Chapter 5 - Present Worth Analysis Click here for Streaming Audio To Accompany Presentation (optional)

1. Chapter 5 - Present Worth AnalysisClick here for Streaming Audio To Accompany Presentation (optional) EGR 403 Capital Allocation Theory Dr. Phillip R. Rosenkrantz Industrial & Manufacturing Engineering Department Cal Poly Pomona

2. EGR 403 - The Big Picture • Framework:Accounting& Breakeven Analysis • “Time-value of money” concepts - Ch. 3, 4 • Analysis methods • Ch. 5 - Present Worth • Ch. 6 - Annual Worth • Ch. 7, 8 - Rate of Return (incremental analysis) • Ch. 9 - Benefit Cost Ratio & other techniques • Refining the analysis • Ch. 10, 11 - Depreciation & Taxes • Ch. 12 - Replacement Analysis EGR 403 - Cal Poly Pomona - SA7

3. Where we have been: • Equivalence concept • Cash flows • Compound interest factors Where we are going in this chapter: • Understanding economic criteria. • Applying present worth techniques. • Assumptions in solving economic analysis problems. EGR 403 - Cal Poly Pomona - SA7

4. Economic Decision Making Problems Fall Into Three Categories • Three criteria that apply to all of our analysis techniques: • For fixed input situations, maximize the benefits or other outputs. • For fixed output situations, minimize the costs or other inputs. • Where inputs and outputs vary, maximize = benefits – costs. • First step is to decide which category applies. • See the back inside cover of the text. EGR 403 - Cal Poly Pomona - SA7

5. Situation Criterion Fixed input Amount of capital available fixed Maximize present worth of benefits Fixed output $ amount of benefit is fixed or fixed outcome Minimize present worth of costs Neither fixed Neither capital nor $ benefits are fixed Maximize net present worth (NPW) Economic Criteria Restated Present Worth Techniques EGR 403 - Cal Poly Pomona - SA7

6. Alt Situation Example Criterion A Fixed input $150,000 budgeted for raw materials Purchase the most you can for the money. Maximize output. B Fixed output 20,000 sq ft building needed Negotiate for minimum cost/sq ft. Minimize input C Neither fixed Purchasing rental property Maximize the “profit” - The biggest margin between benefit & cost. Maximize PWB - PWC Economic Criteria - Examples EGR 403 - Cal Poly Pomona - SA7

7. Applying Present Worth Techniques • With PW analysis the analysis period used is a major consideration. Several cases: • Useful life of the alternative(s) equals the analysis period. • Alternatives have useful lives different from the analysis period. • The analysis period is infinite or long enough to be treated as infinite, n = ¥. EGR 403 - Cal Poly Pomona - SA7

8. Useful Lives Equal the Analysis Period • Example 5-1: Require a project to last five years. • The equipment and tooling will last five years. • Calculate the PW or NPW over a five year span and junk the equipment at the end of the five years (salvage value = 0). • Two alternatives with cost of $1000 and useful live of 5 years. Assume i = 7%. EGR 403 - Cal Poly Pomona - SA7

9. Alternative A Find the PW of all cash flows related to benefits of Alternative A. Also include additional costs that come later. PW of Benefits = 300 (P/A, 7%, 5) = 300 (4.100) = $1230 Example 5-1: Fixed input, therefore maximize PW of Benefits. EGR 403 - Cal Poly Pomona - SA7

10. Alternative B - Here we have a combination of a uniform series (A = 400) and a negative gradient (G = 50). Decompose to use the factors available. PW of Benefits = 400 (P/A, 7%, 5) - 50 (P/G, 7%, 5) = 400 (4.100) - 50 (7.647) = $1257.65 Example 5-1: Fixed input, therefore maximize PW of Benefits (cont’d) EGR 403 - Cal Poly Pomona - SA7

11. PWB Alternative A = $1230.00 PWB Alternative B = $1257.65 Since our criteria was to maximize PW of Benefits, Alternative B is preferred. Notice that each alternative provided the same total cash flow, but alternative B provided it sooner so that it was available sooner to the company to use. MONEY NOW IS BETTER THAN MONEY LATER Example 5-1 Cont’d EGR 403 - Cal Poly Pomona - SA7

12. More Examples • Example 5-2: Two stage construction. • Fixed output so Minimize PW of Cost • Use PW factors to find PW of second stage costs and benefits at time 0. • Example 5-3: Salvage value included • Fixed output, so Minimize PW of Cost • Use PW factors to find PW of salvage value. • Operating & maintenance costs were assumed equal. • Example 5-4: Neither input nor output fixed • Maximize (PWB - PWC) or Maximize NPW • Salvage value treated as a negative cost ( a benefit) EGR 403 - Cal Poly Pomona - SA7

13. Useful Lives Different From the Analysis Period • Consider (based on Example 5-3): • “Speedy”: Useful life = 5 years. P = 1500, S = 200, PWC = $1357 • “Allied”: Suppose useful life = 10 years instead of 5 years. P = 1600, Salvage value = 325. PWC = $1435. • If we have two alternatives with different useful lives, is it proper to compare PWB and/or PWC directly? • Answer: No, because we have 5 additional years of benefits for Allied that would be ignored • Solution: Require the project to last 10 years. • For “Speedy” assume that you will purchase new equipment and tooling twice: At the beginning of year one and six. • Junk the equipment and tooling at the end of each five year period and replace with the same equipment. EGR 403 - Cal Poly Pomona - SA7

14. Useful Lives Different From the Analysis Period • Calculate the PW or NPW over a 10 year span. • Speedy: PWC = $2325 • Now Allied is the preferred choice since PWC is less than for Speedy EGR 403 - Cal Poly Pomona - SA7

15. Techniques for Dealing with Unequal Useful Lives • “Repeated Project Policy” - We will assume the same costs and benefits and repeat a project all the way to the end of the analysis period. This is a major part of PW analysis. • Least Common Multiple - Find useful life that coincides with multiple lives of each alternative under consideration: e.g. If useful lives are 3 years and 4 years, then the least common multiple is 12 years. EGR 403 - Cal Poly Pomona - SA7

16. Techniques for Dealing with Unequal Useful Lives • Terminal year • Sometimes the least common multiple method (LCM) creates an unrealistic useful life (e.g., 13 years and 7 years = LCM of 91 years). • Instead, pick a terminal year and repeat all projects up until the terminal year. • Truncate all costs and benefits after the terminal year • (See Figure 5-1 on page 175 for an illustration) EGR 403 - Cal Poly Pomona - SA7

17. Infinite Analysis Period • For n = infinity, A = i P • Therefore: • P = A / i • i = A / P • When you have a very long analysis period, use the infinity assumption to simplify problems. • Example 5-6: If we can resolve our desired task or service into an equivalent A, then we can use P = A / i to simplify the process of finding P. EGR 403 - Cal Poly Pomona - SA7

18. Assumptions in Solving Economic Analysis Problems • End-of-year (or period) convention (simplifies calculations) • Viewpoint (generally the firm) • Sunk costs (past has no bearing) • Borrowed money (consider investing only) • Effect of inflation (prices are not stable) • Income taxes (must be considered for realism) EGR 403 - Cal Poly Pomona - SA7