# CLA 1 Paper - Financial Management

voyageCHAPTER 11

PROJECT ANALYSIS AND EVALUATION

Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

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Perform and interpret a sensitivity analysis for a proposed investment

Perform and interpret a scenario analysis for a proposed investment

Determine and interpret cash, accounting, and financial break-even points

Explain how the degree of operating leverage can affect the cash flows of a project

Discuss how capital rationing affects the ability of a company to accept projects

Key Concepts and Skills

Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

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Evaluating NPV Estimates

Scenario and Other What-If Analyses

Break-Even Analysis

Operating Cash Flow, Sales Volume, and Break-Even

Operating Leverage

Capital Rationing

Chapter Outline

Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

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NPV estimates are just that – estimates.

A positive NPV is a good start – now we need to take a closer look.

Forecasting risk – how sensitive is our NPV to changes in the cash flow estimates; the more sensitive, the greater the forecasting risk.

Sources of value – why does this project create value?

Evaluating NPV Estimates

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4

Section 11.1

There are two primary reasons for a positive NPV: (1) we have constructed a good project or (2) we have done a bad job of estimating NPV.

Lecture Tip: With the lower flat-tax for corporations, previously unattractive projects may not have positive NPVs. So, there may be a one-time exception to the two reasons for finding positive NPV projects. Lecture Tip: Perhaps the single largest source of positive NPVs is the economic concept of monopoly rents – positive profits that occur from being the only one able or allowed to do something. Monopoly rents are often associated with patent rights and technological edges and they quickly disappear in a competitive market. Introducing this notion in class provides a springboard for discussions of both business and financial strategy, as well as for discussion of the application of economic theory to the real world.

According to Alan Shapiro, the following are project characteristics associated with positive NPVs.

1) Economies of scale

2) Product differentiation

3) Cost advantages

4) Access to distribution channels

5) Favorable government policy

What happens to the NPV under different cash flow scenarios?

At the very least, look at:

Best case – high revenues, low costs

Worst case – low revenues, high costs

Measures of the range of possible outcomes

Best case and worst case are not necessarily probable, but they can still be possible.

Scenario Analysis

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Section 11.2 (B)

A good example of the worst case actually happening is the sinking of the Titanic. There were a lot of little things that went wrong, none of which were that important by themselves, but in combination they were deadly.

A more recent example of the worst case scenario happening is the 2004 hurricane season in Florida. During the months of August and September, 4 hurricanes (Charley, Frances, Ivan, Jeanne) hit the state of Florida (the most previously had been 3 in the state of Texas in the late 1880s). This is ignoring tropical storm Bonnie that hit the panhandle a week before Charley came through. The eyes of 3 of the 4 hurricanes (all but Ivan, who tore through the panhandle) passed over Polk County in central Florida. The probability of 3 hurricanes passing over the same location in the span of 6 weeks is extremely low. The eyes of two of the hurricanes (Frances and Jeanne) made landfall on the east side of Florida within 10 miles of each other. Again, the probability of this happening 3 weeks apart is very, very small. To imagine anything more devastating would have been difficult, making this truly a worst-case scenario…until Katrina paid a visit to New Orleans and the levees failed!

Lecture Tip: A major misconception about a project’s estimated NPV at this point is that it depends upon how the cash flows actually turn out. This thinking misses the point that NPV is an ex ante valuation of an uncertain future. The distinction between the valuation of what is expected versus the ex post value of what transpired is often difficult for students to appreciate.

A useful analogy for getting this point across is the market value of a new car. The potential to be a “lemon” is in every car, as is the possibility of being a “cream puff.” The greater the likelihood that a car will have problems, the lower the price will be. The point, however, is that a new car doesn’t have many different prices right now – one for each conceivable repair record. Rather, there is one price embodying the different potential outcomes and their expected value. So it is with NPV – the potential for good and bad cash flows is reflected in a single market value.

Consider the project discussed in the text in section 11.2.

The initial cost is $200,000, and the project has a 5-year life. There is no salvage.

Depreciation is straight-line, the required return is 12%, and the tax rate is 21%.

The base, lower, and upper values are given for unit sales, price per unit, variable costs per unit, and fixed costs.

Click on the Excel icon to see base case, best case, and worst case scenarios results.

New Project Example

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Section 11.2 (B)

Click on the Excel icon to go to a spreadsheet that includes both the scenario analysis and the sensitivity analysis presented in the book.

Scenario | Net Income | Cash Flow | NPV | IRR |

Base case | 23,700 | 63,700 | 29,624 | 17.8% |

Worst Case | -18,565 | 21,435 | -122,732 | -17.7% |

Best Case | 71,495 | 111,495 | 201,915 | 47.9% |

Summary of Scenario Analysis

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Section 11.2 (B)

Lecture Tip: You may wish to integrate this discussion of risk with some of the topics to be discussed in forthcoming chapters. The variability between best- and worst-case scenarios is the essence of forecasting risk. Similarly, we link the risk of a security with the variability of its expected return. This point provides another opportunity to link economic theory (investor/manager rationality versus required returns) with real-world decision-making. You might also want to point out that the cases examined in this type of analysis typically aren’t literally the best and worst cases possible. The true worst-case scenario is something absurdly unlikely, such as an earthquake that swallows our production plant. Instead, the worst-case used in scenario analysis is simply a pessimistic (but possible) forecast used to develop expected cash flows.

What happens to NPV when we change one variable at a time?

This is a subset of scenario analysis where we are looking at the effect of specific variables on NPV.

The greater the volatility in NPV in relation to a specific variable, the larger the forecasting risk associated with that variable, and the more attention we want to pay to its estimation.

Sensitivity Analysis

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Section 11.2 (C)

Click on the Excel icon to return to the new project spreadsheet. If desired, it may be a good point at which to demonstrate the Solver function in Excel, as you can identify how high/low an input could go before NPV becomes negative.

Scenario | Unit Sales | Cash Flow | NPV | IRR |

Base case | 6,000 | 63,700 | 29,624 | 17.8% |

Worst case | 5,500 | 55,800 | 1,147 | 12.2% |

Best case | 6,500 | 71,600 | 58,102 | 23.2% |

Summary of Sensitivity Analysis for New Project

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Section 11.2 (C)

Using an older standard tax rate of 34%, the worst case scenario gives a negative NPV. This illustrates that the reduction in taxes will make some previously unattractive investments favorable.

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Simulation is really just an expanded sensitivity and scenario analysis.

Monte Carlo simulation can estimate thousands of possible outcomes based on conditional probability distributions and constraints for each of the variables.

The output is a probability distribution for NPV with an estimate of the probability of obtaining a positive net present value.

The simulation only works as well as the information that is entered, and very bad decisions can be made if care is not taken to analyze the interaction between variables.

Simulation Analysis

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Section 11.2 (D)

Lecture Tip: A very useful software is Crystal Ball, which is a simulation package that integrates with Excel. It is relatively inexpensive, yet it is very useful for basic-to-moderate simulation analysis. For example, the software allows you to build models (such as NPV) in Excel, then define the assumptions behind the inputs (such as distribution, possible extreme values, etc.), as well as the interaction (i.e., correlation) between the inputs. Output is then generated based on a simulation of 1,000 runs, providing distribution analysis and numerical summary statistics.

Beware “Paralysis of Analysis”

At some point you have to make a decision.

If the majority of your scenarios have positive NPVs, then you can feel reasonably comfortable about accepting the project.

If you have a crucial variable that leads to a negative NPV with a small change in the estimates, then you may want to forego the project.

Making a Decision

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Section 11.2 (D)

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Common tool for analyzing the relationship between sales volume and profitability

There are three common break-even measures:

Accounting break-even:

sales volume at which NI = 0

Cash break-even:

sales volume at which OCF = 0

Financial break-even:

sales volume at which NPV = 0

Break-Even Analysis

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Section 11.3

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There are two types of costs that are important in breakeven analysis: variable and fixed.

Total variable costs = quantity × cost per unit

Fixed costs are constant, regardless of output, over some time period.

Total costs = fixed + variable = FC + vQ

Example:

Your firm pays $3,000 per month in fixed costs. You also pay $15 per unit to produce your product.

What is your total cost if you produce 1,000 units?

What if you produce 5,000 units?

Example: Costs

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Section 11.3 (A)

Produce 1000 units: TC = 3000 + 15 × 1000 = 18,000

Produce 5000 units: TC = 3000 + 15 × 5000 = 78,000

Lecture Tip: You may wish to emphasize that, in computing total variable costs, the only relevant costs are those that are directly related to the manufacture and sale of the product. Allocated (or indirect) costs should not enter the analysis. Suggest to the students that when they are uncertain, they should use the “with/without” criterion: will the costs be different if the investment is made? If not, the cost is, by definition, not directly related to the decision and should not be included.

Average Cost

TC / # of units

Will decrease as # of units increases

Marginal Cost

The cost to produce one more unit

Same as variable cost per unit

Example: What is the average cost and marginal cost under each situation in the previous example?

Produce 1,000 units: Average = 18,000 / 1000 = $18

Produce 5,000 units: Average = 78,000 / 5000 = $15.60

Average vs. Marginal Cost

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Section 11.3 (A)

Lecture Tip: Students should recognize that as quantity increases, total fixed costs remain constant, but on a per unit basis, they decrease with increasing volume. And, as quantity increases, total cost per unit approaches variable cost per unit. If a company expects a high unit sales volume, the company may desire to exploit the possible economies of scale by investing more in fixed costs in an effort to lower variable cost per unit. However, this could create future financial problems if sales expectations fail to materialize. You might mention that this sensitivity to earnings declines will be examined later in this chapter through the discussion of the degree of operating leverage.

The quantity that leads to a zero net income

NI = (Sales – VC – FC – D)(1 – T) = 0

QP – vQ – FC – D = 0

Q(P – v) = FC + D

Q = (FC + D) / (P – v)

Accounting Break-Even

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Section 11.3 (B)

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Accounting break-even is often used as an early stage screening number.

If a project cannot break-even on an accounting basis, then it is not going to be a worthwhile project.

Accounting break-even gives managers an indication of how a project will impact accounting profit.

Using Accounting Break-Even

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Section 11.3 (C)

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We are more interested in cash flow than we are in accounting numbers.

As long as a firm has non-cash deductions, there will be a positive cash flow.

If a firm just breaks even on an accounting basis, cash flow = depreciation.

If a firm just breaks even on an accounting basis, NPV will generally be < 0.

Accounting Break-Even and Cash Flow

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Section 11.4 (A)

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Consider the following project:

A new product requires an initial investment of $5 million and will be depreciated to an expected salvage of zero over 5 years.

The price of the new product is expected to be $25,000, and the variable cost per unit is $15,000.

The fixed cost is $1 million.

What is the accounting break-even point each year?

Depreciation = 5,000,000 / 5 = 1,000,000

Q = (1,000,000 + 1,000,000)/(25,000 – 15,000) = 200 units

Example

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Section 11.4 (A)

What is the operating cash flow at the accounting break-even point (ignoring taxes)?

OCF = (S – VC – FC - D) + D

OCF = (200 × 25,000 – 200 × 15,000 – 1,000,000 -1,000,000) + 1,000,000 = 1,000,000

What is the cash break-even quantity (ignoring taxes)?

OCF = [(P-v)Q – FC – D] + D = (P-v)Q – FC

Q = (OCF + FC) / (P – v)

Q = (0 + 1,000,000) / (25,000 – 15,000) = 100 units

Sales Volume and Operating Cash Flow

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Section 11.4 (B)

Cash break-even occurs where operating cash flow = 0.

Accounting Break-even

Where NI = 0

Q = (FC + D)/(P – v)

Cash Break-even

Where OCF = 0

Q = (FC + OCF)/(P – v); (ignoring taxes)

Financial Break-even

Where NPV = 0

Cash BE < Accounting BE < Financial BE

Three Types of Break-Even Analysis

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Section 11.4 (C)

Lecture Tip: Inquisitive students may ask how the computations change when you include taxes. The equations change as follows:

OCF = [(P − v)Q − FC − D](1 − T) + D

Use a tax rate = 21% and rework the Wettways example from the book:

Need 1170 in OCF to break-even on a financial basis

OCF = [(40 − 20)(Q) − 500 − 700](1 − .21) + 700 = 1170 Q = 89.75

You end up with a new quantity of 90 units. The firm must sell an additional 16 units to offset the effects of taxes. Although, with the recent tax cuts, this difference is not as large as it previously was.

Consider the previous example.

Assume a required return of 18%

Accounting break-even = 200

Cash break-even = 100 (ignoring taxes)

What is the financial break-even point (ignoring taxes)?

What OCF (or payment) makes NPV = 0?

N = 5; PV = 5,000,000; I/Y = 18;

CPT PMT = 1,598,889 = OCF

Q = (1,000,000 + 1,598,889) / (25,000 – 15,000)

= 260 units (ignoring taxes)

The question now becomes: Can we sell at least 260 units per year?

Example: Break-Even Analysis

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Section 11.4 (C)

Assumptions: Cash flows are the same every year, no salvage and no NWC. If there were salvage and NWC, you would net it out to year 0 so that all you have in future years is OCF.

Operating leverage is the relationship between sales and operating cash flow.

Degree of operating leverage measures this relationship.

The higher the DOL, the greater the variability in operating cash flow.

The higher the fixed costs, the higher the DOL.

DOL depends on the sales level you are starting from.

DOL = 1 + (FC / OCF)

Operating Leverage

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Section 11.5

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Consider the previous example.

Suppose sales are 300 units.

This meets all three break-even measures.

What is the DOL at this sales level?

OCF = (25,000 – 15,000) × 300 – 1,000,000 = 2,000,000

DOL = 1 + 1,000,000 / 2,000,000 = 1.5

What will happen to OCF if unit sales increases by 20%?

Percentage change in OCF = DOL × Percentage change in Q

Percentage change in OCF = 1.5(.2) = .3 or 30%

OCF would increase to 2,000,000(1.3) = 2,600,000

Example: DOL

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Section 11.5 (C)

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Capital rationing occurs when a firm or division has limited resources.

Soft rationing – the limited resources are temporary, often self-imposed

Hard rationing – capital will never be available for this project

The profitability index is a useful tool when a manager is faced with soft rationing.

Capital Rationing

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Section 11.6

If you face hard rationing, you need to reevaluate your analysis. If you truly estimated the required return and expected cash flows appropriately and computed a positive NPV, then capital should be available.

Lecture Tip: In 2008, the economy was suffering from a real estate and credit crisis. As a result, lenders essentially withdrew from the market and credit dried up. This is a perfect example of an issue that would create a situation very close to hard rationing for many businesses. Lecture Tip: If lower tax rates result in higher cash flows and more attractive projects, then the issue of capital rationing will become even more pronounced.

What is sensitivity analysis, scenario analysis and simulation?

Why are these analyses important, and how should they be used?

What are the three types of break-even analysis, and how should each be used?

What is the degree of operating leverage?

What is the difference between hard rationing and soft rationing?

Quick Quiz

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Section 11.7

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Is it ethical for a medical patient to pay for a portion of R&D costs (since experimental procedures are not covered by insurance) prior to the introduction of the final product?

Is it proper for physicians to recommend this procedure when they have a vested interest in its usage?

Ethics Issues

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Case: Researchers associated with South Miami Hospital (SMH) developed a new experimental laser treatment for heart patients. Its development team and the physicians who use the laser consider it to be a lifesaving advance. It should be noted that the physicians who are touting the laser hold a significant stake in the company that produces the laser. To offer a substitute for a balloon angioplasty to treat heart blockages, the experimental laser was developed at a cost of $250,000. SMH estimates that it will cost $20,000 to install the laser. The procedure requires a nurse at $50 per hour, a technician at $30 per hour, and a physician who is paid $750 per hour. Patients are billed $3,000 for the procedure compared to $1,500 for the traditional balloon treatment.

Now ask the students to determine the break-even quantity for the new procedure:

Fixed cost = 250,000 + 20,000 = 270,000

Variable cost = 50 + 30 + 750 = 830 per hour

Cash Break-Even = 250,000 / (3,000 – 830) = 115.2 hours,

or approximately 116 patients (assuming a one-hour procedure per patient).

A project requires an initial investment of $1,000,000 and is depreciated straight-line to zero salvage over its 10-year life.

The project produces items that sell for $1,000 each, with variable costs of $700 per unit. Fixed costs are $350,000 per year.

What is the accounting break-even quantity, operating cash flow at accounting break-even (ignoring taxes), and DOL at that output level?

Comprehensive Problem

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Section 11.7

Accounting break-even:

Q = (FC + D) / (P – V) = ($350,000 + $100,000) / ($1,000 - $700) = 1,500 units

OCF = ( S – VC – FC – D) + D = (1,500 × $1,000 – 1,500 × $700 - $350,000 - $100,000) + $100,000 = $100,000

DOL = 1 + (FC / OCF) = 1 + ($350,000 / 100,000) = 4.5

End of Chapter

CHAPTER 11

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Microsoft Excel

97-2003 Worksheet

## Scenario

Base | Lower | Upper | |||||||||||

Unit Sales | 6000 | 5500 | 6500 | Depreciation | 40000 | ||||||||

Price per unit | 80 | 75 | 85 | ||||||||||

VC per unit | 60 | 58 | 62 | No NWC | |||||||||

FC per unit | 50000 | 45000 | 55000 | ||||||||||

Base Case Analysis | Best Case | Worst Case | |||||||||||

Pro Forma Statement | Pro Forma Statement | Pro Forma Statement | |||||||||||

Sales | 480000 | Sales | 552500 | Sales | 412500 | ||||||||

VC | 360000 | VC | 377000 | VC | 341000 | ||||||||

FC | 50000 | FC | 45000 | FC | 55000 | ||||||||

Depreciation | 40000 | Depreciation | 40000 | Depreciation | 40000 | ||||||||

EBIT | 30000 | EBIT | 90500 | EBIT | -23500 | ||||||||

Taxes | 6300 | Taxes | 19005 | Taxes | -4935 | ||||||||

NI | 23700 | NI | 71495 | NI | -18565 | ||||||||

Cash Flows | |||||||||||||

Year | OCF | NCS | CFFA | Year | OCF | NCS | CFFA | Year | OCF | NCS | CFFA | ||

0 | -200000 | -200000 | 0 | -200000 | -200000 | 0 | -200000 | -200000 | |||||

1 | 63700 | 63700 | 1 | 111495 | 111495 | 1 | 21435 | 21435 | |||||

2 | 63700 | 63700 | 2 | 111495 | 111495 | 2 | 21435 | 21435 | |||||

3 | 63700 | 63700 | 3 | 111495 | 111495 | 3 | 21435 | 21435 | |||||

4 | 63700 | 63700 | 4 | 111495 | 111495 | 4 | 21435 | 21435 | |||||

5 | 63700 | 63700 | 5 | 111495 | 111495 | 5 | 21435 | 21435 | |||||

NPV | $29,624.24 | NPV | $201,914.52 | NPV | -$122,731.62 | ||||||||

Sensitivity Analysis For Unit Sales | |||||||||||||

Pro Forma Statement | Base | Lower | Upper | ||||||||||

Sales | 480000 | 440000 | 520000 | ||||||||||

VC | 360000 | 330000 | 390000 | ||||||||||

FC | 50000 | 50000 | 50000 | ||||||||||

Depreciation | 40000 | 40000 | 40000 | ||||||||||

EBIT | 30000 | 20000 | 40000 | ||||||||||

Taxes | 6300 | 4200 | 8400 | ||||||||||

NI | 23700 | 15800 | 31600 | ||||||||||

Cash Flows | |||||||||||||

Year | |||||||||||||

0 | -200,000 | -200,000 | -200,000 | ||||||||||

1 | 63700 | 55800 | 71600 | ||||||||||

2 | 63700 | 55800 | 71600 | ||||||||||

3 | 63700 | 55800 | 71600 | ||||||||||

4 | 63700 | 55800 | 71600 | ||||||||||

5 | 63700 | 55800 | 71600 | ||||||||||

NPV | $29,624.24 | $1,146.51 | $58,101.98 | ||||||||||

Numbers in blue were computed in Excel. |

## Sensitivity

Base | Lower | Upper | |||||||||||

Unit Sales | 6000 | 5500 | 6500 | Depreciation | 40000 | ||||||||

Price per unit | 80 | 75 | 85 | ||||||||||

VC per unit | 60 | 58 | 62 | No NWC | |||||||||

FC per unit | 50000 | 45000 | 55000 | ||||||||||

Base Case Analysis | Best Case | Worst Case | |||||||||||

Pro Forma Statement | Pro Forma Statement | Pro Forma Statement | |||||||||||

Sales | 480000 | Sales | 552500 | Sales | 412500 | ||||||||

VC | 360000 | VC | 377000 | VC | 341000 | ||||||||

FC | 50000 | FC | 45000 | FC | 55000 | ||||||||

Depreciation | 40000 | Depreciation | 40000 | Depreciation | 40000 | ||||||||

EBIT | 30000 | EBIT | 90500 | EBIT | -23500 | ||||||||

Taxes | 6300 | Taxes | 19005 | Taxes | -4935 | ||||||||

NI | 23700 | NI | 71495 | NI | -18565 | ||||||||

Cash Flows | |||||||||||||

Year | OCF | NCS | CFFA | Year | OCF | NCS | CFFA | Year | OCF | NCS | CFFA | ||

0 | -200000 | -200000 | 0 | -200000 | -200000 | 0 | -200000 | -200000 | |||||

1 | 63700 | 63700 | 1 | 111495 | 111495 | 1 | 21435 | 21435 | |||||

2 | 63700 | 63700 | 2 | 111495 | 111495 | 2 | 21435 | 21435 | |||||

3 | 63700 | 63700 | 3 | 111495 | 111495 | 3 | 21435 | 21435 | |||||

4 | 63700 | 63700 | 4 | 111495 | 111495 | 4 | 21435 | 21435 | |||||

5 | 63700 | 63700 | 5 | 111495 | 111495 | 5 | 21435 | 21435 | |||||

NPV | $29,624.24 | NPV | $201,914.52 | NPV | -$122,731.62 | ||||||||

Sensitivity Analysis For Unit Sales | |||||||||||||

Pro Forma Statement | Base | Lower | Upper | ||||||||||

Sales | 480000 | 440000 | 520000 | ||||||||||

VC | 360000 | 330000 | 390000 | ||||||||||

FC | 50000 | 50000 | 50000 | ||||||||||

Depreciation | 40000 | 40000 | 40000 | ||||||||||

EBIT | 30000 | 20000 | 40000 | ||||||||||

Taxes | 6300 | 4200 | 8400 | ||||||||||

NI | 23700 | 15800 | 31600 | ||||||||||

Cash Flows | |||||||||||||

Year | |||||||||||||

0 | -200,000 | -200,000 | -200,000 | ||||||||||

1 | 63700 | 55800 | 71600 | ||||||||||

2 | 63700 | 55800 | 71600 | ||||||||||

3 | 63700 | 55800 | 71600 | ||||||||||

4 | 63700 | 55800 | 71600 | ||||||||||

5 | 63700 | 55800 | 71600 | ||||||||||

NPV | $29,624.24 | $1,146.51 | $58,101.98 | ||||||||||

Numbers in blue were computed in Excel. |