Project Analysis and Evaluation 11 Project Analysis and Evaluation

Key Concepts and Skills Scenario and sensitivity analysis Forms of break-even analysis Leverage

Chapter Outline NPV Estimates Scenario Break-Even Analysis Operating Cash Flow and Break-Even Leverage

Evaluating NPV Estimates 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?

Scenario Analysis What happens to the NPV under different cash flows scenarios? At the very least look at: Best case – high revenues, low costs Worst case – low revenues, high costs Best and worst between Measure of the range of possible outcomes Best case and worst case are not necessarily probable, but they can still be possible, American financial crisis 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. For those of us who lived through this, it was definitely a worst case scenario.

New Project Example Consider the project discussed in the text 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 34% The base case NPV is 15,567 Click on the excel icon to go to a spreadsheet that includes both the scenario analysis and the sensitivity analysis presented in the book.

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(year) 50000

Base Case Analysis Pro Forma Statement Sales 480000 VC 360000 FC 50000 Depreciation 40000 EBIT 30000 Taxes 10200 NI 19800

Best Case Pro Forma Statement Sales 552500 VC 403000 FC 50000 Depreciation 40000 EBIT 59500 Taxes 20230 NI 39270

Worst Case Pro Forma Statement Sales 412500 VC 319000 FC 50000 Depreciation 40000 EBIT 3500 Taxes 1190 NI 2310

Cash Flows 基年 year OCF NCS CFFA -200000 1 59800 2 3 4 5 NPV $15,565.62

Year（丰年） OCF NCS CFFA -200000 1 75970 2 3 4 5 NPV $73,854.85

Year（欠年） OCF NCS CFFA -200000 1 45610 2 3 4 5 NPV -$35,586.16

Summary of Sensitivity Analysis for New Project Scenario Unit Sales Cash Flow NPV IRR Base case 6000 59,800 15,567 15.1% Worst case 5500 53,200 -8,226 10.3% Best case 6500 66,400 39,357 19.7%

Simulation Analysis Simulation Monte Carlo simulation The output The simulation：interaction between variables

Sensitivity Analysis For Unit Sales Pro Forma Statement Base Lower Upper Sales 480000 440000 520000 VC 360000 330000 390000 FC 50000 Depreciation 40000 EBIT 30000 20000 Taxes 10200 6800 13600 NI 19800 13200 26400

Sensitivity Analysis What happens to NPV when we vary 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 Click on the Excel icon to return to the new project spreadsheet.

Making A Decision 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

Break-Even Analysis 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 net income = 0 Cash break-even ：sales volume at which operating cash flow = 0 Financial break-even ：sales volume at which net present value = 0

Example: Costs 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 $3000 per month in fixed costs. You also pay $15 per unit to produce your product. What is your total cost if you produce 1000 units? What if you produce 5000 units? Produce 1000 units: TC = 3000 + 15*1000 = 18,000 Produce 5000 units: TC = 3000 + 15*5000 = 78,000

Average vs. Marginal Cost 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 1000 units: Average = 18,000 / 1000 = $18 Produce 5000 units: Average = 78,000 / 5000 = $15.60

Accounting Break-Even 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)

Using Accounting Break-Even 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

Accounting Break-Even and Cash Flow 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 < 0

Example 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

Sales Volume and Operating Cash Flow 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 What is the cash break-even quantity? 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 Cash break-even occurs where operating cash flow = 0.

Example: Break-Even Analysis Consider the previous example Assume a required return of 18% Accounting break-even = 200 Cash break-even = 100 What is the financial break-even point? Similar process to that of finding the bid price 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 The question now becomes: Can we sell at least 260 units per year? 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.

Three Types of Break-Even Analysis 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

Operating Leverage 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)

Example: DOL 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

问题 跨国公司为什么扩大市场份额? 跨国公司为什么降低财务成本? 跨国公司为什么要提高每股盈利?

三种关系 经营杠杆， 财务杠杆 总杠杆

经营杠杆 陈德铭： 人民币汇率升值3%， 进出口企业利润降低：30%-50% 使得企业销售量的变动可能导致营业利润（或亏损）的更大比例的变动，这是经营杠杆的一个可能效应。

公式 因为结果大于 1，所以经营杠杆存在。 公式： DOL=Q×(P－VC)/[Q×(P－VC)－FC]（2）

DOL计算 DOL=1 000×（$10－$4.5）/[1 000×（$10－$4.5）－ $3 000]=2.2

固定经营与经营杠杆度关系 相对于可变经营成本，固定经营成本越大，经营杠杆度越大。所以，目前许多跨国航运公司都不惜任何代价地扩大销售额，尤其是像马斯基等大型航运集团更是采取低价策略来吸引顾客，以满足销售增加的需要。

财务杠杆 由于固定融资成本（债务的利息和优先股的股利）的存在，使得企业营业利润变动可能导致每股盈利的更大比例的变动，这是财务杠杆的一个可能效应。

财务杠杆结论 财务杠杆起的作用是双向的，营业利润的增加导致每股盈利更大比例的增加，营业利润的减少导致每股盈利更大比例的减少。

DFL敏感度 DFL=每股盈利变动百分比/营业利润变动百分比（3） 第一种情况：－100%/－50%=2.0 第二种情况：+100%/+50%=2.0

判别标准 结果大于 1，所以财务杠杆存在。对于一个给定的营业利润水平，应用公式所得的值越大，财务杠杆度越大。

公式 DFL=EBIT/[EBIT－I－PD×1/（1－T）]

总杠杆 企业由于同时使用固定营业成本和固定融资成本，使得销售的变动能导致每股盈利的更大比例的变动，这是总杠杆的一个可能效应。 企业的每股盈利对企业的销售变动的总的敏感性的数量化度量称为总杠杆度

公式 DTL=每股盈利变动百分比/销售额变动百分比（5） DTL=Q×(P－VC）／［Q×(P－VC）－FC－I－PD×1/(1－T)] （6） 总杠杆是财务杠杆和经营杠杆的联合，它将销售的任何变动都两步放大为每股盈利的更大相对变动。总杠杆度也因此可以表示为： DTL=DOL×DFL（7）

杠杆策略 1 拥有较高经营风险的企业往往选择较低的财务风险; 2 拥有较低经营风险的企业往往选择较高的财务风险; 1 拥有较高经营风险的企业往往选择较低的财务风险; 2 拥有较低经营风险的企业往往选择较高的财务风险; 3 相互抵消的结果，使企业的总风险维持在一个可以接受的水平上。 特殊的企业或某一企业在其生存发展的某一特定时期，采用高（低）的财务风险与高（低）的经营风险相结合的策略。 权衡过程与股东价值最大化的财务目标相一致。

Capital Rationing 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 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.

Quick Quiz 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 and how should each be used? What is degree of operating leverage? What is the difference between hard rationing and soft rationing?

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