Discounted Cash Flow Application

Discounted Cash Flow Application
Schweser Notes - Reading #6

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

Net present value (NPV)
LOS 6.a: NPV and IRR 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. CF2 CF1 LOS: Calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment. Pages 40–41 The discount rate is most often going to be the firm’s weighted average cost of capital, but it doesn’t have to be. That will only be the case when the project has a level of risk similar to that of the existing company. The discount rate should be a rate that is commensurate to the level of risk the project creates for the firm. CF4 t = 0 t = 3 t = 0 t = 3 t = 1 t = 2 t = 4 t = 1 t = 2 t = 4 r = req’d return –CF3 Initial Outlay0 NPV0 = ?

LOS 6.a: NPV and IRR Net present value (NPV) Steps in calculating NPV Identify all the cash flows associated with the project, both cash inflows and outflows during the project period. Determine the appropriate discount rate: normally it will be the cost of capital or opportunity costs. Using that discount rate, calculate the present value of all of the inflows (positive sign) and outflows (negative sign). Sum the present values together  the result is the project’s NPV. Apply the NPV decision rule. If you have mutually exclusive projects  accept the one with the highest NPV. Where N is the estimated life cycle of the project, CFt: the expected net cash flows. NPV= 𝑡=0 𝑁 CF𝑡 1+𝑟 𝑡 LOS: Calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment. Pages 40–41 The period of time associated with the discount rate and the frequency of cash flows must be the same. Normally, this will be annual rates and cash flows. The discount rate is most often going to be the firm’s weighted average cost of capital, but it doesn’t have to be. That will only be the case when the project has a level of risk similar to that of the existing company. The discount rate should be a rate that is commensurate to the level of risk the project creates for the firm.

LOS 6.a: NPV and IRR Net present value (NPV) $75,000 $45,000 $40,000 $20,000 Consider Project A with the following cash flows: The NPV for this project is…? Decision? Consider Project B with the following cash flows: t = 0 t = 1 t = 2 t = 3 t = 4 r = 10% –$100,000 $55,000 $45,000 $35,000 LOS: Calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment [Page No: 40] The period of time associated with the discount rate and the frequency of cash flows must be the same. Normally, this will be annual rates and cash flows. The discount rate is most often going to be the firm’s weighted average cost of capital, but it doesn’t have to be. That will only be the case when the project has a level of risk similar to that of the existing company. The discount rate should be a rate that is commensurate to the level of risk the project creates for the firm. $25,000 t = 0 t = 1 t = 2 t = 3 t = 4 r = 10% –$100,000

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

LOS 6.a: NPV and IRR Net present value (NPV) $75,000 $45,000 $40,000 $20,000 Consider Project A with the following cash flows: The NPV for this project is $36, Decision  Accept the project. Consider Project B with the following cash flows: The NPV for this project is $30, t = 0 t = 1 t = 2 t = 3 t = 4 r = 10% –$100,000 $55,000 $45,000 $35,000 LOS: Calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment [Page No: 40] The period of time associated with the discount rate and the frequency of cash flows must be the same. Normally, this will be annual rates and cash flows. The discount rate is most often going to be the firm’s weighted average cost of capital, but it doesn’t have to be. That will only be the case when the project has a level of risk similar to that of the existing company. The discount rate should be a rate that is commensurate to the level of risk the project creates for the firm. $25,000 t = 0 t = 1 t = 2 t = 3 t = 4 r = 10% –$100,000

LOS 6.a: NPV and IRR

LOS 6.a: NPV and IRR 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 = ?

LOS 6.a: NPV and IRR 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

LOS 6.a: NPV and IRR 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 = ?

LOS 6.a: NPV and IRR 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%? Calculation: NPV= Pv (Cash inflows) + Pv(Cash Outflows) 𝑃𝑉 𝑝𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦 = 𝑃𝑀𝑇 𝐼|𝑌 𝑃𝑉 𝑝𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦 = = NPV = – 15 NPV = $2.142

Internal rate of return (IRR)
LOS 6.a: NPV and IRR Internal rate of return (IRR) The internal rate of return is the discount rate that sets the sum of the present value of the positive cash flows equal to the sum of the present value of the negative cash flows. The discount rate at which NPV = 0 Interpretation: IRR is the expected compound return when all intervening cash flows in the project can be reinvested at exactly the IRR and the investment will be held until maturity. Calculation: In practice, use a spreadsheet, financial software, or financial calculator to determine IRR. Decision: Accept projects for which IRR > hurdle rate  increases shareholder wealth. These criteria guarantee that the firm will earn at least its required return. Such an outcome should increase the market value of the firm and, therefore, the wealth of its owners. 𝑁𝑃𝑉= 𝑡=0 𝑁 𝐶𝐹 𝑡 (1+𝑟) 𝑡 =0= 𝐶𝐹 0 + 𝐶𝐹 1 (1+𝐼𝑅𝑅) 𝐶𝐹 2 (1+𝐼𝑅𝑅) 2 +…+ 𝐶𝐹 𝑁 (1+𝐼𝑅𝑅) 𝑁 If discount rate > IRR ---> NPV < 0 If discount rate < IRR ---> NPV > 0 Therefore, the higher of IRR the better potential growth rate or required rate of return could be. LOS: Calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment. Pages 42–45 This concept is the same as yield to maturity with the same reinvestment rate limitation, but an additional limitation with IRR is the possibility of multiple IRRs occurring because projects can have late-life negative cash flows. This concept is also the same as the money-weighted return to a portfolio. The big problem with IRR as a criteria lies in interpretation: The better (higher) it looks, the less likely the investor will actually receive that rate. Consider an IRR of 80%. To actually receive 80%, all the intervening cash flows have to be reinvested at 80%, which is unlikely in most firms. The hurdle rate is most often going to be the firm’s weighted average cost of capital, but it doesn’t have to be. That will only be the case when the project has a level of risk similar to that of the existing company. It should be the opportunity cost of capital for projects with a similar level of risk. The hurdle rate should be a rate that is commensurate to the level of risk the project creates for the firm.

LOS 6.a: NPV and IRR 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 = ?

LOS 6.a: NPV and IRR 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%

LOS 6.a: NPV and IRR

LOS 6.a: NPV and IRR 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. LOS: Calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment. Pages 42–45 This concept is the same as yield to maturity with the same reinvestment rate limitation, but an additional limitation with IRR is the possibility of multiple IRRs occurring because projects can have late-life negative cash flows. This concept is also the same as the money-weighted return to a portfolio. The big problem with IRR as a criteria lies in interpretation: The better (higher) it looks, the less likely the investor will actually receive that rate. Consider an IRR of 80%. To actually receive 80%, all the intervening cash flows have to be reinvested at 80%, which is unlikely in most firms. The hurdle rate is most often going to be the firm’s weighted average cost of capital, but it doesn’t have to be. That will only be the case when the project has a level of risk similar to that of the existing company. It should be the opportunity cost of capital for projects with a similar level of risk. The hurdle rate should be a rate that is commensurate to the level of risk the project creates for the firm.

LOS 6.a: NPV and IRR 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. LOS: Calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment. Pages 42–45 This concept is the same as yield to maturity with the same reinvestment rate limitation, but an additional limitation with IRR is the possibility of multiple IRRs occurring because projects can have late-life negative cash flows. This concept is also the same as the money-weighted return to a portfolio. The big problem with IRR as a criteria lies in interpretation: The better (higher) it looks, the less likely the investor will actually receive that rate. Consider an IRR of 80%. To actually receive 80%, all the intervening cash flows have to be reinvested at 80%, which is unlikely in most firms. The hurdle rate is most often going to be the firm’s weighted average cost of capital, but it doesn’t have to be. That will only be the case when the project has a level of risk similar to that of the existing company. It should be the opportunity cost of capital for projects with a similar level of risk. The hurdle rate should be a rate that is commensurate to the level of risk the project creates for the firm.

LOS 6.b: Problems with IRR
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?) LOS: Contrast the NPV rule to the IRR rule. Pages 45–47 The decisions are the same because the hurdle rate with which the IRR is compared is also the discount rate used to calculate NPV. By definition, if the hurdle rate is the rate that the IRR has to beat, an IRR > hurdle rate must lead to a positive NPV because the IRR is the rate at which NPV = 0.

NPV vs. IRR Consider Project C with the following cash flows:
LOS 6.b: Problems with IRR NPV vs. IRR $45,000 $40,000 $40,000 $30,000 t = 0 Consider Project C with the following cash flows: The NPV is $31, The IRR is 24.42%. t = 1 t = 2 t = 3 t = 4 Hurdle rate = 10% r = 10% –$90,000 Project A Project B Project C NPV $32,872.52 $29,783.12 $31,460.28 IRR 21.84% 25.62% 24.42% Decision Accept LOS: Contrast the NPV rule to the IRR rule. Pages 45–47 The decisions are the same because the hurdle rate with which the IRR is compared is also the discount rate used to calculate NPV. By definition, if the hurdle rate is the rate that the IRR has to beat, an IRR > hurdle rate must lead to a positive NPV because the IRR is the rate at which NPV = 0.

NPV vs. IRR Consider Project C with the following cash flows:
LOS 6.b: Problems with IRR NPV vs. IRR $45,000 $40,000 $40,000 $30,000 t = 0 Consider Project C with the following cash flows: The NPV is $31, 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. t = 1 t = 2 t = 3 t = 4 Hurdle rate = 10% r = 10% –$90,000 Project A Project B Project C NPV $32,872.52 $29,783.12 $31,460.28 IRR 21.84% 25.62% 24.42% Decision Accept LOS: Contrast the NPV rule to the IRR rule. Pages 45–47 The decisions are the same because the hurdle rate with which the IRR is compared is also the discount rate used to calculate NPV. By definition, if the hurdle rate is the rate that the IRR has to beat, an IRR > hurdle rate must lead to a positive NPV because the IRR is the rate at which NPV = 0.

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

LOS 6.c: Holding period return (HPR) or Total return
The percentage change in the value of an investment over the period it is held. Holding period returns are one fundamental building block of performance measurement. If the asset has CF, such as dividend or interest payments, we refer to the return, including the value of these interim CF, as total return Ex. Treasury bill purchased for 980 and sold 3 months later for 992. 𝐻𝑃𝑅= 𝑒𝑛𝑑𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 𝑏𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 −1= −1= 𝑜𝑟 1.22% We could say the 3-month HPR is 1.22% Ex. A stock purchased for 30 and sold for 33 six months later, during which time it paid 0.5 as dividends. 𝐻𝑃𝑅= 𝑒𝑛𝑑𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒+𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑏𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 −1= −1= 𝑜𝑟 11.67% We could say the 6-month HPR is 11.67%

Holding Period return Calculations
LOS 6.c: Holding period return (HPR) or Total return Holding Period return Calculations You recently purchased shares of a dividend-paying utility, Old Dominion Co., for $ Today, ODC has just paid a $1.34 dividend, and you have decided to sell your shares. Your market sell order is executed at $ What is your holding period return? P1 = $24.36 D1 = $1.34 HPR = ? Page 47 P0 = $23.50

Holding Period return Calculations
LOS 6.c: Holding period return (HPR) or Total return Holding Period return Calculations You recently purchased shares of a dividend-paying utility, Old Dominion Co., for $ Today, ODC has just paid a $1.34 dividend, and you have decided to sell your shares. Your market sell order is executed at $ What is your holding period return? P1 = $24.36 D1 = $1.34 HPR = ? Page 47 P0 = $23.50 𝐻𝑃𝑅= 𝑒𝑛𝑑𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒+𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑏𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 −1 HPR= $24.36+$1.34 $23.50 −1 =0.0936=9.36%

Money-weighted Rate of return
LOS 6.d: Money and time weighted rates of return 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. Time 1 2 3 Share Price $300 $325 $315 $320 Activity Buy 2 shares Div = $2.50/shares Sell 1 share after Buy 1 share Sell 2 shares Inflows: -- $ $325 $2.50 $640 Outflows –$600 –$315 Net CF $330 –$312.50 LOS: Distinguish between money-weighted and time-weighted rates of return. Pages 47–49

Money-weighted Rate of Return
LOS 6.d: Money and time weighted rates of return Money-weighted Rate of Return Focus On: Calculations Recall: Money-weighted return (MWR below) is inherently an IRR. 0=−$600+ $ MWR 1 + −$ MWR 2 + $ MWR 3 MWR = ? CF3 = $640 CF1 = $330 t = 2 t = 0 t = 1 t = 3 CF2 = –$312.50 CF0 = –$600 LOS: Calculate the money-weighted and time-weighted rates of return of a portfolio. Pages 47–49 The answer is %.

Money-weighted Rate of Return
LOS 6.d: Money and time weighted rates of return Money-weighted Rate of Return Focus On: Calculations Recall: Money-weighted return (MWR below) is inherently an IRR. 0=−$600+ $ MWR 1 + −$ MWR 2 + $ MWR 3 MWR = % CF3 = $640 CF1 = $330 t = 2 t = 0 t = 1 t = 3 CF2 = –$312.50 CF0 = –$600 LOS: Calculate the money-weighted and time-weighted rates of return of a portfolio. Pages 47–49 The answer is %.

LOS 6.d: Money and time weighted rates of return
Time-weighted Rate of return 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.

Time-Weighted Rate of return
LOS 6.d: Money and time weighted rates of return Time-Weighted Rate of return Calculations Time 1 2 3 Share Price $300 $325 $315 $320 Activity Buy 2 shr Div = $2.50/shr Sell 1 shr at the end Buy 1 shr at the end Sell 2 shrs Change in Value $650 + $5.00 – $600 $315 + $2.50 – $325 $640 – 630 Initial Value -600 $600 $630 HPR – LOS: Calculate the money-weighted and time-weighted rates of return of a portfolio. Pages 49–54 The answer is , or 2.706%. TWR = ?

Time-Weighted Rate of return
LOS 6.d: Money and time weighted rates of return Time-Weighted Rate of return Focus On: Calculations Time 1 2 3 Share Price $300 $325 $315 $320 Activity Buy 2 shr Div = $2.50/shr Sell 1 shr after Buy 1 shr Sell 2 shrs Change in Value $650 + $5.00 – $600 $315 + $2.50 – $325 $640 – 630 Initial Value $600 $630 HPR – LOS: Calculate the money-weighted and time-weighted rates of return of a portfolio. Pages 49–54 The answer is , or 2.706%. TWR = [( ) ( ) ( )] ^(1/3) -1 TWR = 2.706%

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. LOS: Distinguish between money-weighted and time-weighted rates of return. Pages 52–54

TWR vs. MWR 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

Differing Money Market Yields
LOS 6.e: BDY, HPY, EAY, MMY 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 LOS: Calculate the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury bill. Pages 54–59

LOS 6.e: BDY, HPY, EAY, MMY By convention, Treasury instruments of less than a year in original maturity (T-bills) have yield quoted on a bank discount basis. Bank discount yield (BDY): is the percentage of face value instead of price and assumes 360 days in a year. 𝑟 𝐵𝐷 = 𝐷 𝐹 × 360 𝑡 𝑟 𝐵𝐷 : the annualized yield on a bank discount basis D : the dollar discount, the difference between the face value of the bill and the purchase price F : the face value (par value) of the bill t : number of days remaining until maturity 360 : bank convention of number of days in a year Example: For a $10,000 par value T-bill trading at $9, with 67 days to maturity, the bank discount yield is 𝑟𝐵𝐷= $10,000−$9, $10, =0.0292=2.92% Noted: BDY does not show the effective (real) returns that investor can receive from the bills. BDY assumes simple interest (no compounding effect) BDY is based on the face value of a bond, not the effective purchase price BDY is based on 360 days rather than 365 days

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

Holding period yield (HPY)
LOS 6.e: BDY, HPY, EAY, MMY Holding period yield (HPY) Calculated the same way as a holding period return. HPY measures the (un-annualized) return over the remaining life of the investment when P1 is the return of face value. : initial price : price at maturity : interest payment For a $10,000 par value T-bill trading at $9, with 67 days to maturity, the HPY is LOS: Calculate the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury bill. Pages 54–59 P0 = the initial purchase price of the instrument P1 = the price received for the instrument at its maturity D1 = the cash distribution paid by the instrument at its maturity (i.e., interest)

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

Effective annual yield (EAY)
LOS 6.e: BDY, HPY, EAY, MMY 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. The annualized expression of the holding period yield is EAY= (1+HPY) 365/𝑡 −1 The power of 365/t means: Power of 1/t to compute the daily return Power of 365 to annualize the daily return to a whole year For a $10,000 par value T-bill trading at $9, with 67 days to maturity, the EAY is EAY= ( ) 365/67 −1= =3.011% LOS: Calculate the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury bill. Pages 54–59

Effective annual yield (EAY)
LOS 6.e: BDY, HPY, EAY, MMY Effective annual yield (EAY) LOS: Calculate the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury bill. Pages 54–59

Money market yield Also known as the CD equivalent yield.
LOS 6.e: BDY, HPY, EAY, MMY 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. Also known as the CD equivalent yield. Generally, the money market yield will be equivalent to the holding period yield adjusted to a 360-day basis. For a $10,000 par value T-bill trading at $9, with 67 days to maturity, the money market yield is LOS: Calculate the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury bill. Pages 54–59

Money market yield LOS 6.e: BDY, HPY, EAY, MMY
LOS: Calculate the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury bill. Pages 54–59

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

𝑟 𝑀𝑀 =𝐻𝑃𝑌×( 360 𝑡 ) EAY= (1+HPY) 365/𝑡 −1

Bond-equivalent yield (BEY)
LOS 6.f: Conversion of HPY, EAY, MMY 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. LOS: Calculate bond-equivalent yield. Page 59

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.

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?

Discounted Cash Flow Application

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Discounted Cash Flow Application

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Presentation on theme: "Discounted Cash Flow Application"— Presentation transcript:

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About project

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