ENGM 661 Engineering Economics for Managers. Investment Worth. Investment Worth. MARR Suppose a company can earn 12% / annum in U. S. Treasury bills No way would they ever invest in a project earning < 12% Def: The Investment Worth of all projects are measured at the Minimum Attractive

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ENGM 661 Engineering Economics for Managers

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Investment Worth MARR Suppose a company can earn 12% / annum in U. S. Treasury bills No way would they ever invest in a project earning < 12% Def:The Investment Worth of all projects are measured at the Minimum Attractive Rate of Return (MARR) of a company.

MARR MARRis company specific • utilities - MARR = 10 - 15% • mutuals - MARR = 12 - 18% • new venture - MARR = 20 - 30% MARR based on • firms cost of capital • Price Index • Treasury bills

Investment Worth Alternatives • NPW(MARR) > 0 Good Investment • EUAW(MARR) > 0 Good Investment • IRR > MARR Good Investment

Present Worth Example: Suppose you buy and sell a piece of equipment. Purchase Price $16,000 Sell Price (5 years) $ 4,000 Annual Maintenance $ 3,000 Net Profit Contribution $ 6,000 MARR 12% Is it worth it to the company to buy the machine?

216 100 1 2 3 16 School Funding We know i = 4.93%, is that significant growth?

216 100 1 2 3 16 School Funding We know i = 4.93%, is that significant growth? Suppose inflation = 3.5% over that same period.

216 100 1 2 3 16 i j . 0493 . 0350 d 1 j 1 . 0350 School Funding We know i = 4.93%, is that significant growth? Suppose inflation = 3.5% over that same period. d= 1.4%

216 100 1 2 3 16 School Funding We know that d, the real increase in school funding after we discount for the effects of inflation is 1.4%. So schools have experienced a real increase in funding?

216 100 1 2 3 16 School Funding We know that d, the real increase in school funding after we discount for the effects of inflation is 1.4%. So schools have experienced a real increase in funding? Rapid City growth rate 3% / yr.

4,100 2,520 0 1 2 3 n 1,000 5,580 IRR Problems Consider the following cash flow diagram. We wish to find the Internal Rate-of-Return (IRR).

4,100 2,520 0 1 2 3 n 1,000 5,580 IRR Problems Consider the following cash flow diagram. We wish to find the Internal Rate-of-Return (IRR). PWR(i*) = PWC(i*) 4,100(1+i*)-1 + 2,520(1+i*)-3 = 1,000 + 5,580(1+i*)-2

NPV vs. Interest $25 $20 $15 $10 Net Present Value $5 $0 0% 10% 20% 30% 40% 50% 60% ($5) Interest Rate IRR Problems

External Rate of Return Purpose: to get around a problem of multiple roots in IRR method Notation: At = net cash flow of investment in period t At , At > 0 0 , else -At , At < 0 0 , else rt = reinvestment rate (+) cash flows (MARR) i’ = rate return (-) cash flows Rt = Ct =

External Rate of Return Method find i = ERR such that Rt (1 + rt) n - t = Ct (1 + i’) n - t Evaluation If i’ = ERR > MARR Investment is Good

4,100 2,520 0 2 3 1 1,000 5,580 External Rate of Return ExampleMARR = 15% Rt (1 + .15) n - t = Ct (1 + i’) n - t 4,100(1.15)2 + 2,520 = 1,000(1 + i’)3 + 5,580(1 + i’)1 i’ = .1505

4,100 2,520 0 2 3 1 1,000 5,580 External Rate of Return ExampleMARR = 15% Rt (1 + .15) n - t = Ct (1 + i’) n - t 4,100(1.15)2 + 2,520 = 1,000(1 + i’)3 + 5,580(1 + i’)1 i’ = .1505 ERR > MARR

4,100 2,520 0 2 3 1 1,000 5,580 External Rate of Return ExampleMARR = 15% Rt (1 + .15) n - t = Ct (1 + i’) n - t 4,100(1.15)2 + 2,520 = 1,000(1 + i’)3 + 5,580(1 + i’)1 i’ = .1505 ERR > MARR Good Investment

Critical Thinking IRR < MARR a. IRR < MARR < ERR b. IRR < ERR < MARR c. ERR < IRR < MARR