University:
CFA Institute
Course:
CFA Level 1 - Quantitative Methods
Academic year:

2023
Views:

14

Pages:

29
Author:

anon

CFA Level 1 - Quantitative Methods Session 2 - Reading 6 (Notes, Practice Questions, Sample Questions) 1. The capital budgeting director of Green Manufacturing is evaluating a laser imaging project with the following characteristics: Cost: $150,000 Expected life: 3 years After-tax cash flows: $60,317 per year Salvage value: $0 If Green Manufacturing’s cost of capital is 11.5%, what is the project’s internal rate of return (IRR)? A)13.6%. B)$3,875. C)10.0%. C — Since we are seeking the IRR, the answer has to be in terms of a rate of return, this eliminates the option not written in a percentage. Since they payments (cash flows) are equals, we can calculate the IRR as: N = 3; PV = 150,000; PMT = 60,317; CPT → I/Y = 9.999 2. In order to calculate the net present value (NPV) of a project, an analyst would least likely need to know the: A)timing of the expected cash flows from the project. B)internal rate of return (IRR) of the project. C)opportunity cost of capital for the project. B — The NPV is calculated using the opportunity cost, discount rate, expected cash flows, and timing of the expected cash flows from the project. The project’s IRR is not used to calculate the NPV 3. An investment with a cost of $5,000 is expected to have cash inflows of $3,000 in year 1, and $4,000 in year 2. The internal rate of return (IRR) for this investment is closest to: A)15%. B)25%. C)30%. B — The IRR is the discount rate that makes the net present value of the investment equal to 0. This means -$5,000 + $3,000 / (1 + IRR) + $4,000 / (1 + IRR)2 = 0 One way to compute this problem is to use trial and error with the existing answer choices and choose the discount rate that makes the PV of the cash flows closest to 5,000. $3,000 / (1.25) + $4,000 / (1.25)2 = 4,960. Alternatively: CFO = -5,000; CF1 = 3,000; CF2 = 4,000; CPT → IRR = 24.3% 4. The estimated annual after-tax cash flows of a proposed investment are shown below: Year 1: $10,000 Year 2: $15,000 Year 3: $18,000 After-tax cash flow from sale of investment at the end of year 3 is $120,000 The initial cost of the investment is $100,000, and the required rate of return is 12%. The net present value (NPV) of the project is closest to: A)$19,113. B)$63,000. C)-$66,301 A — 10,000 / 1.12 = 8,929 15,000 / (1.12)2 = 11,958 138,000 / (1.12)3 = 98,226 NPV = 8,929 + 11,958 + 98,226 − 100,000 = $19,113 Alternatively: CFO = -100,000; CF1 = 10,000; CF2 = 15,000; CF3 = 138,000; I = 12; CPT → NPV = $19,112 5. Fisher, Inc., is evaluating the benefits of investing in a new industrial printer. The printer will cost $28,000 and increase after-tax cash flows by $8,000 during each of the next five years. What are the respective internal rate of return (IRR) and net present value (NPV) of the printer project if Fisher’s required rate of return is 11%? A)13.20%; $1,567. B)17.97%; $5,844. C)5.56%; −$3,180. A — IRR Keystrokes: CF0 = -$28,000; CF1 = $8,000; F1 = 5; CPT → IRR = 13.2%. NPV Keystrokes: CF0 = -$28,000; CF1 = $8,000; F1 = 5; I = 11; CPT → NPV = 1,567. Since cash flows are level, an alternative is: IRR: N = 5; PMT = 8,000; PV = -28,000; CPT → I/Y = 13.2%. NPV: I/Y = 11; CPT → PV = -29,567 + 28,000 = 1,567 6. The financial manager at Genesis Company is looking into the purchase of an apartment complex for $550,000. Net after-tax cash flows are expected to be $65,000 for each of the next five years, then drop to $50,000 for four years. Genesis’ required rate of return is 9% on projects of this nature. After nine years, Genesis Company expects to sell the property for after-tax proceeds of $300,000. What is the respective internal rate of return (IRR) and net present value (NPV) on this project? A)7.01%; −$53,765. B)13.99%; $166,177. C)6.66%; −$64,170 A — IRR Keystrokes: CF0 = -$550,000; CF1 = $65,000; F1 = 5; CF2 = $50,000; F2 = 3; CF3 = $350,000; F3 = 1. NPV Keystrokes: CF0 = -$550,000; CF1 = $65,000; F1 = 5; CF2 = $50,000; F2 = 3; CF3 = $350,000; F3 = 1. Compute NPV, I = 9. Note: Although the rate of return is positive, the IRR is less than the required rate of 9%. Hence, the NPV is negative 7. The internal rate of return (IRR) method and net present value (NPV) method of project selection will always provide the same accept or reject decision when: A)the projects are independent. B)the projects are mutually exclusive. C)up-front project costs are under $1.0 million. A — If a project’s IRR exceeds the cost of capital, the project’s NPV will be positive. The only way in which accepting a positive NPV project would reduce firm value is if its selection precludes selection of a project that would have enhanced firm value to a greater extent (i.e., had a higher NPV). IRR and NPV method accuracy do not depend upon project duration or costs 8. Sarah Kelley, CFA, is analyzing two mutually exclusive investment projects. Kelley has calculated the net present value (NPV) and internal rate of return (IRR) for each project: Project 1: NPV = $230; IRR = 15% Project 2: NPV = $4,000; IRR = 6% Kelley should make which of the following recommendations concerning the two projects? A)Accept Project 1 only. B)Accept both projects. C)Accept Project 2 only C — Because the investment projects are mutually exclusive, only one project can be chosen. The NPV and IRR criteria are giving conflicting project rankings. When decision criteria conflict, always use the NPV criteria because NPV evaluates projects using an appropriate discount rate, the weighted average cost of capital. The IRR may not be a market rate, therefore future cash flows associated with the project may not be capable of earning a rate of return equal to the IRR 9. Which of the following is least likely a problem associated with the internal rate of return (IRR) method for making investment decisions? A)An investment project may have more than one internal rate of return. B)The IRR method determines the discount rate that sets the net present value of a project equal to zero. C)IRR and NPV criteria can give conflicting decisions for mutually exclusive projects. B — The IRR method equates an investment’s present value of inflows to its present value of outflows. The IRR by definition is the discount rate that sets the net present value of a project equal to zero. Therefore, the decision rule for independent projects is as follows: if the IRR is above the firm’s cost of capital, the project should be accepted, and if the IRR is below the cost of capital, the project should be rejected 10. Which of the following is NOT a problem with the internal rate of return (IRR)? A)Sometimes the IRR exceeds the cost of capital. B)Non-normal cash flow patterns may result in multiple IRRs. C)A higher IRR does not necessarily indicate a more-profitable project A — If the IRR exceeds the cost of capital, that merely indicates that the project is acceptable—this is not a problem associated with IRR. Non-normal cash flow patterns such as cash outflows during the project's life can result in multiple IRRs, leaving open the question as to which one is valid. A higher IRR will only be realized if the project’s cash flows can be reinvested at the IRR, and the true profitability of a project also depends on project size, not just IRR 11. Jack Smith, CFA, is analyzing independent investment projects X and Y. Smith has calculated the net present value (NPV) and internal rate of return (IRR) for each project: Project X: NPV = $250; IRR = 15% Project Y: NPV = $5,000; IRR = 8% Smith should make which of the following recommendations concerning the two projects? A)Accept Project X only. B)Accept Project Y only. C)Accept both projects C — The projects are independent, meaning that either one or both projects may be chosen. Both projects have positive NPVs, therefore both projects add to shareholder wealth and both projects should be accepted 12. Which of the following statements regarding making investment decisions using net present value (NPV) and internal rate of return (IRR) is least accurate? A)If two projects are mutually exclusive, one should always choose the project with the highest IRR. B)Projects with a positive NPVs increase shareholder wealth. C)If a firm undertakes a zero-NPV project, the firm will get larger, but shareholder wealth will not change A — If two projects are mutually exclusive, the firm should always choose the project with the highest NPV rather than the highest IRR. If two projects are mutually exclusive, the firm may only choose one. It is possible for NPV and IRR to give conflicting decisions for projects of different sizes. Because NPV is a direct measure of the change in shareholder wealth, NPV criteria should be used when NPV and IRR decisions conflict. When a project has a positive NPV, it will add to shareholder wealth because the project is earning more than the opportunity cost of capital needed to undertake the project. If a firm takes on a zero-NPV project, the firm will earn exactly enough to cover the opportunity cost of capital. The firm will increase in size by taking the project, but shareholder wealth will not change 13. Williams Warehousing currently has a warehouse lease that calls for five annual payments of $120,000. The warehouse owner, who needs cash, is offering Williams a deal wherein Williams will pay $200,000 this year and then pay only $80,000 each of the remaining 4 years. (Assume that all lease payments are made at the beginning of the year.) Should Williams Warehousing accept the offer if its required rate of return is 9%, and why? A)Yes, there is a savings of $45,494 in present value terms. B)Yes, there is a savings of $49,589 in present value terms. C)No, there is an additional $80,000 payment in this year. B — The present value of the current lease is $508,766.38, while the present value of the lease being offered is $459,177.59; a savings of 49,589. Alternatively, the present value of the extra $40,000 at the beginning of each of the next 4 years is $129,589 which is $49,589 more than the extra $80,000 added to the payment today 14. Financial managers should always select the project that provides the highest net present value (NPV) whenever NPV and IRR methods conflict, because maximizing: A)the shareholders' rate of return is the goal of financial management. B)shareholder wealth is the goal of financial management. C)revenues is the goal of financial management B — Focusing on the maximization of earnings does not consider the differences in risk across projects, while focusing on revenues precludes concern for the expenses incurred. Earning a higher return on a small project provides less of a benefit than earning a slightly lower rate of return on a much larger project 15. The financial manager at Johnson & Smith estimates that its required rate of return is 11%. Which of the following independent projects should Johnson & Smith accept? A)Project A requires an up-front expenditure of $1,000,000 and generates an NPV of -$4,600. B)Project C requires an up-front expenditure of $600,000 and generates a positive internal rate of return of 12.0%. C)Project B requires an up-front expenditure of $800,000 and generates a positive IRR of 10.5%. B — When projects are independent, you can use either the NPV method or IRR method to make the accept or reject decision. Only Project C has an IRR in excess of 11%. Acceptance of Project A reduces the firm’s value by $4,600 16. An investor expects a stock currently selling for $20 per share to increase to $25 by year-end. The dividend last year was $1 but he expects this year's dividend to be $1.25. What is the expected holding period return on this stock? A)24.00%. B)28.50%. C)31.25%. C — Return = [dividend + (end − begin)] / beginning price R = [1.25 + (25 − 20)] / 20 = 6.25 / 20 = 0.3125 17. An investor is considering investing in Tawari Company for one year. He expects to receive $2 in dividends over the year and feels he can sell the stock for $30 at the end of the year. To realize a return on the investment over the year of 14%, the price the investor would pay for the stock today is closest to: A)$28. B)$29. C)$32. A — HPR = [Dividend + (Ending price − Beginning price)] / Beginning price 0.14 = [2 + (30 − P)] / P 1.14P = 32 so P = $28.07 18. Banca Hakala purchases two front row concert tickets over the Internet for $90 per seat. One month later, the rock group announces that it is dissolving due to personality conflicts and the concert that Hakala has tickets for will be the “farewell” concert. Hakala sees a chance to raise some quick cash, so she puts the tickets up for sale on the same internet site. The auction closes at $250 per ticket. After paying a 10% commission to the site on the amount of the sale and paying $10 in shipping costs, Hakala’s one-month holding period return is approximately: A)44%. B)144%. C)139%. B — The holding period return is calculated as: (ending price – beginning price +/- any cash flows) / beginning price. Here, the beginning and ending prices are given. The other cash flows consist of the commission of 0.10 × $250 × 2 tickets = $50 and the shipping cost of $10 (total for both tickets). Thus, her one-month holding period return is: [(2 × $250) – (2 × $90) – $50 − $10] / (2 × $90) = 1.44, or approximately 144% 19. An investor buys a 10 3/8 treasury note for 103 11/32 and sells it one year later for 101 13/32. What is the holding period yield? A)8.14%. B)8.16%. C)8.22%. B — 103 11/32 = 103.344% or $1,033.44 101 13/32 = 101.406% or $1,014.06 A coupon of 10 3/8 = 10.375% or $103.75 The rate of return equals the [(ending cash flows − the beginning cash flows) / beginning price] × 100 = [(1014.06 + 103.75 − 1033.44) / 1033.44] × 100 = 8.16% 20. A bond that pays $100 in interest each year was purchased at the beginning of the year for $1,050 and sold at the end of the year for $1,100. An investor's holding period return is: A)10.5%. B)14.3%. C)10.0%. B — Input into your calculator: N = 1; FV = 1,100; PMT = 100; PV = -1,050; CPT → I/Y = 14.29 21. When Annette Famigletti hears that a baseball-loving friend is coming to visit, she purchases two premium-seating tickets for $45 per ticket for an evening game. As the date of the game approaches, Famigletti’s friend telephones and says that his trip has been cancelled. Fortunately for Famigletti, the tickets she holds are in high demand as there is chance that the leading Major League Baseball hitter will break the home run record during the game. Seeing an opportunity to earn a high return, Famigletti puts the tickets up for sale on an internet site. The auction closes at $150 per ticket. After paying a 10% commission to the site (on the amount of the sale) and paying $8 total in shipping costs, Familgletti’s holding period return is approximately: A)182%. B)202%. C)191%. C — The holding period return is calculated as: (ending price − beginning price +/- any cash flows) / beginning price. Here, the beginning and ending prices are given. The other cash flows consist of the commission of $30 (0.10 × 150 × 2 tickets) and the shipping cost of $8 (total for both tickets). Thus, her holding period return is: (2 × 150 − 2 × 45 − 30 − 8) / (2 × 45) = 1.91, or approximately 191% 22. An investor sold a 30-year bond at a price of $850 after he purchased it at $800 a year ago. He received $50 of interest at the time of the sale. The annualized holding period return is: A)6.25%. B)12.5%. C)15.0%. B — The holding period return (HPR) is calculated as follows: HPR = (Pt − Pt-1 + Dt) / Pt where: Pt = price per share at the end of time period t Dt = cash distributions received during time period t. Here, HPR = (850 − 800 + 50) / 800 = 0.1250, or 12.50% 23. A stock is currently worth $75. If the stock was purchased one year ago for $60, and the stock paid a $1.50 dividend over the course of the year, what is the holding period return? A)27.5%. B)22.0%. C)24.0% A — (75 − 60 + 1.50) / 60 = 27.5% 24. If an investor bought a stock for $32 and sold it one year later for $37.50 after receiving $2 in dividends, what was the holding period return on this investment? A)17.19%. B)23.44%. C)6.25%. B — HPR = [D + End Price − Beg Price] / Beg Price HPR = [2 + 37.50 − 32] / 32 = 0.2344 25. A bond was purchased exactly one year ago for $910 and was sold today for $1,020. During the year, the bond made two semi-annual coupon payments of $30. What is the holding period return? A)12.1%. B)18.7%. C)6.0%. B — HPY = (1,020 + 30 + 30 – 910) / 910 = 0.1868 or 18.7% 26. An investor buys one share of stock for $100. At the end of year one she buys three more shares at $89 per share. At the end of year two she sells all four shares for $98 each. The stock paid a dividend of $1.00 per share at the end of year one and year two. What is the investor’s time-weighted rate of return? A)0.06%. B)6.35%. C)11.24%. A — The holding period return in year one is ($89.00 − $100.00 + $1.00) / $100.00 = -10.00%. The holding period return in year two is ($98.00 − $89.00 + $1.00) / $89 = 11.24%. The time-weighted return is [{1 + (-0.1000)}{1 + 0.1124}]1/2 – 1 = 0.06% 27. An investor buys one share of stock for $100. At the end of year one she buys three more shares at $89 per share. At the end of year two she sells all four shares for $98 each. The stock paid a dividend of $1.00 per share at the end of year one and year two. What is the investor’s money-weighted rate of return? A)6.35%. B)5.29%. C)0.06%. A — T = 0: Purchase of first share = -$100.00 T = 1: Dividend from first share = +$1.00 Purchase of 3 more shares = -$267.00 T = 2: Dividend from four shares = +4.00 Proceeds from selling shares = +$392.00 The money-weighted return is the rate that solves the equation: $100.00 = -$266.00 / (1 + r) + 396.00 / (1 + r)2. CFO = -100; CF1 = -266; CF2 = 396; CPT → IRR = 6.35% 28. An investor buys four shares of stock for $50 per share. At the end of year one she sells two shares for $50 per share. At the end of year two she sells the two remaining shares for $80 each. The stock paid no dividend at the end of year one and a dividend of $5.00 per share at the end of year two. What is the difference between the time-weighted rate of return and the money-weighted rate of return? A)9.86%. B)20.52%. C)14.48%. A — T = 0: Purchase of four shares = -$200.00 T = 1: Dividend from four shares = +$0.00 Sale of two shares = +$100.00 T = 2: Dividend from two shares = +$10.00 Proceeds from selling shares = +$160.00 The money-weighted return is the rate that solves the equation: $200.00 = $100.00 / (1 + r) + $170.00 / (1 + r)2. Cfo = -200, CF1 = 100, Cf2 = 170, CPT → IRR = 20.52%. The holding period return in year one is ($50.00 − $50.00 + $0.00) / $50.00 = 0.00%. The holding period return in year two is ($80.00 − $50.00 + $5.00) / $50 = 70.00%. The time-weighted return is [(1 + 0.00)(1 + 0.70)]1/2 − 1 = 30.38%. The difference between the two is 30.38% − 20.52% = 9.86% 29. An investor makes the following investments: She purchases a share of stock for $50.00. After one year, she purchases an additional share for $75.00. After one more year, she sells both shares for $100.00 each. There are no transaction costs or taxes. During year one, the stock paid a $5.00 per share dividend. In year 2, the stock paid a $7.50 per share dividend. The investor’s required return is 35%. Her money-weighted return is closest to: A)-7.5%. B)16.1%. C)48.9% C — To determine the money weighted rate of return, use your calculator's cash flow and IRR functions. The cash flows are as follows: CF0: initial cash outflow for purchase = $50 CF1: dividend inflow of $5 - cash outflow for additional purchase of $75 = net cash outflow of -$70 CF2: dividend inflow (2 × $7.50 = $15) + cash inflow from sale (2 × $100 = $200) = net cash inflow of $215 Enter the cash flows and compute IRR: CF0 = -50; CF1 = -70; CF2 = +215; CPT IRR = 48.8607 30. Which of the following statements about money-weighted and time-weighted returns is least accurate? A)The money-weighted return applies the concept of internal rate of return to investment portfolios. B)If the investment period is greater than one year, an analyst must use the geometric mean to calculate the annual time-weighted return. C)If a client adds funds to an investment prior to an unfavorable market, the time-weighted return will be depressed C — The time-weighted method is not affected by the timing of cash flows. The other statements are true 31. An investor buys a share of stock for $200.00 at time t = 0. At time t = 1, the investor buys an additional share for $225.00. At time t = 2 the investor sells both shares for $235.00. During both years, the stock paid a per share dividend of $5.00. What are the approximate time-weighted and money-weighted returns respectively? A)10.8%; 9.4%. B)7.7%; 7.7%. C)9.0%; 15.0%. A — Time-weighted return = (225 + 5 − 200) / 200 = 15%; (470 + 10 − 450) / 450 = 6.67%; [(1.15)(1.0667)]1/2 − 1 = 10.8% Money-weighted return: 200 + [225 / (1 + return)] = [5 / (1 + return)] + [480 / (1 + return)2]; money return = approximately 9.4% Note that the easiest way to solve for the money-weighted return is to set up the equation and plug in the answer choices to find the discount rate that makes outflows equal to inflows. Using the financial calculators to calculate the money-weighted return: (The following keystrokes assume that the financial memory registers are cleared of prior work.) TI Business Analyst II Plus® Enter CF0: 200, +/-, Enter, down arrow Enter CF1: 220, +/-, Enter, down arrow, down arrow Enter CF2: 480, Enter, down arrow, down arrow, Compute IRR: IRR, CPT Result: 9.39 HP 12C® Enter CF0: 200, CHS, g, CF0 Enter CF1: 220, CHS, g, CFj Enter CF2: 480, g, CFj Compute IRR: f, IRR Result: 9.39 32. Assume an investor makes the following investments: Today, she purchases a share of stock in Redwood Alternatives for $50.00. After one year, she purchases an additional share for $75.00. After one more year, she sells both shares for $100.00 each. There are no transaction costs or taxes. The investor’s required return is 35.0%. During year one, the stock paid a $5.00 per share dividend. In year two, the stock paid a $7.50 per share dividend. The time-weighted return is: A)23.2%. B)51.4%. C)51.7% B — To calculate the time-weighted return: Step 1: Separate the time periods into holding periods and calculate the return over that period: Holding period 1: P0 = $50.00 D1 = $5.00 P1 = $75.00 (from information on second stock purchase) HPR1 = (75 − 50 + 5) / 50 = 0.60, or 60% Holding period 2: P1 = $75.00 D2 = $7.50 P2 = $100.00 HPR2 = (100 − 75 + 7.50) / 75 = 0.433, or 43.3%. Step 2: Use the geometric mean to calculate the return over both periods Return = [(1 + HPR1) × (1 + HPR2)]1/2 − 1 = [(1.60) × (1.433)]1/2 − 1 = 0.5142, or 51.4% 33. On January 1, Jonathan Wood invests $50,000. At the end of March, his investment is worth $51,000. On April 1, Wood deposits $10,000 into his account, and by the end of June, his account is worth $60,000. Wood withdraws $30,000 on July 1 and makes no additional deposits or withdrawals the rest of the year. By the end of the year, his account is worth $33,000. The time-weighted return for the year is closest to: A)7.0%. B)10.4%. C)5.5% B — January – March return = 51,000 / 50,000 − 1 = 2.00% April – June return = 60,000 / (51,000 + 10,000) − 1 = –1.64% July – December return = 33,000 / (60,000 − 30,000) − 1 = 10.00% Time-weighted return = [(1 + 0.02)(1 − 0.0164)(1 + 0.10)] − 1 = 0.1036 or 10.36% 34. Which of the following is most accurate with respect to the relationship of the money-weighted return to the time-weighted return? If funds are contributed to a portfolio just prior to a period of favorable performance, the: A)time-weighted rate of return will tend to be elevated. B)money-weighted rate of return will tend to be elevated. C)money-weighted rate of return will tend to be depressed. B — The time-weighted returns are what they are and will not be affected by cash inflows or outflows. The money-weighted return is susceptible to distortions resulting from cash inflows and outflows. The money-weighted return will be biased upward if the funds are invested just prior to a period of favorable performance and will be biased downward if funds are invested just prior to a period of relatively unfavorable performance. The opposite will be true for cash outflows 35. The money-weighted return also is known as the: A)return on invested capital. B)internal rate of return (IRR) of a portfolio. C)measure of the compound rate of growth of $1 over a stated measurement period B — It is the IRR of a portfolio, taking into account all of the cash inflows and outflows 36. Which of the following statements regarding the money-weighted and time-weighted rates of return is least accurate? A)The time-weighted rate of return reflects the compound rate of growth of one unit of currency over a stated measurement period. B)The time-weighted rate of return is the standard in the investment management industry. C)The money-weighted rate of return removes the effects of the timing of additions and withdrawals to a portfolio C — The money-weighted return is actually highly sensitive to the timing and amount of withdrawals and additions to a portfolio. The time-weighted return removes the effects of timing and amount of withdrawals to a portfolio and reflects the compound rate of growth of $1 over a stated measurement period. Because the time-weighted rate of return removes the effects of timing, it is the standard in the investment management industry 37. A Treasury bill (T-bill) with 38 days until maturity has a bank discount yield of 3.82%. Which of the following is closest to the money market yield on the T-bill? A)3.81%. B)3.87%. C)3.84% C — The formula for the money market yield is: [360 × bank discount yield] / [360 − (t × bank discount yield)]. Therefore, the money market yield is: [360 × 0.0382] / [360 − (38 × 0.0382)] = (13.752) / (358.548) = 0.0384, or 3.84%. Alternatively: Actual discount = 3.82%(38 / 360) = 0.4032%. T-Bill price = 100 − 0.4032 = 99.5968%. HPR = (100 / 99.5968) − 1 = 0.4048%. MMY = 0.4048% × (360 / 38) = 3.835% 38. A Treasury bill has 40 days to maturity, a par value of $10,000, and was just purchased by an investor for $9,900. Its holding period yield is closest to: A)1.01%. B)9.00%. C)1.00% A — The holding period yield is the return that the investor will earn if the bill is held until it matures. The holding period yield formula is (price received at maturity − initial price + interest payments) / (initial price) = (10,000 − 9,900 + 0) / (9,900) = 1.01%. Recall that when buying a T-bill, investors pay the face value less the discount and receive the face value at maturity 39. A Treasury bill (T-bill) with a face value of $10,000 and 137 days until maturity is selling for 98.125% of face value. Which of the following is closest to the bank discount yield on the T-bill? A)4.56%. B)4.93%. C)5.06% B — The formula for bank discount yield is: (D / F) × (360 / t). Actual discount is 1 − 0.98125 = 0.01875. Annualized is: 0.01875 × (360 / 137) = 0.04927 40. What is the yield on a discount basis for a Treasury bill priced at $97,965 with a face value of $100,000 that has 172 days to maturity? A)2.04%. B)3.95%. C)4.26% C — ($2,035 / $100,000) × (360 / 172) = 0.04259 = 4.26% = bank discount yield 41. A Treasury bill has 40 days to maturity, a par value of $10,000, and is currently selling for $9,900. Its effective annual yield is closest to: A)1.00%. B)9.00%. C)9.60% C — The effective annual yield (EAY) is based on a 365-day year and accounts for compound interest. EAY = (1 + holding period yield)365/t − 1. The holding period yield formula is (price received at maturity − initial price + interest payments) / (initial price) = (10,000 − 9,900 + 0) / (9,900) = 1.01%. EAY = (1.0101)365/40 − 1 = 9.60% 42. The bank discount of a $1,000,000 T-bill with 135 days until maturity that is currently selling for $979,000 is: A)6.1%. B)5.8%. C)5.6% C — ($21,000 / 1,000,000) × (360 / 135) = 5.6% 43. An investor has just purchased a Treasury bill for $99,400. If the security matures in 40 days and has a holding period yield of 0.604%, what is its money market yield? A)5.650%. B)5.512%. C)5.436% C — The money market yield is the annualized yield on the basis of a 360-day year and does not take into account the effect of compounding. The money market yield = (holding period yield)(360 / number of days until maturity) = (0.604%)(360 / 40) = 5.436% 44. The effective annual yield (EAY) for a T-bill maturing in 150 days is 5.04%. What are the holding period yield (HPY) and money market yield (MMY) respectively? A)2.04%; 4.90%. B)5.25%; 2.04%. C)2.80%; 5.41% A — The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. The HPY = (1 + 0.0504)150/365 = 1.2041 − 1 = 2.04%. Using the HPY to compute the money market yield = HPY × (360/t) = 0.0204 × (360/150) = 0.04896 = 4.90% 45. A Treasury bill, with 80 days until maturity, has an effective annual yield of 8%. Its holding period yield is closest to: A)1.72%. B)1.70%. C)1.75% B — The effective annual yield (EAY) is equal to the annualized holding period yield (HPY) based on a 365-day year. EAY = (1 + HPY)365/t − 1. HPY = (EAY + 1)t/365 − 1 = (1.08)80/365 − 1 = 1.70% 46. The holding period yield for a T-Bill maturing in 110 days is 1.90%. What are the equivalent annual yield (EAY) and the money market yield (MMY) respectively? A)6.90%; 6.80%. B)6.44%; 6.22%. C)5.25%; 5.59% B — The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. (1 + 0.0190)365/110 − 1 = 1.06444 − 1 = 6.44%. Using the HPY to compute the money market yield = HPY × (360 / t) = 0.0190 × (360 / 110) = 0.06218 = 6.22% 47. If the money market yield is 3.792% on a T-bill with 79 days to maturity, what is the holding period yield? A)0.77%. B)0.83%. C)0.89% B — The holding period yield can be calculated from the money market yield as: (money market yield) ÷ (360 ÷ t). Therefore, the HPY is (0.03792) × (79 ÷ 360) = 0.0083 = 0.83% 48. A broker calls with a proposal to buy a Treasury bill (T-bill) with 186 days to maturity. He says the effective annual yield on the T-bill is 4.217%. What is the holding period yield if you hold the bill until maturity? A)8.44%. B)2.13%. C)2.02% B — To calculate the HPY from the EAY, the formula is: (1 + EAY)(t/365) − 1. Therefore, the HPY is: (1.04217)(186/365) − 1 = 0.0213, or 2.13% 49. If the holding period yield on a Treasury bill (T-bill) with 197 days until maturity is 1.07%, what is the effective annual yield? A)0.58%. B)1.07%. C)1.99% C — To calculate the EAY from the HPY, the formula is: (1 + HPY)(365/t) − 1. Therefore, the EAY is: (1.0107)(365/197) − 1 = 0.0199, or 1.99% 50. The effective annual yield for an investment is 10%. What is the yield for this investment on a bond-equivalent basis? A)9.76%. B)4.88%. C)10.00% A — First, the annual yield must be converted to a semiannual yield. The result is then doubled to obtain the bond-equivalent yield. Semiannual yield = 1.10.5 − 1 = 0.0488088. The bond-equivalent yield = 2 × 0.0488088 = 0.097618 51. The holding period yield of a T-bill that has a bank discount yield of 4.70% and a money market yield of 4.86% and matures in 240 days is closest to: A)3.2%. B)2.8%. C)4.9% A — 4.86 × (240/360) = 3.24% 52. What is the effective annual yield of a T-bill that has a money market yield of 5.665% and 255 days to maturity? A)5.79%. B)5.92%. C)4.01% A — Holding Period Yield = 4.0127% = 5.665% × (255 / 360) Effective Annual Yield = (1.040127)365/255 = 1.0571 − 1 = 5.79% 53. A Treasury bill has 90 days until its maturity and a holding period yield of 3.17%. Its effective annual yield is closest to: A)13.49%. B)13.30%. C)12.68% A — The effective annual yield (EAY) is equal to the annualized holding period yield (HPY) based on a 365-day year. EAY = (1 + HPY)365/t − 1 = (1.0317) 365/90 − 1 = 13.49% 54. A Treasury bill, with 45 days until maturity, has an effective annual yield of 12.50%. The bill's holding period yield is closest to: A)1.57%. B)1.54%. C)1.46% C — The effective annual yield (EAY) is equal to the annualized holding period yield (HPY) based on a 365-day year. EAY = (1 + HPY)365/t − 1. HPY = (EAY + 1)t/365 − 1 = (1.125)45/365 − 1 = 1.46%

CFA Level 1 - Quantitative Methods Session 2 - Reading 6

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