1. Matakuliah: D0762 – Ekonomi Teknik Tahun: 2009 RATE OF RETURN ANALYSIS Course Outline 7

2. Outline 2 Definition ROR Facts ROR for Single project ROR for Multiple project Spreadsheet Refererences -Engineering Economy – Leland T. Blank, Anthoy J. Tarquin p.200-246 -Engineering Economic Analysis, Donald G. Newman, p. 163-196 -Engineering Economy, William G. Sulivan, p.137-194, p. 212-284 Next

3. Definition Synonym: IRR (Internal Rate of Return) Popular measurement on investment worth Which one represent the correct interpretation of ROR? Rate of Return on the un-recovered balance Rate of Return on the initial balance ROR (i*) is the interest rate earned on the un-recovered balance or the interest rate paid on the unpaid balance of a loan in which the final payment or receipt brings the terminal value to exactly equal “0” 3 KGA-Spr09®Reserved

4. ROR Facts If i… > MARR, investment is justified = MARR, investment is justified (indifferent decision) < MARR, investment is not justified i is ranges …. –100% < i ≤ +  –100%: means total lost of capital >0%: means positive return on investment Some CF might have multiple ROR If there is a reinvestment option, use the composite rate 4 KGA-Spr09®Reserved

5. Single Project Equation for computing ROR –Present Worth of benefits – PW of costs = 0 –PW of benefits/PW of costs = 1 –Net Present Worth = 0 –EUAB – EUAC = 0 –PW of cost = PW of benefits Note : EUAB : equivalent uniform annual benefit EUAC : equivalent uniform annual cost 5

6. Example. 1 An investment $8200 investment returned $2000 per year over a five – year useful life. What was the rate of return on the investment ? Solution 6 From interest table (P/A,i,5): i(P/A,i,5) 6%4.212 7%4.100 8%3.993 The rate of return for the investment is 7%:

7. ROR Calculation 7 Trial & Error… Draw the CF Diagram Set up the equivalence equation and set equal to 0 Select values of i and solve the equation Repeat until you find the i which give a balanced equation Sometimes might need to interpolate to find the approximate value of i* KGA-Spr09®Reserved

8. Example 7.2 The table shows an investment cash flow Find rate of return for the investment above Solution : EUAB –EUAC = 0 100 + 75(A/G,i, 4) -7000(A/P,i,4) = 0 8 YearCashflow 0-$7000 1+100 2+175 3+250 4+325 There are two different interest factor. Solve the equation by trial and error

9. Solution for Example 7.2. Try i = 5% EUAB –EUAC = 0 100 + 75(G/A,5%, 4) -7000(A/P,5%,4) = 0 100 + 75(1.439) -7000(0.282) = 0 208 – 197 = +6 The EUAB –EUAC > 0, too low. If interest rate is increased, EUAC will increase. Try i = 8% EUAB –EUAC = 0 100 + 75(A/G,8%, 4) -7000(A/P,8%,4) = 0 100 + 75(1.404) -7000(0.3019) = 0 205 – 211 = -6 The EUAB –EUAC < 0, too high 9 Try i = 7% EUAB –EUAC = 0 100 + 75(A/G,7%, 4) -7000(A/P,7%,4) = 0 100 + 75(1.416) -7000(0.2952) = 0 206 – 206 = 0 The Rate Of Return = 7%

10. So far we have learnt IRR not ERR (External Rate of Return) The difference between IRR and ERR is… Un-recovered balance versus positive CF generated becomes released/external funds Solve it by… Basic guesses (must performed both!): Descartes’ rule: sign change in the series of net CF Norstrom’s rule: sign change in the series of cumulative CF Graphically Better way: Composite Rate of Return (CRR) 10 Multiple Values of ROR KGA-Spr09®Reserved

11. Example 101 11 For the CF below, how many ROR at most we could have? Use Descartes’ Rule! 123456Max i* values -+++--2 +-+-++4 -+++++1 KGA-Spr09®Reserved

12. Composite Rate of Return (CRR or ERR) CRR/ERR/RIC: the unique ROR for a project which assumes that net positive CF, which represent money not immediately needed by the project are reinvested at the reinvestment rate “c” To summarize… any positive CF available in year X Let’s consider the funds released from a project in calculating the overall ROR of a project Reinvestment rate, “c” Composite rate of return =i’ 12 KGA-Spr09®Reserved

13. Equation for CRR F t = F t-1 (1+i) + C t Where t = 1, 2, …, n n = total years in project C t = net CF in year t i = c, if F t-1 > 0 i’, if F t-1 < 0 13 KGA-Spr09®Reserved

14. Example 1 14 Find the ROR! ROR = 16.82% on the un-recovered investment balances over 5 years -$10,000 0 1 2 3 4 5 +$8,000 +$9,000 KGA-Spr09®Reserved

15. Example 2 15 Reinvestment rate, c = 15%. What is the CRR? Answer… F 0 = 50, F 1 = -142.50 F 2 = -142.50 (1+i’) + 50 F 3 = F 2 (1+i’) + 100 Set F 3 = 0 to find the i’ YearCash Flow, $ 050 1-200 250 3100 KGA-Spr09®Reserved

16. Example 3 - CF Diagram Purchase price: P - $800/bond. Bond interest at 4% paid semiannually for $1000 face value. Life = 20 years. If you pay the $800 per bond, what is the ROR (yield) on this investment? 16 …. …. …. 0 1 2 3 4 39 40 $800 F 40 = $1000 A= $1000(0.04/2) = $20.00 every 6 months for 20 years A = +$20/6 months From the bond purchaser’s perspective Pay $800 per bond to receive the $20each 6-months in interest cash flow plus $1,000 at the end of 40 time periods. What is the ROR of this cash flow?

17. Example 3 (Cont’d) Equation: 0 = -$800 + $20(P/A, i*, 40) + $1000 (P/F, i*, 40) Solve for i*, we get 2.87% per semiannual Not done yet, thus find the … Nominal ROR/year = (2.87%)(2) = 5.74%/year Effective ROR/year = 5.82%/year 17 KGA-Spr09®Reserved

18. Multiple Projects Incremental Analysis, Introduction ROR on Extra Investment ROR Analysis Multiple Alternatives 18 KGA-Spr09®Reserved

19. Incremental Analysis MARR Definition Example: A company uses a MARR of 16% per year. The company has $90,000 available for investment and that two alternatives (A and B) are being evaluated. Alternative A requires an investment of $50,000 and will yield an IRR of 35% per year. Alternative B requires $85,000 and will yield an IRR of 29% per year. Which alternative will be the best? Overall ROR(A) = [50k (.35) + 40k (.16)]/90k = 26.6% Overall ROR(B) = [85k (.29) + 5k (.16)]/90k = 28.3% 19 KGA-Spr09®Reserved

20. Tabulation for Incremental CF For 2 Alternatives 20 Equal lives versus Unequal lives ROR Analysis on incremental CF: Need to use LCM (no matter what!) Larger initial investment  alternative B! Incremental CF = CF B – CF A Check the sign changes like in Descartes’ and Norstorm’s rules KGA-Spr09®Reserved

21. ROR on Extra Investment Decision: Do-Nothing alternative Equivalent worth of the savings > equivalent worth of the extra investment using company’s MARR DO the extra investment If the extra investment is not justified by the savings Choose LOWER first-cost proposal 21 KGA-Spr09®Reserved

22. ROR Analysis Procedure Sort the alternative by initial investment in an ascending order Develop CF and incremental CF series Draw if necessary Count the # of sign changes Set up PW equation for the incremental CF & find i* B-A If i* B-A < MARR: choose A, Otherwise: choose B 22 KGA-Spr09®Reserved

23. Example 8.3 23 A leather clothes manufacturer is considering the purchase of one new industrial sewing machine, which is either semiautomatic or fully automatic. Which machine should be selected if the MARR is 15% per year? The estimates are listed in the table below. SORT!  Incremental CF  # sign Δ (max #ROR)  PW Incremental CF  trial & error 12.65% < MARR  choose the lower-cost (Semiautomatic) Fully AutomaticSemiautomatic First cost, $13,0008,000 Annual disbursement, $1,6003,500 Salvage value, $2,0000 Life, years510 KGA-Spr09®Reserved

24. What if… MARR is 12.65%, which alternative is better? MARR = 10%, which one will you choose? MARR = 20%, semiautomatic or full automatic? 24 Example 8.3 KGA-Spr09®Reserved

25. Multiple Alternatives Criteria: Select one alternative that requires the largest investment AND indicated that the extra investment over another acceptable alternative is justified

26. KGA-Spr09®Reserved Multiple Alternatives Procedure 1.Sort them in an ascending order 2.Determine the nature of the CF series Some positive CF: do nothing (defender) vs. lowest-initial investment alternative. Go to step 3 All negative CF: lowest-initial investment (defender) vs. next-higher investment 3.Find the i* of the defender If i* < MARR, remove the lowest-investment alternative Compute the next one. Repeat until i* ≥ MARR, this alternative  defender and compares it with the next one 4.Find the annual incremental CF between the challenger and defender 5.Find i* using PW-based or AW 6.If i* ≥ MARR, challenger  new defender, o/w next challenger vs. defender 7.Repeat until only 1 alternative remains, OPTIMAL

27. KGA-Spr09®Reserved Example 8.7 (T. Blank, p. 247) Four different prefab-building locations have been suggested, of which only one will be selected. Cost and annual net cash-flow information are detailed in table below. The annual net cash-flow series vary due to differences in maintenance, labor costs, transportation charges, etc. If the MARR is 10%, use ROR analysis to select the one economically-best location Answer: Sort C, A, B, D Start comparing one by one, i = 9.63%; 10.49%, 17.28%, 8.55% Choose B LocationABCD Building cost, $-200,000-275,000-190,000-350,000 Annual Cash flow, $+22,000+35,000+19,500+42,000 Life, years30

28. Spreadsheet Example 28