L14: Evaluating Business and Engineering Assets – Part II ECON 320 Engineering Economics Mahmut Ali GOKCE Industrial Systems Engineering Computer Sciences

Payback Period Lecture No.14

Chapter 5 Present-Worth Analysis Loan versus Project Cash Flows Initial Project Screening Methods Present-Worth Analysis Methods to Compare Mutually Exclusive Alternatives

Chapter Opening Story – Federal Express Nature of Project: Equip 40,000 couriers with PowerPads Save 10 seconds per pickup stop Investment cost: $150 million Expected savings: $20 million per year Federal Express

Ultimate Questions Is it worth investing $150 million to save $20 million per year, say over 10 years? How long does it take to recover the initial investment? What kind of interest rate should be used in evaluating business investment opportunities?

Mr. Bracewell’s Investment Problem Built a hydroelectric plant using his personal savings of $800,000 Power generating capacity of 6 million kwhs Estimated annual power sales after taxes - $120,000 Expected service life of 50 years  Was Bracewell's $800,000 investment a wise one?  How long does he have to wait to recover his initial investment, and will he ever make a profit?

Mr. Brcewell’s Hydro Project

Bank Loan vs. Investment Project Bank Customer Loan Repayment Company Project Investment Return  Bank Loan  Investment Project

Describing Project Cash Flows Year (n) Cash Inflows (Benefits) Cash Outflows (Costs) Net Cash Flows 00$650,000-$650, ,50053,000162, ,50053,000162,500 ………… 8215,50053,000162,500

Payback Period  Principle: How fast can I recover my initial investment?  Method: Based on cumulative cash flow (or accounting profit)  Screening Guideline: If the payback period is less than or equal to some specified payback period, the project would be considered for further analysis.  Weakness: Does not consider the time value of money

Fails to measure profitability. Assumes no profit made during payback period. Does not consider the timing of the cashflows  What if –10000, 9000, 500, 500 vs. –10000, 500, 500, 9000  Same payback, very different situation

Example 5.1 Payback Period NCash FlowCum. Flow $105,000+$20,000 $35,000 $45,000 $50,000 $45,000 $35,000 -$85,000 -$50,000 -$5,000 $45,000 $95,000 $140,000 $175,000 Payback period should occurs somewhere between N = 2 and N = 3.

-100, , , , , Years (n) 3.2 years Payback period $85,000 $15,000 $25,000 $35,000 $45,000 $35, Years Annual cash flow Cumulative cash flow ($)

Practice Problem How long does it take to recover the initial investment for Federal Express? How long does it take to recover the investments made by Mr. Bracewell from his hydroelectric project?

Discounted Payback Period  Principle: How fast can I recover my initial investment plus interest?  Method: Based on cumulative discounted cash flow  Screening Guideline: If the discounted payback period (DPP) is less than or equal to some specified payback period, the project would be considered for further analysis.  Weakness: Cash flows occurring after DPP are ignored

Example 5.2 Discounted Payback Period Calculation PeriodCash FlowCost of Funds (15%)* Cumulative Cash Flow 0-$85, ,000-$85,000(0.15) = -$12,750-82, ,000-$82,750(0.15) = -12,413-70, ,000-$70,163(0.15) = -10,524-45, ,000-$45,687(0.15) =-6,853-7, ,000-$7,540(0.15) = -1,13136, ,000$36,329(0.15) = 5,44976,778 * Cost of funds = (Unrecovered beginning balance) X (interest rate)

Summary Payback periods can be used as a screening tool for liquidity, but we need a measure of investment worth for profitability.