long is required for an investment’s cash inflows to recover an investment’s cost (the initial cash outflow). If an investment costs $1,000 and the annual cash inflows are $250, the payback period is four years ($1,000/$250). If four years are an acceptable period of time to recover the initial cost, the investment is made. Notice that management must determinate what is an acceptable time period, and that determination may be subjective. The payback period may also be used to rank alternative investments. The more rapidly the initial cash outflow is recovered, the more preferred the investment. If four $1,000 investments have the following cash inflows:

Year A B C D

1 $250 $334 $400 $100

2 250 333 300 200

3 250 333 200 300

4 250 — 100 400

5 250 — — —

investment B would be preferred since it recoups the $1,000 in three years while the other investments take four years.

Payback Examples:

Consider a five year investment whose cash flow consequences are summarized in the table below. The primary data for calculating payback period are the expected cash inflows and outflows from the action:

- Cash Inflows: $300 cash inflows are expected each year for years 1 through 5.
- Cash outflows: The initial cost is a cash outflow of $800 in year 1, followed by a cost (outflow) of $150 in year 2. There are no expected costs in years 3 through 5.

From these figures, the analyst creates two sets of cash flow numbers to use for the calculation (the bottom two rows of the table):

- Net cash flow. The net of cash inflows and outflows for each year.
- Cumulative cash flow. The sum of all cash inflows and outflows for all preceding years and the current year.

Expected Cash Flow | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
---|---|---|---|---|---|

Cash Inflows | 300 | 300 | 300 | 300 | 300 |

Cash Outflows | – 800 | –150 | 0 | 0 | 0 |

Net Cash Flow | – 500 | 150 | 300 | 300 | 300 |

Cumulative Cash Flow | – 500 | – 350 | – 50 | 250 | 550 |

At what point in time does the investment break even? Look first to the cumulative cash flow line at the table bottom, and it is clear that payback occurs sometime in Year 4. We know it occurs in Year 4 because cumulative cash flow is negative at the end of Year 3 and positive at the end of Year 4. But where, precisely, is the break even event in Year 4? The answer can be seen roughly on a graph, showing the PB event as the point in time when cumulative cash flow crosses from negative to positive:

In reality, break even may occur any time in year 4 at the moment when the cumulative cash flow becomes 0. However, if the analyst has only annual cash flow data to work with (as in this example) and no further information about when cash flow appears within year 4, the analyst must assume the year’s cash flows are spread evenly through the year. In this case, payback period must be estimated by interpolation. That approach is illustrated here and in the next section. The assumption that cash flow is spread evenly through the years is represented by the straight lines between year end data points above.

Using the tabled data above, where cumulative cash flow clearly reaches 0 in Year 4, PB can be calculated (estimated) as follows;

Payback Period = Y + ( A / B ) where

Y = The number of years *before* the payback year. In the example, Y = 3.0 years.

A = Total remaining to be paid back at the start of the break even year, to bring cumulative cash flow to 0. In the example, A = $50.

B = Total (net) paid back in the entire payback year. In the example B = 300.

For the example,

Payback Period = 3+ (50) / (300)

= 3 + 1/6

= 3.17 Years

PB calculated this way is an estimate based on interpolation between two period end points (between the end of Year 3 and the end of Year 4). Interpolation was necessary because we have only annual cash flow data to work with.

## Payback period, mathematically speaking

The “formula” in the previous section is easy to understand because it describes in simple verbal terms the amounts to be added or divided. However, when the analyst attempts to implement these instructions in a spreadsheet formula, the implementation becomes somewhat cumbersome. In any case, the spreadsheet programmer needs at least a simple understanding of the quantities that must be identified and used in calculating payback period.

Consider again the cumulative cash flow curve (such as that shown above for the tabled example), but now focused on the break even year (here, Year 4) and the year before that (Year 3).

The blue line rising from lower left to upper right is cumulative cash flow, graphed as straight line segments between year end points. With simple principles of plane geometry, it is possible to show that two ratios in the above figure are equivalent:

| A | / | B | = C / 1.0

This fraction, C, plus the number of whole years before the payback year (Y), is PB:

Payback Period = Y + C.

To implement the PB metric in a spreadsheet, the sheet must have access to the individual annual figures for both net cash flow and cumulative cash flow (the last two rows of the table above). The programmer builds logical tests ( “IF” expressions in Microsoft Excel) to find the first year of positive cumulative cash flow. Then, with the payback year known, the calculations use annual and cumulative cash flows from the break even year and the year before that, to calculate the lengths of line segments A and B from the diagram above. (See Financial Metrics Pro for working examples.)

Breakeven Examples:

If you can accurately forecast your costs and sales, conducting a breakeven analysis is a matter of simple math. A company has broken even when its total sales or revenues equal its total expenses. At the breakeven point, no profit has been made, nor have any losses been incurred. This calculation is critical for any business owner, because the breakeven point is the lower limit of profit when determining margins.

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