1. 1 Project Selection

2. 2 I. Project Selection: Non-Numeric Models Sacred Cow Operating Necessity Competitive Necessity Product Line Extension Comparative Benefit (E.g. Q-SORT: Projects are Divided into Rated Groups. If a Group Has More than Eight Members, It is Divided into Two Groups. Then Projects within Groups are Ranked).

3. 3 II. Project Selection: Numeric Models Payback Period Initial Fixed Investment / Annual Cash Inflow E.g. $10,000 / $2000 = 5 Years Mean Rate of Return Annual Return / Initial Investment E.g. $3,000 / $10,000 = 0.30

4. 4 II. Project Selection: Numeric Models Present Value (Discounted Cash Flow) 1.In One Year: (Net Present Value)(1+k) = (Future Value) Where k is Interest Rate E.g. ($10,000 or NPV) (1.1) = $11,000 = F 2.In t Years: NPV (1+k) t = F E.g. ($10,000) (1.1) (1.1) = $12,100

5. 5 II. Project Selection: Numeric Models Present Value (Discounted Cash Flow) 3.Solving for NPV: NPV = F / (1+k) t E.g. NPV = $12,100 / 1.21 = $10,000 4.If You Have F’s in Different Years (or Periods) NPV = -A 0 + [F 1 /(1+k) 1 ] + [F 2 /(1+k) 2 ] + Etc. NPV = -$7,000+($5,000/1.1)+($5,000/1.21) NPV = $1,677.68

6. 6 II. Project Selection: Numeric Models Profitability Index (Cost-Benefit) Index = NPV / Initial Investment ( A 0 ) E.g. Index = $1,677.68 / $7000.00 = 0.24

7. 7 II. Project Selection: Numeric Models Scoring Methods 1.Unweighted 0-1 Factor 2.Unweighted Factor Scoring Example – Project A QualifyNo Qualify S Environmental Impact x 8 Need for Consultants x 3 Impact on Image x 7 Totals2 1 18

8. 8 II. Project Selection: Numeric Models Scoring Methods 3.Weighted Factor Scoring For Each Project i: S i = S i1 W 1 + S i2 W 2 + S i3 W 3 + Etc. E.g. S 1 = (10)(0.5) + (10)(0.3) + (5)(0.2) = 9 Select Projects with Highest Scores (S i ’s)

9. 9 II. Project Selection: Linear Programming Scoring Methods Linear (Integer) Programming Maximize Z = S 1 X 1 + S 2 X 2 + S 3 X 3 + Etc. Subject to: m 1 X 1 + m 2 X 2 + Etc.  M X i = 0 or 1 E.g. Max. Z = 10 X 1 + 10X 2 + 5X 3 s.t. 2X 1 + 5X 2 + 3X 3  7 Workers X 1,X 2,X 3 = 0 or 1

10. 10 Answers Below

11. 11 II. Project Selection: Numeric Models Analysis of Projects Under Uncertainty Primary Source of Uncertainty: Time and Cost We Can Use Monte Carlo Simulation Computer Can Generate Typical (E.g. Normally Distributed) Activity Times and Costs. After 1000’s of Runs a Cost Probability Distribution Can be Generated for Each Proposed Project. ProbabilityCost.3 $1000.42000.33000

12. 12 Summary Numeric Methods Can Assist in: Project Selection Bidding through Cost Estimation and Computer Software Such as Quickest (Constructive Computing)