1. Powerpoint Templates Page 1 Powerpoint Templates Chapter 7 An Economic Appraisal II: NPV, AE, IRR Technique

2. Powerpoint Templates Page 2 Net Present Value Technique NPV=The Sum of The Present Values of All Cash Inflows – The Sum of The Present Value of All Cash Outflows 2 3 4 5 0 1 Cash Inflows Cash Outflows 0 PV(i) CIF PV(i) COF NPV NPV(i) > 0

3. Powerpoint Templates Page 3 NPV.... -Equation -Decision Rule NPV(MARR) > 0 Accept it NPV(MARR) = 0 Indifferent NPV(MARR) < 0 Reject it Where, CF t : cash flow at time t, MARR: minimum attractive rate of return on a project

4. Powerpoint Templates Page 4 The Steps to Make a Decision with the NPV Technique -Step 1: Determine an MARR. -Step 2: Estimate a project life. -Step 3: Calculate a net cash flow(all cash inflows – all cash outlfows) -Step 4: Calculate a net present value with an MARR. -Step 5: Make a Decision on the Project with the NPV Derived in Step 4.

5. Powerpoint Templates Page 5 Ex 7.1] An Investment Decision on A Construction Project of A Small Power Plant with A NPVNPV Given] Cash Flows Diagram, MARR=8% 50 60 80 50 100 150 100 60 120 0-2-3-4-5-6-7-8-9-10 123504948 …………… n (unit: Million won)

6. Powerpoint Templates Page 6 Sol] - Step 1: MARR=8% Already Determined. - Step 2: A project life turns out be 60 years including a construction time of 10 years. - Step 3: A net cash flows are presented in the cash flow diagram. - Step 4: Calculate the net present value. (1) a present value of all the net cash flows incurred under construction. (2) a present value of all the net cash flows incurred during the commercialization stage of 50 years Continued……..

7. Powerpoint Templates Page 7 - Step 5: Make an investment decision on the project with NPV(8%) Since NPV(8%)=170.15 M >0, accept the project Continued…….. MARR(  100%) ( NPV Unit: $ M Break_Even Interest Rate=IRR=9.78% The Sensitivity Analysis of the NPV with A Varying Interest Rate

8. Powerpoint Templates Page 8 8 Net Future Value Technique  Given: Cash Flows and MARR (i)  Find: A Net Equivalent Value at the End of a Project Life 75,000 24,400 27,340 55,760 0 12 3 Project Life (unit: 000 won)

9. Powerpoint Templates Page 9 Sol] (1) A future value of all the cash flows incurred under construction (2) A present value of all the cash flows incurred during the commercialization stage An Investment Decision with A NFW for Ex. 7.1

10. Powerpoint Templates Page 10 -Project Balance (PB): Cash Flows Left inside A Project -Equation  PB 0 =PB 0  PB n =PB n-1 (1+MARR)+CF n Ex 7.2] An Economic Meaning of An NPV Based on A PB A Project Balance Concept n 012345 NCF (62,500)33,98233,72633,20533,13582,013 (unit: 000 won)

11. Powerpoint Templates Page 11 Continued… NPV(15%) = 149,049 (P/F, 15%, 5) =74,107,000 (unit: 000 won) Beginning Bal. Interest Ending Bal. NFV(15%) N 0 1 2 3 4 5 -62,500 -9,375 +33,982 -37,893 -5,684 +33,726 -9,851 -1,478 +33,205 +21,876 +3,281 +33,135 +58,292 +8,744 +82,013 +149,049 -62,500

12. Powerpoint Templates Page 12 -62,500 -37,893 -9,851 21,876 58,292 160,000 140,000 120,000 100,000 80,000 60,000 40,000 20,000 0 -20,000 -40,000 -60,000 -80,000 n PB at the End of a Project Life Discounted Payback Peirod PB 0 1 2 3 4 5 149,049 A Project Balance Diagram as A Function of Time

13. Powerpoint Templates Page 13  Principle: a present value of cash flows which are oriented with an equivalent amount of money of “A” over an infinite period of time.  Equation Capitalized Equivalent A P = CE(i)

14. Powerpoint Templates Page 14 Ex 7.3] CE Given] A=200 M won, i= 8%, N= ∞ Sol] Calculate a CE to prepare for an annual maintenance and repair cost of a building Continued …. 200M P = CE(8%)=2.5B ∞

15. Powerpoint Templates Page 15 Annual Equivalent 2 3 4 5 N 1 A 0 1 2 3 4 5 N AE(i) =NPV(i)(A/P, i, N) 0 NPV ( i ) 0 ……  Decision Rule - if AE(i) > 0, accept the project -if AE(i) = 0, remain indifferent -if AE(i) <, reject the project

16. Powerpoint Templates Page 16 Ex 7.4] Convert the irregular cash flows into an equivalent worth Continued….. 2 3 4 5 6 1 A=$1.835 0 1 2 3 4 5 6 0 Unit:: $M 0 15 3.5 5 9 12 10 8

17. Powerpoint Templates Page 17 1.Consistency of report formats: Financial managers more commonly work with annual rather than with overall costs in any number of internal and external reports. Engineering managers may be requires to submit project analyses on an annual basis for consistency and ease of use by other members of the corporation and stockholders. 2.Need for unit costs/profits: In many situations, projects must be broken into unit costs/profits for ease of comparison with alternatives. Make-or-buy and reimbursement analyses aree key examples. 3.Unequal project lives: Comparing projects with unequal service lives is complicated by the need to determine the lowest common multiple life. For the special situation of an indefinite service period and replacement with identical projects, we can avoid this complication by use of AN analysis. The Advantages of An AE Technique

18. Powerpoint Templates Page 18  Operating Costs : to be costs which are incurred repeatedly over the life of a project by the operation of physical plant and or equipment needed to provide servicee suck as labor and raw materials.  Capital Costs : to be costs which are incurred only one time over the life of a project by purchasing assets to be used in production and service such as a purchase cost and sales taxes. Capital Cost and Operating Cost

19. Powerpoint Templates Page 19  When only costs are involved, an AE cost analysis may be useful.  A profit must exceed a sum of operating and capital costs such that a project be economically viable. Annual Equivalence Analysis CC OC + AE Cost

20. Powerpoint Templates Page 20 Capital Recovery Cost(CR)  Definition: to be an annul equivalent of capital costs Items of costs (1) Initial cost being the same as the cost basis(I) (2) Salvage value(S)  CR(i) : Considering two costs above, we obtain the following expression. 0 N I S 0 1 2 3 N CR(i) ………………

21. Powerpoint Templates Page 21 Calculate a CR(i) - CR(i) for Mini Cooper Unit: 000 won TypeModel Purchase Cost SV at the end of year 3 SmallMini Cooper19,80012,078

22. Powerpoint Templates Page 22 A Relationship between a CR(i) and a Depreciation Cost In a practical term, a CR(i) cost consists of (1)a depreciation cost and (2) an interest on the investment cost. I=19.8M, N = 3 years, i=6%, S=12.078M A Depreciation Method: A SL Method nBegin. Inv. CostInterest with i= 6%PV of the interest 119.8001.1881.188(P/F,6%,1)=1.12075 217.2261.033561.03356(P/F,6%,2)=0.919.6 314.6520.87912o.87912(P/F,6%,3)=0.73813 총액 2.77874 AE of the Interest = 2,778.74(A/P, 10%, 3)=1.03995M

23. Powerpoint Templates Page 23 Ex 7.5] Given] I=20M, S=4M, A=4.4M, N=5 years, i= 10% Sol] An investment decision-making with AE, and make a decision with the AE - Method 1: first obtain the NPV and transform it into AE - Method 2: Make a decision with CR(i) AE-CR(i)

24. Powerpoint Templates Page 24 Ex 7.6] profit/machine time used – when the operating time is constant Given] NPV=3.553M, N=3 years, i= 15%, machine time used /year: 2,000 hrs Sol] Saving/machine time used 24,400 0 1 2 3 55,760 27,340 75,000 Operating hrs 2,000hrs

25. Powerpoint Templates Page 25 - Def 1: ROR is the interest rate earned on the unpaid balance of an amortized loan - Ex: A bank lend 10 million won and receives 4.021 million won each year over the next 3 years. Then, it can be said that this bank earns 10% of ROR on the loan. Rate of Return or Internal Rate of Return 01230123 Unit:000 n Begin. Unrecovered Bal. -10,000 -6,979 -3,656 -1,000 -698 -366 Interest on the Unrec. Bal.(10%) Recov. Money +4,021 Ending. Unrec.Bal -10,000 -6,979 -3,656 0

26. Powerpoint Templates Page 26 - Def 2: ROR is the break-even interest rate, i*, which equates the present value of a project’s cash outflows to the present value of its cash inflows. - Equation ROR

27. Powerpoint Templates Page 27 ROR=IRR Internal rate of return is the interest rate charged on the unrecovered project balance of the investment such that, when the project terminates, the unrecovered project balance will be zero 01230123 Unit:000 n Begin. Unrecovered Bal. -10,000 -6,979 -3,656 -1,000 -698 -366 Interest on the Unrec. Bal.(10%) Recov. Money +4,021 Ending. Unrec.Bal -10,000 -6,979 -3,656 0

28. Powerpoint Templates Page 28 28 Simple Investment Def: one in which the initial cash flows are negative, and only one sign change occurs in the net cash flow series. Example: -100, 250,300 (-, +, +) i * : Only one unique i* i * becomes the IRR Nonsimple Investment Def: one in which more than one sign change occurrs in the cash flow series Example: -100, 250,300(-, +, +,-) i * : the real i* may exist as many as a number of sign changes in the cash flow series. So, any i* can not be the IRR. The Types of Projects

29. Powerpoint Templates Page 29 Ex 7.7] Given] cash flows(refer to the table below) Simple and Nonsimple Investment Project Period (N) Project AProject BProject C 0-225-270-450 1135158270 22,02515890 3 4 -45 590 667 Unit: 000

30. Powerpoint Templates Page 30 Sol] Identify a number of sign changes in the net cash flows Continued…. n0123456 # of sign changes S or NS Project A-++1S Project B-++++1S Project C -+++-++3NS

31. Powerpoint Templates Page 31 Ex 7.8] understanding the IRR conept given] I= 49.950M, Cash Inflow= 18.5M, Life= 6 years Sol] Determine the IRR -obtain # of real root using Mathematica IRR Concept Plot[- 49950+18500/(1+i) 1 +18500/(1+i) 2 +18500/(1+ i) 3 +18500/(1+i) 4 +18500/(1+i) 5 +18500/(1+i) 6,{i, -1, 1}, PlotRange  {-50000,300000}] i IRR=29%

32. Powerpoint Templates Page 32 - Check up IRR=29% with the PB concept Prove it with a PB  PB at “0” :  PB at “1” :  PB at “2” :  PB at “3” :  PB at “4” :  PB at “5” :  PB at “6” :

33. Powerpoint Templates Page 33 A Decision Rule for the case in which there exists only a unique i *. if IRR > MARR, accept the project if IRR = MARR, remain indifferent if IRR > MARR, reject the project Note that this decision rule can not be applied for the case in which there exist more than one i*.

34. Powerpoint Templates Page 34 Ex 7.9] Determine the IRR of the project Given] Cash Flow Diagrams Calculate IRR (a) investing project 123 4 년 5,000 5 1,318.99 0 12 34567 년 90,000 180,000 90,000 80,000 120,000 150,000 (b) borrowing project 0 Unit: 000

35. Powerpoint Templates Page 35 Sol] 1) Determine the IRR of Project (a) - Obtain a numberr of i * - Determine the IRR Continued….. Plot[-90000-180000/(1+i)-90000/(1+i) 2 +80000/(1+i) 3 + 80000/(1+i) 4 +120000/(1+i) 5 +120000/(1+i) 6 +150000/(1+i) 7,{i,-1,1},PlotRange  {-200000,500000}] i NPV FindRoot[-90000-180000/(1+i)- 90000/(1+i) 2 +80000/(1+i) 3 +80000/(1+i) 4 +120000/(1+i) 5 +120000/(1+i) 6 +150000/(1+i) 7 Š0, {i,0.05}] {i*  0.10473633423827057}

36. Powerpoint Templates Page 36 1) Determine the IRR of Project (b) - Obtain a number of i *. - Find out the IRR Continued…… Plot[5000-1318.99/(1+i)-1318.99/(1+i) 2 -1318.99/(1+i) 3 -1318.99/(1+i) 4 -1318.99/(1+i) 5, {i,1,1}, PlotRange  {-5000,5000}] i NPV FindRoot[5000-1318.99/(1+i)-1318.99/(1+i) 2 -1318.99/(1+i) 3 -1318.99/(1+i) 4 -1318.99/(1+i) 5 Š0, {i,0.05}]{i  0.100001}

37. Powerpoint Templates Page 37 Ex 7.11] An Economic Analysis with a Variety of The Techniques Given] Cash Flows, MARR=8% Sol ] An Example Which Is Economically Analyzed with a Variety of The Appraisal Techniques n NCF of Project A NCF of Project B NCF of Project C 01234560123456 -200,000 20,000 40,000 60,000 68,000 -200,000 80,000 60,000 40,000 -200,000 60,000 40,000 20,000 총 이익 108,00040,000100,000 PBP(Pref. B, C,A)4.3 yrs3yrs3.3 yrs DPBP(Pref.: B, C,A)More than 6yrs3.9 yrs4.05yrs ARR*9%5%8.3% NPV(8%)28,2302,54638,554 IRR12%8.5%15% Unit: 000

38. Powerpoint Templates Page 38 1. Keep the alternatives independent or mutually exclusive one another 2. Set up a common time period 3. Perform an incremental analysis if neccessay(IRR) The Conditions to Compare Alternatives

39. Powerpoint Templates Page 39 (1)NPV - It is most widely used by companies - Its final result is expressed in an absolute value (2) AE - Its format is consistent with a fiscal year - It provides a unit cost and profit - It makes us convenient to compare alternatives whose lives are different (3) IRR - Its final result is expressed as percentage such that managers easily understand its meaning - It is also one of the techniques which are most widely used by companies The Reasons for Why NPV, AE, and IRR Techniques Are Chosen to Determine A Preference Ordering

40. Powerpoint Templates Page 40 Ex 7.12] Determine a preference ordering of the alternatives with a variety of the techniques Given] Cash Flow, MARR=10%, It is assumed that a capital budgett can be provided without limit Determine a preference ordering of the alternatives n A B C D 01230123 -100,000 200,000 -100,000 140,000 -10,000 -100,000 50,000 -50,000 200,000 -100,000 470,000 -720,000 360,000 Unit: 000

41. Powerpoint Templates Page 41 -In case which the alternatives are independent( A, C, D)  Conclusion: Since all the alternatives are independent and their NPVs are greater than 0, it is better to undertake all of them. - In case which they are mutually exclusive ( A, C, D)  Conclusion: It is required to undertake alternative “A” only because its NPV is greater than others A Preference Ordering with the NPV

42. Powerpoint Templates Page 42 (1) Obtain the AE with a least common multiple of 6 years Cash Flow of “A” over 6 years n 01 23 100,000 200,000 100,000 4 5 6 n 0 1 23 140,000 456 Cash Flow of “B” 10,000 Determine a preference ordering with the AE 10,000 100,000

43. Powerpoint Templates Page 43 -A LCM of 6 years  Calculate the AE of “A” n A B C D 01234560123456 -100,000 200,000 100,000 -100,000 200,000 -100,000 140,000 -110,000 140,000 -110,000 140,000 -10,000 -100,000 50,000 -50,000 100,000 50,000 -50,000 200,000 -100,000 470,000 -720,000 260,000 470,000 -720,000 360,000 A Comparison with the AE Technique

44. Powerpoint Templates Page 44  For “B”  For “C” Continued…

45. Powerpoint Templates Page 45  For “D” Way to Calculate the AE of the Alternatives with a single cycle of cash flows  For “ A” Continued…

46. Powerpoint Templates Page 46  For “B”  For “ D”  it is recommended to use the AE techniques for which the project lives are different - When the alternatives are independent - Select the alternative with a highest AE  for “ C” Continued…

47. Powerpoint Templates Page 47 -Question: Can we determine the preference ordering of the alternatives according to the seize of the IRR? n 0 1 IRR NPV(10%) Unit: 000 A1 -1,000 2,000 100% 818 A2 -5,000 7,000 40% 1,364 ><>< A Comparison with the IRR

48. Powerpoint Templates Page 48 Incremental Analysis If MARR=10%, it implies that the project earns a profitability of 10% is guaranteed. That is to say, the investment of 4 million won will grow up to 4.4 million won. We can earn 5 million won one year after once we invest 4 million won in A2. Since the IRR of 25% is greater than the MARR, it is desirable to undertake the project. nA1 A2(A2 – A1) 0101 -1,000 2,000 -5,000 7,000 -4,000 5,000 IRR NPV(10%) 100% 818 40% 1,364 25% 546 Unit: 0000

49. Powerpoint Templates Page 49 Step 1: Subtract the cash flows of Project (A) whose initial investment cost is less than the other from the cash flows of Project(B) whose initial investment cost is greater -Step 2: Calculate the the IRR B-A of the incremental project. Step 3: Select the project based the following decision rules. If IRR B-A > MARR, undertake Project B If IRR B-A = MARR, remain indifferent If IRR B-A < MARR, undertake Project A. 49 The Steps of The Incremental Analysis

50. Powerpoint Templates Page 50 Ex 7.13] The Example for the Incremental Analysis with the IRR Technique Given] Cash Flows for two projects, MARR=10% Example Unit: 000 nB1B2B2 - B1 01230123 -3,000 1,350 1,800 1,500 -12,000 4,200 6,225 6,330 -9,000 2,850 4,425 4,830 IRR25%17.43%15% If MARR = 10%, which one is the better in an economic sense? Since IRR B2-B1 >15% > 10% which is greater than MARR=10%,, it is recommended to undertake Project B2