1. InvestmentWorth Investment Worth

2. 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.

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

4. Investment Worth Alternatives u NPW( MARR ) > 0Good Investment

5. Investment Worth Alternatives u NPW( MARR ) > 0Good Investment u EUAW( MARR ) > 0Good Investment

6. Investment Worth Alternatives u NPW( MARR ) > 0Good Investment u EUAW( MARR ) > 0Good Investment u IRR > MARRGood Investment

7. 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?

8. Present Worth 16,000 6,000 3,000 5 0 4,000 NPW= -16 + 3(P/A,12,5) + 4(P/F,12,5) 16,000 3,000 5 0 4,000

9. Present Worth 16,000 6,000 3,000 5 0 4,000 NPW= -16 + 3(P/A,12,5) + 4(P/F,12,5) = -16 +3(3.6048) + 4(.5674) 16,000 3,000 5 0 4,000

10. Present Worth 16,000 6,000 3,000 5 0 4,000 NPW= -16 + 3(P/A,12,5) + 4(P/F,12,5) = -16 +3(3.6048) + 4(.5674) = -2.916 = -$2,916 16,000 3,000 5 0 4,000

11. Annual Worth Annual Worth (AW or EUAW) AW(i) = PW(i) (A/P, i%, n) = [ A t (P/F, i%, t)](A/P, i%, n) AW(i) = Annual Worth of Investment AW(i) > 0 **OK Investment** 

12. Annual Worth; Example Repeating our PW example, we have AW(12)= -16(A/P,12,5) + 3 + 4(A/F,12,5) 3,000 5 0 4,000 16,000

13. Annual Worth; Example Repeating our PW example, we have AW(12)= -16(A/P,12,5) + 3 + 4(A/F,12,5) = -16(.2774) + 3 + 4(.1574) 3,000 5 0 4,000 16,000

14. Annual Worth; Example Repeating our PW example, we have AW(12)= -16(A/P,12,5) + 3 + 4(A/F,12,5) = -16(.2774) + 3 + 4(.1574) = -.808 = -$808 3,000 5 0 4,000 16,000

15. Alternately AW(12) = PW(12) (A/P, 12%, 5) = -2.92 (.2774) = - $810 < 0 NO GOOD 3,000 5 0 4,000 16,000

16. Internal Rate of Return Internal Rate-of-Return IRR - internal rate of return is that return for which NPW(i*) = 0 i* = IRR i* > MARR **OK Investment**

17. Internal Rate of Return Internal Rate-of-Return IRR - internal rate of return is that return for which NPW(i*) = 0 i* = IRR i* > MARR **OK Investment** Alt: PW revenue (i*) = PW costs (i*)

18. Internal Rate of Return Example PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5) 3,000 5 0 4,000 16,000

19. Internal Rate of Return Example PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5) 3,000 5 0 4,000 16,000

20. Internal Rate of Return Example PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5) i* = 5 1 / 4 % i* < MARR 3,000 5 0 4,000 16,000

21. Summary u NPW > 0 Good Investment

22. Summary u NPW > 0 Good Investment u EUAW > 0 Good Investment

23. Summary u NPW > 0 Good Investment u EUAW > 0 Good Investment u IRR > MARR Good Investment

24. Summary u NPW > 0 Good Investment u EUAW > 0 Good Investment u IRR > MARR Good Investment Note: If NPW > 0 EUAW > 0 IRR > MARR

25. Internal Rate of Return Internal Rate-of-Return IRR - internal rate of return is that return for which NPW(i*) = 0 i* = IRR i* > MARR **OK Investment** Alt: FW(i*) = 0 = A t (1 + i*) n - t PW revenue (i*) = PW costs (i*) 

26. Internal Rate of Return Example PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5) 3,000 5 0 4,000 16,000

27. Internal Rate of Return Example PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5) i* = 5 1 / 4 % i* < MARR 3,000 5 0 4,000 16,000

28. Spreadsheet Example