1. Discounted Cash Flow Application Schweser Notes - Reading #6 1

2. LOS Structure 6.a : NPV and IRR 6.b : Problems with IRR 6.c : Holding period return (HPR) 6.d : Money and time weighted return 6.e : Bank discount yield, holding period yield, effective annual yield, money market yield for U.S. Treasury bills 6.f : Conversion among yields 2

3. Net present value (NPV) Net present value is the sum of the present values of all the positive cash flows minus the sum of the present values of all the negative cash flows. Interpretation: When the discount rate applied is an appropriate hurdle rate (minimum expected rate of return), it measures the contribution of the project to shareholder wealth. Decision rule: Accept positive NPV projects  they increase shareholder wealth. 3 t = 0 t = 1t = 2 t = 0 t = 2t = 4 Initial Outlay 0 NPV 0 = ? r = req’d return t = 4 t = 3 t = 1 t = 3 CF 1 CF 2 –CF 3 CF 4 LOS 6.a: NPV and IRR

4. Net present value (NPV) 4 LOS 6.a: NPV and IRR

5. Net present value (NPV) Consider Project A with the following cash flows: The NPV for this project is…? Decision? Consider Project B with the following cash flows: The NPV for this project is…? Decision? 5 t = 0 t = 1t = 2 –$100,000 r = 10% t = 3 $20,000 $40,000 $45,000 $75,000 t = 4 t = 0 t = 1t = 2 –$100,000 r = 10% t = 3 $55,000 $45,000 $35,000 $25,000 t = 4 LOS 6.a: NPV and IRR

6. NPV and IRR: How to use financial calculator 6 Remember to clear the cash flow memory by press CF, then 2 ND, then press CE|C

7. Net present value (NPV) 7 t = 0 t = 1t = 2 –$100,000 r = 10% t = 3 $20,000 $40,000 $45,000 $75,000 t = 4 t = 0 t = 1t = 2 –$100,000 r = 10% t = 3 $55,000 $45,000 $35,000 $25,000 t = 4 LOS 6.a: NPV and IRR Consider Project A with the following cash flows: The NPV for this project is $36,274.84. Decision  Accept the project. Consider Project B with the following cash flows: The NPV for this project is $30,561.43. Decision  Accept the project.

8. LOS 6.a: NPV and IRR 8

9. 9 A company is considering entering into a joint venture that will require an investment of $10 million. The project is expected to generate cash flows of $4 million, $3 million, and $4 million in each of the next three years, respectively. Assuming a discount rate of 10%, what is the project’s NPV? NPV = ?

10. LOS 6.a: NPV and IRR 10 A company is considering entering into a joint venture that will require an investment of $10 million. The project is expected to generate cash flows of $4 million, $3 million, and $4 million in each of the next three years, respectively. Assuming a discount rate of 10%, what is the project’s NPV? NPV = -$879,000

11. LOS 6.a: NPV and IRR 11 A company is considering the purchase of new material handling system for a cost of $15 million. The system is expected to generate a positive cash flow of $1.8 million per year in perpetuity. What is the NPV of the proposed investment if the appropriate discount rate is 10.5%? NPV = ?

12. LOS 6.a: NPV and IRR 12

13. Internal rate of return (IRR) 13 LOS 6.a: NPV and IRR

14. 14 A company is considering entering into a joint venture that will require an investment of $10 million. The project is expected to generate cash flows of $4 million, $3 million, and $4 million in each of the next three years, respectively. Assuming a discount rate of 10%, what is the project’s approximate IRR? IRR = ?

15. LOS 6.a: NPV and IRR 15 A company is considering entering into a joint venture that will require an investment of $10 million. The project is expected to generate cash flows of $4 million, $3 million, and $4 million in each of the next three years, respectively. Assuming a discount rate of 10%, what is the project’s approximate IRR? IRR = 4.9%

16. 16 LOS 6.a: NPV and IRR

17. Internal rate of return (IRR) Example: Tony is evaluating an investment opportunity. He feels that this investment must earn a minimum compound annual after-tax return of 9% in order to be acceptable. Tony’s initial investment would be $7,500, and he expects to receive annual after-tax cash flows of $500 per year in each of the first 4 years, followed by $700 per year at the end of years 5 through 8. He plans to sell the investment at the end of year 8 and net $9,000, after taxes. 17 LOS 6.a: NPV and IRR

18. Internal rate of return (IRR) Example: Tony is evaluating an investment opportunity. He feels that this investment must earn a minimum compound annual after-tax return of 9% in order to be acceptable. Tony’s initial investment would be $7,500, and he expects to receive annual after-tax cash flows of $500 per year in each of the first 4 years, followed by $700 per year at the end of years 5 through 8. He plans to sell the investment at the end of year 8 and net $9,000, after taxes. So, whether Tony should accept this investment based on IRR? Tony finds the investment’s IRR of 9.54%. Given that the expected IRR of 9.54% exceeds Tony’s required minimum IRR of 9%, the investment is acceptable. 18 LOS 6.a: NPV and IRR

19. NPV vs. IRR If projects are independent, the decision to invest in one does not preclude investment in the other. NPV and IRR will yield the same investment decisions. Accept if NPV > 0 projects or IRR > investor’s required rate of return Reject if NPV < 0 projects or IRR < investor’s required rate of return Projects are mutually exclusive if the selection of one project precludes the selection of another project  project selection is determined by rank. NPV and IRR may give different ranks when The projects have different scales (sizes) The timing of the cash flows differs If projects have different ranks  use NPV. (Question: why don’t we need to consider IRR in this case?) 19 LOS 6.b: Problems with IRR

20. NPV vs. IRR Consider Project C with the following cash flows: The NPV is $31,460.28. The IRR is 24.42%. 20 t = 0 t = 1 t = 2 –$90,000 Hurdle rate = 10% r = 10% t = 3 $30,000 $40,000 $45,000 $40,000 t = 4 Project AProject BProject C NPV$32,872.52$29,783.12$31,460.28 IRR21.84%25.62%24.42% DecisionAccept LOS 6.b: Problems with IRR

21. NPV vs. IRR Consider Project C with the following cash flows: The NPV is $31,460.28. The IRR is 24.42%. If the projects are independent, you accept all three. If the projects are mutually exclusive, you accept Project A even though it has the smallest IRR. If Projects B and C are mutually exclusive, you accept Project C. 21 t = 0 t = 1 t = 2 –$90,000 Hurdle rate = 10% r = 10% t = 3 $30,000 $40,000 $45,000 $40,000 t = 4 Project AProject BProject C NPV$32,872.52$29,783.12$31,460.28 IRR21.84%25.62%24.42% DecisionAccept LOS 6.b: Problems with IRR

22. 22

23. LOS 6.b: Problems with IRR Reason: NPV assumes the CF reinvested at the opportunity cost of capital IRR assumes the CF reinvested at IRR In some cases for project with short duration, IRR could be high but low NPV while long project might have low IRR but adding large amount of value to the company over time. Initial investment costs also affect to IRR. NPV is reasonable to use opportunity cost, which is the required return of shareholders Always select highest NPV project when IRR and NPV rules give contradictory decisions 23

24. LOS 6.c: Holding period return (HPR) or Total return 24

25. Holding Period return Calculations You recently purchased shares of a dividend-paying utility, Old Dominion Co., for $23.50. Today, ODC has just paid a $1.34 dividend, and you have decided to sell your shares. Your market sell order is executed at $24.36. What is your holding period return? 25 P 0 = $23.50 P 1 = $24.36 D 1 = $1.34 HPR = ? LOS 6.c: Holding period return (HPR) or Total return

26. Holding Period return Calculations You recently purchased shares of a dividend-paying utility, Old Dominion Co., for $23.50. Today, ODC has just paid a $1.34 dividend, and you have decided to sell your shares. Your market sell order is executed at $24.36. What is your holding period return? 26 P 0 = $23.50 P 1 = $24.36 D 1 = $1.34 HPR = ? LOS 6.c: Holding period return (HPR) or Total return

27. Money-weighted Rate of return The internal rate of return calculated on a portfolio is called the “money- weighted rate of return.” It is the discount rate on which the NPV = 0 or the present value of inflows = present value of outflows. Money-weighted rate of return accounts for the timing and amount of dollar flows into and out of the portfolio. More weight is placed on periods in which more is invested. Consider the following cash flows for a portfolio over three years. 27 Time 0123 Share Price$300$325$315$320 ActivityBuy 2 sharesDiv = $2.50/shares Sell 1 share after Div = $2.50/shares Buy 1 share Sell 2 shares Inflows:--$5.00 + $325$2.50$640 Outflows–$600--–$315-- Net CF–$600$330–$312.50$640 LOS 6.d: Money and time weighted rates of return

28. Money-weighted Rate of Return Focus On: Calculations 28 t = 0 t = 1 t = 2 CF 0 = –$600 t = 3 CF 1 = $330 CF 3 = $640 CF 2 = –$312.50 LOS 6.d: Money and time weighted rates of return

29. Money-weighted Rate of Return Focus On: Calculations 29 t = 0 t = 1 t = 2 CF 0 = –$600 t = 3 CF 1 = $330 CF 3 = $640 CF 2 = –$312.50 LOS 6.d: Money and time weighted rates of return

30. It measures the compound growth, the rate at which $1 compounds over a specified performance horizon. Time-weighting is the process of averaging a set of values over time. The annual time-weighted return for an investment may by performing the following steps: Steps for calculations: Value the portfolio immediately preceding (come before) significant additions or withdrawals. Form sub-periods over the evaluation period that correspond to the dates of deposits and withdraws. Compute the holding period return (HPR) of the portfolio for each sub-period. Compute the product of (1+HPR) for each sub-period (multiply) to obtain a total return for the entire measurement period. [i.e., (1+HPR1)*(1+HPR2)…(1+HPRn)]. If the total investment period is greater than one year, you must take the geometric mean of the measurement period return to find the annual time-weighted rate of return. Time-weighted rate of return implies the annual compound rate, or it is geometric mean return that we have mentioned before, and will be discovered later in statistical concepts. 30 Time-weighted Rate of return

31. Time-Weighted Rate of return Calculations 31 Time 0123 Share Price$300$325$315$320 ActivityBuy 2 shrDiv = $2.50/shr Sell 1 shr at the end Div = $2.50/shr Buy 1 shr at the end Sell 2 shrs Change in Value0$650 + $5.00 – $600$315 + $2.50 – $325$640 – 630 Initial Value-600$600$325$630 HPR00.09167–0.023070.01587 TWR = ? LOS 6.d: Money and time weighted rates of return

32. Time-Weighted Rate of return Focus On: Calculations 32 Time 0123 Share Price$300$325$315$320 ActivityBuy 2 shrDiv = $2.50/shr Sell 1 shr after Div = $2.50/shr Buy 1 shr Sell 2 shrs Change in Value$650 + $5.00 – $600$315 + $2.50 – $325$640 – 630 Initial Value$600$325$630 HPR0.09167–0.023070.01587 TWR = 2.706% LOS 6.d: Money and time weighted rates of return

33. TWR vs. MWR Money-weighted returns place greater weight on those periods in which investment is higher and, therefore, give a “better” picture of the actual investor experience. Time-weighted returns remove the effect of inflows and outflows to the portfolio and are, therefore, a better indicator of managerial skill. In the example, the fund had significantly more money invested during the positive return years, from t = 0 to t = 1 and from t = 2 to t = 3, causing the money-weighted return to be much higher than the time-weighted return. 33 LOS 6.d: Money and time weighted rates of return

34. 34 LOS 6.d: Money and time weighted rates of return

35. 35 LOS 6.d: Money and time weighted rates of return

36. 36

37. LOS 6.d: Money and time weighted rates of return MWR of 13.86%, TWR of 15.84% Because MWR gives larger weight to Year 2 HPR of 10%, comparing to Year 1 HPR of 22%. TWR is preferred because it removes the distortion and provides a better measure 37 TWR vs. MWR

38. Differing Money Market Yields Instruments that mature in less than a year are known as money market instruments. Monetary market: to raise capital but in short-term, not more than 1 year. Capital market: to raise capital (stock and bonds) but often for long term There are a number of different conventions for calculating yields on money market instruments. Bank discount yield Holding period yield Effective annual yield Money market yield 38 LOS 6.e: BDY, HPY, EAY, MMY

39. 39

40. LOS 6.e: BDY, HPY, EAY, MMY 40

41. Holding period yield (HPY) Calculated the same way as a holding period return. 41 LOS 6.e: BDY, HPY, EAY, MMY

42. 42 LOS 6.e: BDY, HPY, EAY, MMY Holding period yield (HPY)

43. Effective annual yield (EAY) It is an annualized value, based on 365-day year, that accounts for compound interest. Calculated the same way as equivalent annual yield using the holding period yield. 43 LOS 6.e: BDY, HPY, EAY, MMY

44. Effective annual yield (EAY) 44 LOS 6.e: BDY, HPY, EAY, MMY

45. Money market yield This convention makes the quoted yield on a T-bill comparable to yield quotations on interest- bearing money market instruments that pay interest on a 360-day basis. 45 LOS 6.e: BDY, HPY, EAY, MMY

46. Money market yield 46 LOS 6.e: BDY, HPY, EAY, MMY

47. LOS 6.f: Conversion of HPY, EAY, MMY HPY : actual return of the investment EAY : annualized HPY on 365-day basis incorporating the effect of compounding MMY : annualized yield based on 360-day but do not account for compounding effect 47

48. LOS 6.f: Conversion of HPY, EAY, MMY 48

49. Bond-equivalent yield (BEY) By convention, the yield on most bonds is expressed as a bond-equivalent yield instead of as an equivalent annual yield. This refers to 2 x the semiannual discount rate. U.S. bonds are quoted as twice the semiannual rate because the coupon interest is paid in two semiannual payments Problem: This process ignores intra-period compounding. 49 LOS 6.f: Conversion of HPY, EAY, MMY

50. 50

51. Summary The process of evaluating projects incorporates two primary decision criteria known as net present value (NPV) and internal rate of return (IRR). When projects are independent, NPV and IRR can be used interchangeably. When projects are mutually exclusive, analysts should use the NPV criteria. Portfolio performance measurement can be determined in several ways, including money-weighted rate of return and time-weighted rate of return. When the investor controls additions and withdrawals from the portfolio, the money-weighted rate of return may be the appropriate measure. The time-weighted rate of return is the standard in the investment management industry because it better represents managerial skill. By tradition, money market instrument yields are calculated using different techniques for different instruments. 51

52. Example A successful investor has decided to set up a scholarship fund for deserving students at her alma mater. Her plan is for the fund to be capable of awarding 25,000$ annually in perpetuity. The 1st scholarship is to be awarded and paid out exactly four years from today. The funds will be deposited into an account immediately and will grow at a rate of 4%, compounded semiannually, for the foreseeable future. How much money must the investor donate today to fund the scholarship? 52