L30: Methods of Handling Project Risk ECON 320 Engineering Economics Mahmut Ali GOKCE Industrial Systems Engineering Computer Sciences

Probability Concepts for Investment Decisions Random variable: variable that can have more than one possible value Discrete random variables: Any random variables that take on only isolated values Continuous random variables: any random variables can have any value in a certain interval Probability distribution: the assessment of probability for each random event

Expected Return/Risk Trade-off

Measure of Expectation (discrete case) (continuous case)  xf(x)dx

Expected Return Calculation EventReturn (%) ProbabilityWeighted % 9% 18% % 2.7% 5.4% Expected Return 10.5%

Measure of Variation Standard Deviation

Variance Calculation

Estimating the amount of Risk involved in an Investment Project 1.Probabilistic Cash Flow Approach 2.Risk-Adjusted Discount Rate Approach

1. Probabilistic Cash Flow Approach

Example PeriodExpected cash flow Estimated standard deviation 0-$2, , ,000500

2. Risk-Adjusted Discount Rate Approach An alternate approach to consider the risk elements in project evaluation is to adjust the discount rate to reflect the degree of perceived investment risk. The most common way to do this is to add an increment to the discount rate, that is, discount the expected value of the risky cash flows at a discount rate that includes a premium for risk. The size of risk premium naturally increases with the perceived risk of the investment

Solution Given: initial investment = $1 million, expected annual cash flow = $250,000, N = 10 years, r = 8%, risk premium = 6% Find: net present value and is it worth investing? First find the risk adjusted discount rate = 8% + 6% = 14%. Then, calculate the NPW using this risk- adjusted discount rate: PW(14%) = -$1 million + $250,000 (P/A, 14%, 10) = $304,028 Because the NPW is positive, the investment is attractive even after adjusting for risk.

Comparing Risky Investment Projects - Comparison Rule If E A > E B and V A  V B, select A. If E A = E B and V A  V B, select A. If E A < E B and V A  V B, select B. If E A > E B and V A > V B, Not clear. Model Type E (NPW) Var (NPW) Model 1$1,950747,500 Model 22,100915,000 Model 32,1001,190,000 Model 42,0001,000,000 Model 2 vs. Model 3  Model 2 >>> Model 3 Model 2 vs. Model 4  Model 2 >>> Model 4 Model 2 vs. Model 1  Can’t decide

Investment Strategies Trade-Off between Risk and Reward  Cash: the least risky with the lowest returns  Debt: moderately risky with moderate returns  Equities: the most risky but offering the greatest payoff Broader diversification reduces risk Broader diversification increase expected return

Broader Diversification Reduces Risk

Broader Diversification Increases Return AmountInvestmentExpected Return $2,000Buying lottery tickets-100% (?) $2,000Under the mattress0% $2,000Term deposit (CD)5% $2,000Corporate bond10% $2,000Mutual fund (stocks)15%

OptionAmountInvestmentExpected Return Value in 25 years 1$10,000Bond7%$54,274 $2,000Lottery tickets-100%$0 $2,000Mattress0%$2,000 2 Term deposit (CD) 5%$6,773 $2,000Corporate bond10%$ $2,000Mutual fund (stocks) 15%$65,838 $96,280 1

Summary Project risk—the possibility that an investment project will not meet our minimum requirements for acceptability and success. Our real task is not to try to find “risk-free” projects—they don’t exist in real life. The challenge is to decide what level of risk we are willing to assume and then, having decided on your risk tolerance, to understand the implications of that choice.

Three of the most basic tools for assessing project risk are as follows: 1. Sensitivity analysis– a means of identifying the project variables which, when varied, have the greatest effect on project acceptability. 2. Break-even analysis– a means of identifying the value of a particular project variable that causes the project to exactly break even. 3. Scenario analysis-- means of comparing a “base –case” or expected project measurement (such as NPW) to one or more additional scenarios, such as best and worst case, to identify the extreme and most likely project outcomes.

Sensitivity, break-even, and scenario analyses are reasonably simple to apply, but also somewhat simplistic and imprecise in cases where we must deal with multifaceted project uncertainty. Probability concepts allow us to further refine the analysis of project risk by assigning numerical values to the likelihood that project variables will have certain values. The end goal of a probabilistic analysis of project variables is to produce a NPW distribution.

From the NPW distribution, we can extract such useful information as the expected NPW value, the extent to which other NPW values vary from, or are clustered around, the expected value, (variance), and the best- and worst-case NPWs. All other things being equal, if the expected returns are approximately the same, choose the portfolio with the lowest expected risk (variance).

Benefit-Cost Analysis

Chapter 12 Benefit-Cost Analysis Framework of Benefit- Cost Analysis Valuation of Benefits and Costs Benefit-Cost Ratios Incremental B-C Analysis

Benefit-Cost Analysis The Benefit-cost analysis is commonly used to evaluate public projects. Benefits of a nonmonetary nature need to be quantified in dollar terms as much as possible and factored into the analysis. A broad range of project users distinct from the sponsor should be considered—benefits and disbenefits to all these users can (and should) be taken into account.

Framework of Benefit-Cost Analysis 1) Identifying all the users and sponsors of the project. 2) Identifying all the benefits and disbenefits of the project. 3) Quantifying all benefits and disbenefits in dollars or some other unit of measure. 4) Selecting an appropriate interest rate at which to discount benefits and costs to a present value.

Benefit-Cost Ratio Criterion If this BC ratio exceeds 1, the project can be justified

b n =Benefit at the end of period n, c n =Expense at the end of period n, A n = b n – c n N = Project life i =Sponsor’s interest rate (discount rate) Definition of Benefit-Cost Ratio

Equivalent capital investment at n = 0 Equivalent O&M costs at n = 0 Breakdown of the Sponsor’s Cost

Example 12.1 BC Analysis $10 $5 $20 $30 K = 1 N = 5 Benefits (b n ) Recurring costs (c n ) Investment (c n )

Solution:

Relationship between B/C Ratio and NPW B > (I + C’) B – (I+ C’) > 0 PW(i) = B – C > 0

Incremental Analysis Based on BC(i)

Example 12.2 Incremental Benefit-Cost Ratios A1A2A3 I$5,000$20,000$14,000 B12,00035,00021,000 C’C’4,0008,0001,000 PW(i)$3,000$7,000$6,000

Solution A1A2A3 BC(i) Ranking Base A1A3A2 I +C’$9,000$15,000$28,000

Summary A benefit-cost analysis is commonly used to evaluate public projects: Difficulties involved in public project analysis include the following: 1)Identifying all the users who can benefit from the project. 2)Identifying all the benefits and disbenefits of the project. 3)Quantifying all benefits and disbenefits in dollars or some other unit of measure. 4)Selecting an appropriate interest rate at which to discount benefits and costs to a present value.

The B/C ratio is defined as: The decision rule is if BC(i) > 1, the project is acceptable. The net B/C ratio is defined as The net B/C ratio expresses the net benefit expected per dollar invested. The same decision rule applies as for the B/C ratio.

Understanding the Financial Statements

Chapter 13 Understanding Financial Statements  Accounting: The Basis of Decision- Making  Financial Statements: Financial Status for Businesses  Financial Ratios: Using Ratios to Make Business Decisions

Chapter Opening Story – WorldCom’s False Reporting Accounting Rule Says: Operating expenses should be expensed during the year they incur. What WorldCom Did: Operating expenses are capitalized by spreading them over 7 years, just like capital expenditure.

Result: WorldCom Reports “Profit” instead of “Loss”

A. Why Engineers need to understand the financial statements?

Accounting – The Language of Business

Financial Status for Business

B. Understanding the Balance Sheet 1.The basic accounting equation and the definition of capital 2.How to instantly determine liquidity and too much debt 3.How the firm gets equity: only two ways

The Basic Accounting Equation For the Balance Sheet Presentation For the Financial Analysis Assets - Liabilities = Owners’ Equity Assets = Liabilities + Owners’ Equity

How Items Are Arranged on the Balance Sheet Assets Liabilities Owners’ Equity

Using the Four Quadrants of the Balance Sheet and Why? ASSETSLIABILITIES Current Assets Long-Term Assets Current Liabilities Long-Term Liabilities Equity = 1.Owner Contributions 2.Retained Earnings

How to Instantly Determine Liquidity and Too Much Debt Liquidity Too Much Debt? Current Ratio (2:1) Debt To Equity Ratio

Liquidity – Current Ratio ASSETSLIABILITIES Current Assets Long-Term Assets Current Liabilities Long-Term Liabilities Equity 1.Owner Contributions 2.Retained Earnings

Too Much Debt? – Debt to Equity Ratio ASSETSLIABILITIES Current Assets Long-Term Assets Current Liabilities Long-Term Liabilities Equity 1.Owner Contributions 2.Retained Earnings Debt

How the Firm Gets Equity: Only Two Ways Owners’ Contributions Retained Earnings

1.How to Use profit check points 2.Why gross margin is the critical measure for engineers? 3.How does inventory production impact profit? C. Using the Income Statement to Manage a Business

Basic Income Statement Equation Revenue Expenses Net Income (Loss) -

Why Gross Margin is the Critical Measure for Engineers? Sales Cost of Goods Sold Gross Margin

How Inventory Production Impacts Profit Calculating the Cost of Goods Sold Beginning Inventory + Additions to Inventory - Ending Inventory Cost of Goods Sold

How to Use Profit Check Points ABC Company, Inc. Statement of Operations (Year Ended December 31, 200x) Sales$5,000, % Less: Cost of Goods Sold3,250, % Gross Profit1,750, % Less: Selling, G&A Expenses1,000, % Operating Profit750, % Less: Interest250,0005.0% Net Income Before Taxes (NIBT)500, % Less: Taxes175,0003.5% Net Income$325,0006.5% Bottom line

Operating Margin versus Net Margin Net margin Operating margin

D. Understanding the Statement of Cash Flows

1.The business operating cycle: How a business earns its cash 2.Sources and Uses of Cash 3.The engineer’s focus on the investing section: Capital Budgeting

Shareholders Fixed Assets Debt holders Inventory Government Customers CASH From cash sales To pay taxes From credit sales To pay labor, materials, and overhead To pay interest and principal From sale of debt To purchase From sale To pay dividend, To purchase back shares From sale of shares

The Cash Flow – Business Cycle Inventory Production Cash Accounts receivable Fixed assets Cash Sales Credit Sales Collection of receivable Investment Depreciation Changes in equity Changes in liabilities Pay taxes Pay interest Pay dividends Labor Materials Overhead