1. F – 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Financial Analysis F For Operations Management, 9e by Krajewski/Ritzman/Malhotra © 2010 Pearson Education PowerPoint Slides by Jeff Heyl

2. F – 2 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Time Value of Money Future value of an investment  Compounded interest  The value of an investment at the end of the period  Requires all values be in the same units of time The value of a $5,000 investment at 12 percent per year, 1 year from now is $5,000(1.12) = $5,600 If the entire amount remains invested, at the end of 2 years you would have $5,600(1.12) = $5,000(1.12) 2 = $6,272

3. F – 3 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. F = P (1 + r ) n where F = future value of the investment at the end of n periods P = amount invested at the beginning, called the principal r = periodic interest rate n = number of time periods for which the interest compounds Time Value of Money In general,

4. F – 4 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 500(1 +.06) 5 = 500(1.338) = $669.11 Application F.1 Future Value of a $500 Investment in 5 Years P = $500 r = 6% n = 5 F = P (1 + r ) n SOLUTION

5. F – 5 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Present Value of a Future Amount The amount that must be invested now to accumulate to a certain amount in future at a specified interest rate Discounting is the process of finding the present value of an investment when the future value and the interest rate are known An investment worth $10,000 at the end of 1 year if the interest rate is 12 percent F = $10,000 = P (1 + 0.12)

6. F – 6 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. where F = future value of the investment at the end of n periods P = amount invested at the beginning, called the principal r = periodic interest rate (discount rate) n = number of time periods for which the interest compounds P =P = F (1 + r ) n Present Value of a Future Amount In general, The interest rate is also called the discount rate

7. F – 7 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. $500/1.338 =$373.63 Application F.2 P =P = F (1 + r ) n F = $500 r = 6% n = 5 Present Value of $500 Received in Five Years SOLUTION

8. F – 8 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. [ 1/(1 + r ) n ] is the present value factor (pf) Found in Table F.1 Present Value Factors The present value of a future amount

9. F – 9 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Present Value Factors TABLE F.1 | PRESENT VALUE FACTORS FOR A SINGLE PAYMENT (Partial) Number of Periods ( n ) Interest Rate ( r ) 0.010.020.030.040.050.060.080.100.120.14 10.99010.98040.97090.96150.95240.94340.92590.90910.89290.8772 20.98030.96120.94260.92460.90700.89000.85730.82640.79720.7695 30.97060.94230.91510.88900.86380.83960.79380.75130.71180.6750 40.96100.92380.88850.85480.82270.79210.73500.68300.63550.5921 50.95150.90570.86260.82190.78350.74730.68060.62090.56740.4194 60.94200.88800.83750.79030.74620.70500.63020.56450.50660.4556 70.93270.87060.81310.75990.71070.66510.58350.51320.45230.3996 80.92350.86350.78940.73070.67680.62740.54030.46650.40390.3506 90.91430.83680.76640.70260.64460.59190.50020.42410.36060.3075 100.90530.82030.74410.67560.61390.55840.46320.38550.32200.2697

10. F – 10 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Present Value Factors An investment will generate $15,000 in 10 years If the interest rate is 12 percent, Table F.1 shows that pf = 0.3220 The present value is P = F (pf) = $15,000(0.3220) = $4,830

11. F – 11 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Application F.2 $500(.7473) =$373.65 P =P = F (1 + r ) n F = $500 r = 6% n = 5 pf=.7473 Present Value of $500 Received in Five Years SOLUTION

12. F – 12 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Present Value Factors TABLE F.1 | PRESENT VALUE FACTORS FOR A SINGLE PAYMENT (Partial) Number of Periods ( n ) Interest Rate ( r ) 0.010.020.030.040.050.060.080.100.120.14 10.99010.98040.97090.96150.95240.94340.92590.90910.89290.8772 20.98030.96120.94260.92460.90700.89000.85730.82640.79720.7695 30.97060.94230.91510.88900.86380.83960.79380.75130.71180.6750 40.96100.92380.88850.85480.82270.79210.73500.68300.63550.5921 50.95150.90570.86260.82190.78350.74730.68060.62090.56740.4194 60.94200.88800.83750.79030.74620.70500.63020.56450.50660.4556 70.93270.87060.81310.75990.71070.66510.58350.51320.45230.3996 80.92350.86350.78940.73070.67680.62740.54030.46650.40390.3506 90.91430.83680.76640.70260.64460.59190.50020.42410.36060.3075 100.90530.82030.74410.67560.61390.55840.46320.38550.32200.2697 For Application F.2

13. F – 13 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Annuities A series of payments of a fixed amount for a specified number of years At a 10% interest rate, how much needs to be invested so that you may draw out $5,000 per year for each of the next 4 years? = $4,545 + $4,132 + $3,757 + $3,415 = $15,849

14. F – 14 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. P = A (af) where P = present value of an investment A = amount of the annuity received each year af= present value factor for an annuity Annuities Find the present value of an annuity (af) using Table F.2 Multiply the amount received each year (A) by the present value factor So P = A (af) = $5,000(3.1699) = $15,849

15. F – 15 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Present Value Factors TABLE F.2 | PRESENT VALUE FACTORS OF AN ANNUITY (Partial) Number of Periods ( n ) Interest Rate ( r ) 0.010.020.030.040.050.060.080.100.120.14 10.99010.98040.97090.96150.95240.94340.92590.90910.89290.8772 21.97041.94161.91351.88611.85941.83341.78331.73551.69011.6467 32.94102.88392.82862.77512.77322.67302.57712.48692.40182.3216 43.90203.80773.71713.62993.54603.46513.31213.16993.03732.9137 54.85344.71354.57974.45184.32954.21243.99273.79083.60483.4331 65.79555.60145.41725.24215.07574.91734.62294.35534.11143.8887 76.72826.47206.23036.00215.78645.58245.20644.86844.56384.2883 87.65177.32557.01976.73276.46326.20985.74665.33494.96764.6389 98.56608.16227.78617.43537.10786.80176.24695.75905.32824.9464 109.47138.98268.33028.11097.72177.36016.72016.14465.65025.2161

16. F – 16 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Application F.3 Present Value of a $500 Annuity for 5 Years P = A (af) A = $500 for 5 years at 6% af = 4.2124 (from table) P = SOLUTION $500(4.2124) = $2,106.20

17. F – 17 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Two important points 1.Consider only incremental cash flows 2.Convert cash flows to after-tax amounts Techniques of Analysis Three basic financial analysis techniques Work with cash flow 1.Net present value method 2.Internal rate of return method 3.Payback method

18. F – 18 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Depreciation is an allowance for the consumption of capital Not a cash flow but it does affect net income Straight-line depreciation Salvage value is the cash flow from disposal at the end useful life General expression for annual depreciation Depreciation and Taxes where D =annual depreciation I =amount of investment S =salvage value n =number of years of project life

19. F – 19 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Accelerated depreciation or Modified Accelerated Cost Recovery System (MACRS)  3-year class  5-year class  7-year class  10-year class Depreciation and Taxes Income-tax rate varies with location Include all relevant income taxes in analysis

20. F – 20 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Accelerated Depreciation TABLE F.3 | MACRS DEPRECIATION ALLOWANCES Class of Investment Year3-Year5-Year7-Year10-Year 133.3320.0014.2910.00 244.4532.0024.4918.00 314.8119.2017.4914.40 47.4111.5212.4911.52 5 8.939.22 65.768.937.37 78.936.55 84.456.55 9 106.55 113.29 100.0%

21. F – 21 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Analysis of Cash Flows Four steps Step 1:Subtract the new expenses attributed to the project from new revenues Step 2:Subtract the depreciation to get pre- tax income Step 3:Subtract taxes to get net operating income (NOI) Step 4:Compute the total after-tax cash flow by adding back depreciation, i.e., NOI + D

22. F – 22 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Calculating After-Tax Cash Flows EXAMPLE F.1 A local restaurant is considering adding a salad bar. The investment required to remodel the dining area and add the salad bar will be $16,000. Other information about the project is as follows: 1.The price and variable cost are $3.50 and $2.00 2.Annual demand should be about 11,000 salads 3.Fixed costs, other than depreciation, will be $8,000 4.The assets go into the MACRS 5-year class for depreciation purposes with no salvage value 5.The tax rate is 40 percent 6.Management wants to earn a return of at least 14 percent Determine the after-tax cash flows for the life of this project

23. F – 23 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Calculating After-Tax Cash Flows SOLUTION The cash flow projections are shown in the following table. Depreciation is based on Table F.3. For example, depreciation in 2009 is $3,200 (or $16,000  0.20). The cash flow in 2014 comes from depreciation’s tax shield in the first half of the year.

24. F – 24 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Calculating After-Tax Cash Flows Year Item2008200920102011201220132014 Initial Information Annual demand (salads) 11,000 Investment$16,000 Interest (discount) rate 0.14 Cash Flows Revenue$38,500 Expenses: Variable costs 22,000 Expenses: Fixed costs 8,000 Depreciation ( D )3,2005,1203,0721,843 922 Pretax income$5,300$3,380$5,428$6,657 – $922 Taxes (40%)2,1201,3522,1712,663 – 369 Net operating income (NOI) $3,180$2,208$3,257$3,994 – $533 Total cash flow (NOI + D ) $6,380$7,148$6,329$5,837 $369

25. F – 25 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Net Present Value Method NPV = the original investment – the present values of all after-tax cash flows  If the result is positive for the discount rate used, the project earns a higher rate of return than the discount rate The discount rate that represents the lowest desired rate of return on an investment is called the hurdle rate

26. F – 26 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Application F.4 Find the NPV for Example Project SOLUTION Year 1: $500 Year 2: $650 Year 3: $900 The discount rate is 12%, and the initial investment is $1,550, so the project’s NPV is: Present value of investment (Year 0): Present value of Year 1 cash flow: Present value of Year 2 cash flow: Present value of Year 3 cash flow: Project NPV: ($1,550.00) 446.40 518.18 640.62 $ 55.20

27. F – 27 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Internal Rate of Return The IRR is the discount rate that makes the NPV of a project zero.  A project is successful only if the IRR exceeds the hurdle rate. The IRR can be found by trial and error, beginning with a low discount rate and calculating the NPV. If the result is greater than zero, try again with a higher discount rate. Repeat until you are near or at zero.

28. F – 28 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Application F.5 IRR for Example Project SOLUTION Discount RateNPV 10%= 12%= 14%=

29. F – 29 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Application F.5 IRR for Example Project SOLUTION Discount RateNPV 10%= 12%= 14%= $500(0.9091) + $650(0.8264) + $900(0.7513)$117.88 $500(0.8929) + $650(0.7972) + $900(0.7188)$55.20 $500(0.8772) + $650(0.7695) + $900(0.6750)($3.72)

30. F – 30 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Payback Method This is a means of determining how much time will elapse before the total after-tax cash flows will equal, or pay back, the initial investment  Payback is widely used, but often criticized for encouraging a focus on the short run

31. F – 31 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Calculating NPV, IRR, Payback Period EXAMPLE F.2 What are the NPV, IRR, and payback period for the salad bar project in Example F.1? SOLUTION Management wants to earn a return of at least 14 percent on its investment, so we use that rate to find the pf values in Table F.1. The present value of each year’s total cash flow and the NPV of the project are as follows: 2009:$6,380(0.8772)=$5,597 2010:$7,148(0.7695)=$5,500 2011:$6,329(0.6750)=$4,272 2012:$5,837(0.5921)=$3,456 2013:$5,837(0.5194)=$3,032 2014:$369(0.4556)=$168

32. F – 32 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Calculating NPV, IRR, Payback Period NPV of project = ($5,597 + $5,500 + $4,272 + $3,456 + $3,032 + $168) – $16,000 = $6,024 Because the NPV is positive, the recommendation would be to approve the project. To find the IRR, let us begin with the 14 percent discount rate, which produced a positive NPV. Incrementing at 4 percent with each step, we reach a negative NPV with a 30 percent discount rate. If we back up to 28 percent to “fine tune” our estimate, the NPV is $322. Therefore, the IRR is about 29 percent. The computer can provide a more precise answer with much less computation.

33. F – 33 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Calculating NPV, IRR, Payback Period To determine the payback period, we add the after-tax cash flows at the bottom of the table in Example F.1 for each year until we get as close as possible to $16,000 without exceeding it. For 2009 and 2010, cash flows are $6,380 + $7,148 = $13,528. The payback method is based on the assumption that cash flows are evenly distributed throughout the year, so in 2011 only $2,472 must be received before the payback point is reached. As $2,472/$6,329 is 0.39, the payback period is 2.39 years. Discount RateNPV 14%$6,025 18%$4,092 22%$2,425 26%$ 977 30%–$ 199

34. F – 34 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Application F.6 Payback for Example Project SOLUTION $500 $500 + $650 $1,150 $(1,550 – $1,150)/$900 0.44 year 2.44 years Payback for Year 1= Payback for Years 1 and 2= = Proportion of Year 3= = Payback periods for project=

35. F – 35 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Computer Support Computer support such as spreadsheets and the Financial Analysis Solver (OM Explorer) allows for efficient financial analysis The analyst can focus on data collection and evaluation, including “what if” analyses

36. F – 36 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Managing by the Numbers The danger is in a preference for short- term results This can be the result of the precision and detachment that come from using the NPV, IRR, or Payback methods and from the reality that projects with the greatest strategic impact may have qualitative benefits that are difficult to quantify Financial analysis should augment, not replace, the insight and judgment that comes from experience

37. F – 37 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Managing by the Numbers Figure F.1 – OM Explorer Output for Salad Bar

38. F – 38 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.