Unit 20 Quizzing
The Smiths are saving money for a down payment on a house. The Smiths have $25,000 in cash, and they estimate that in 5 years they will have approximately $31,000 if they deposit their cash in a savings account that compounds interest yearly. To calculate the $31,000 amount, the Smiths determined A) the future value of the $25,000 B) the net present value of the $25,000 C) the internal rate of the return on the $25,000 D) the present value of $25,000
ANswer: A) Explanation To determine the money's worth at a future date (in this case, 5 years), the Smiths calculated the future value of the funds. Future value is a compounded rate of return, and in this case, the $25,000 was compounded at 5% per year for 5 years. The present value of an investment is the opposite of future value.
Adam has a portfolio of bonds worth approximately $125,000. He is concerned that interest rates will increase in the near term. Which of the following would be the least desirable strategy for Adam? A) Sell Treasury bonds and buy Treasury bills B) Sell long-term bonds and buy short-term bonds C) Sell bonds with lower coupons and buy those with higher coupons D) Sell bonds with a short duration and buy those with a longer duration
ANswer: D)
Which of the following statements about systematic and unsystematic risk is most accurate? A) The unsystematic risk for a specific firm is similar to the unsystematic risk for other firms in the same industry. B) Total risk equals market risk plus company-specific risk. C) As an investor increases the number of stocks in a portfolio, the systematic risk will go down. D) As an investor increases the number of stocks in a portfolio, the unsystematic risk will stay the same.
Answer B) Explanation Total risk equals systematic (market) risk plus unsystematic (company-specific) risk. Standard deviation is the tool that measures total risk. The unsystematic risk for a specific firm is not similar to the unsystematic risk for other firms in the same industry. Unsystematic risk is company-specific or unique risk, and when more stocks are added, the risk will change. The systematic risk of a portfolio can be changed up or down by adding high-beta or low-beta stocks.
The Zxion Corporation has just distributed a 7½ to 1 split of its common stock. Prior to the split, Zxion had EPS of $15, the market price of Zxion common stock was $225 per share, and the price of its $75 par preferred stock was $82.50. As a result of the split, the price-to-earnings (P/E) ratio is now A) 15 x 1. B) 7.5 x 1. C) 2 x 1. D) 6 x 1.
Answer: A) A stock split does not change the PE ratio because both the stock's price and earnings decline by the same proportion. In this question, after the 7.5 to 1 split, the market price will drop to $30 per share ($225 ÷ 7.5) and the earnings per share are now $2 per share ($15 ÷ 7.5). That 30:2 is still a 15-to-1 P/E ratio.
Which of the following statements is correct? A) Beta is a measure of relative systematic risk for stock or portfolio returns. B) Beta is a measure of relative unsystematic risk for stock or portfolio returns. C) Portfolio managers have a goal of reaching zero alpha. D) A stock or portfolio's beta increases as its alpha declines.
Answer: A) Beta is used to measure the variability between a particular stock's (or port) movement and that of the general market. That refers to systematic rather than unsystematic risk. When it comes to alpha, the goal is a positive alpha and there is no correlation between the beta and alpha of a stock.
XYZ Corporation has a beta of 1.0, and ABC has a beta of 1.4. XYZ has returned 12% and ABC 14.8%. Based on this information, ABC had alpha of A) −2% B) 14.8% C) 2.8% D) 2%
Answer: A) Explanation Alpha is the extent to which a security's performance exceeds (or falls short of) that of the market compared to what would be expected based on its beta. A key to this question is that XYZ's beta of 1.0 equals the beta of the market. A stock with a beta of 1.4 would be expected to perform 40% better in an up market than the market itself. Because XYZ with a beta of 1.0 gained 12%, ABC should return 140% of that or 16.8% (12% × 1.4). With an actual return of 14.8%, ABC underperformed the expected by 2% and that is why it has a negative alpha.
XYZ Corporation has a beta of 1, and ABC has a beta of 1.4. XYZ has returned 12% and ABC 18.8%. Based on this information ABC had alpha of A) 2% B) 18.8% C) 6.8% D) 4.8%
Answer: A) Explanation Alpha is the extent to which a security's performance exceeds (or falls short of) what would be expected based on its beta. A stock with a beta of 1.4 would be expected to perform 40% better in an up market than one with a beta of 1.0. Because XYZ with a beta of 1.0 gained 12%, ABC should return 140% of that or 16.8% (12% × 1.4). With an actual return of 18.8%, ABC beat the expected by 2% and that is its alpha. More accurately, this question should also include the risk-free rate, but if, as in this case, it doesn't, the computation is easier. If the RF rate was shown, then that would have to be subtracted from "both sides." If the RF was 2%, then the computation would be (12% − 2%) × 1.4 = 14%. Then, we subtract the 2% RF rate from the 18.8 to get 16.8%. The difference between 16.8% and 14% would be alpha of 2.8%. LO 20.e
Which of the following statements regarding the time value of money is not correct? A) Future value is the future amount to which a sum of money today will increase on the basis of a defined interest rate and period. B) Compound interest is interest earned on interest. C) Future value of an ordinary annuity is the future amount to which a series of deposits of equal size will increase. D) Compound interest is interest earned on the initial investment.
Answer: A) Explanation Compound interest is interest earned on interest that has been added to the original principal. For example, $1,000 earning 5% compounded annually earns $50 the first year and then 5% of $1,050 or $52.50 the 2nd year.
To make a quantitative evaluation using the future value computation, which of the following is NOT needed? A) Account value at the end of the period. B) Rate of return anticipated. C) Time period involved. D) Account value at the start of the period.
Answer: A) Explanation Future value is calculated to determine the value of a specific amount of money at some point in the future. The anticipated interest rate, the present amount to be invested, and a time period for the life of the investment are required to calculate the future value.
Your client has the following bonds in her portfolio: XYZ 3s of 44. TUV 6s of 45. QRS 9s of 43. NOP 12s of 42. If interest rates were to suddenly rise, which of her bonds would suffer the greatest decline in market price? A) XYZ 3s of 44 B) QRS 9s of 43 C) NOP 12s of 42 D) TUV 6s of 45
Answer: A) Explanation The technical method for answering this question is to compare the duration of each of the bonds. The one with the longest duration will be impacted the most by a change in interest rates. Invariably, when the length of time to maturity is relatively close (as is the case here), the bond with the lowest coupon rate will have the longest duration. It should be easy to spot that the bond with the shortest duration is the NOP 12s of 42 - they have both the highest coupon and the nearest maturity and would be the correct answer if the question had asked for the bond suffering the smallest decline in market price.
Five years ago, an investor purchased an ABC Corporation BBB-rated debenture with a coupon of 6% maturing in 2037. Currently, new BBB-rated debentures maturing in 2037 are being issued with coupons of 5%. Based on the discounted cash flow method, one could say that the present value of the investor's security is A) more than the par value B) positive C) equal to the par value D) less than the par value
Answer: A) The discounted cash flow method is a technical way of computing the value of a security that demonstrates an inverse relationship between interest rates and bond prices. The discount rate here is the current market rate of 5%. Because the investor's debenture is paying at a rate of 6%, its cash flow is more valuable than a 5% bond; therefore, it will sell at a premium (above par)
The following numbers (in %) represent the returns from an investment fund over the past seven years: 2016: 13%, 2017: 11%, 2018: 2%, 2019: 6%, 2020: 5%, 2021: 8%, 2022: 6%. Using the range measure would indicate that the seven-year returns from the fund had a mid-range of A) 7.5%. B) 2%. C) 4%. D) 11%.
Answer: A) The midrange of any group of numbers occurs between the highest and lowest numbers in the group. The mid between 13% (highest) and 2% (lowest) is 7.5%. That is slightly higher than the mean (average of the returns)
An investment adviser representative is looking for a suitable investment for a client. The IAR wishes to find something that will offer an attractive return commensurate with its systematic risk. The choices have been narrowed to Security C and Security L, and the selection will be based on alpha. C has a beta of 1.0 and earned 13% which equalled its expected return, while L has a beta of 0.8 and earned 10.1%. The alpha of Security L is A) −0.3 B) +2.9 C) −2.9 D) +0.3
Answer: A) Alpha is obtained by comparing how a security actually performed to the performance would could have expected based on the beta. A beta of 1.0 is used to indicate the volatility. Because Stock C has a beta of 1.0, its 13.0% matches that of the market. Also, Stock C has an alpha of zero because its actual return was the same as expected. With a beta of 0.8, one would expect security L to produce a lower return but how much lower? It's return should be 80% of the market, or 80% of 13% which is 10.4%. However, its actual return fell short of that 0.3%, giving it a negative alpha of 0.3% Had its actual return been 10.7%, it would have had a 0.3 positive alpha. .
The market price of which of the following bonds would have the greatest percentage increase if interest rates fell? A) 30-year maturity, selling at a discount B) 15-year maturity, selling at a premium C) 30-year maturity, selling at a premium D) 15-year maturity, selling at a discount
Answer: A) Explanation The general rule of thumb is that bonds with long-term maturities will have greater fluctuations in price than will short-term maturities, given the same move in interest rates. Furthermore, discounted bonds, with their lower coupon rates, have a longer duration than a bond selling at a premium and will respond more favorably to falling rates than will those premium bonds. Thus, the 30-year discounted bond will have a greater increase, as a percentage, than the others.
Which of the following bonds has the shortest duration? A bond with A) a 10-year maturity, 10% coupon rate. B) a 10-year maturity, 6% coupon rate. C) a 20-year maturity, 10% coupon rate. D) a 20-year maturity, 6% coupon rate.
Answer: A) Explanation Two factors go into the computation of a bond's duration - the length to maturity and the coupon rate. When the maturities are the same, the bond with the highest coupon has the shortest duration. When the coupons are the same, the bond with the nearest maturity has the shortest duration. The 10% bond maturing in 10 years "wins" on both counts. It has the nearest maturity with the highest coupon. All else being equal, a bond with a longer duration will be more sensitive to changes in interest rates.
Which of the following statements regarding standard deviation is true? A) Two investments with the same expected return will not necessarily have the same level of risk and standard deviation. B) Standard deviation is expressed in dollars. C) Standard deviation quantifies expected return. D) The smaller the deviation from the average performance, the riskier the investment becomes.
Answer: A) Explanation Two investments can have the same expected return but have significantly different deviations. The investment with the larger standard deviation is the riskier of the 2 and will be more volatile even if the expected returns are the same. Standard deviation measures the deviation percentage from the average of the expected or historical returns of an investment. The larger the standard deviation, the riskier the investment. Standard deviation is not expressed in dollars, it is expressed in percentages.
A bond's duration is A) identical to its maturity for an interest-bearing bond B) longer for a 10-year bond with a 5% coupon than it is for a 10-year bond with a 10% coupon C) an indication of a bond's yield that ignores its price volatility D) expressed as a percentage
Answer: B)
Duration is A) equivalent to the yield to maturity B) a measure of a bond's volatility with respect to a change in interest rates C) identical to a bond's maturity D) the deviation of a bond's returns from its average returns
Answer: B) Duration measures a bonds volatility with respect to a change in interest rates. The higher the duration, the greater the change in a bond's price with respect to interest rate changes.
In preparing a research report, an investment adviser reviewing the returns on a specific stock over the past 10 years, notices that the median is lower than the mean. The most probable cause for this is A) the distribution of the returns is skewed to the left B) a majority of the returns are less than the mean C) the returns are symmetrical D) a majority of the returns are greater than the mean
Answer: B) Explanation A few high returns, some might refer to them as outliers, will skew the distribution to the right giving us a higher mean than median. When the returns are symmetrical, the mean and median are the same (or very, very close).
Which of the following attributes of common stock best describes why internal rate of return (IRR) is not generally used to determine the return on common stock? A) Uneven cash flows B) Uneven cash flows, no maturity date and price C) No net present value D) Uneven cash flows and no maturity
Answer: B) Explanation Internal rate of return (IRR) best measures investments with a known price and maturity. The internal rate of return is the discount rate that makes the future value of an investment equal to its present value. The yield to maturity on a bond is actually its internal rate of return.
Present value is a computation frequently used to determine the amount of deposit needed now to meet a future need, such as a college education. If an investor uses an expected return of 8%, but the actual return over the period is 6%, A) the yield to maturity will be lower than anticipated B) the present value was insufficient to meet the objective C) the accumulated value will meet the objectives D) the future value will not be able to be computed
Answer: B) Explanation Present value is the amount deposited to meet a future goal based on an expected rate of return. If the return is lower than expected, the amount deposited will not grow to the required amount (a bad thing).
One measure of a corporation's liquidation value is its book value per share. When performing this computation, which of the following must be taken into consideration? I. Goodwill II. Long-term debt III. Retained earnings IV. Par value of the preferred stock A) II and III B) I, II, III, and IV C) I and II D) II, III, and IV
Answer: B) Explanation The computation of book value per share is basically net tangible worth per share of common stock. Included in the net worth are all assets and liabilities (such as long-term debt), as well as the stockholders equity (par value of the preferred stock and par + paid in surplus of the common stock and retained earnings). Subtracted from this to get tangible book value would be the par value of the preferred stock and the value of intangible assets such as goodwill.
Your client wants to have $1 million in her investment account when she retires at age 70. She is currently 50 and has about $215,000 available to invest today. You tell her that if the portfolio can earn at a compounded rate of 8%, she will reach her goal. That 8% rate is A) the future value rate B) the internal rate of return C) the present value rate D) the market rate of return
Answer: B) Explanation The internal rate of return is the earnings rate required to reach a specified future value from an amount that is currently available to invest. This is a future value computation, but there is no such term as future value rate.
Selmer Jones has just inherited some money and wants to set some of it aside for a vacation in Hawaii one year from today. His bank will pay him 5% interest on any funds he deposits. In order to determine how much of the money must be set aside now and held for the trip, he should use the 5% as a A) opportunity cost. B) discount rate. C) nominal rate of return. D) required rate of return.
Answer: B) Explanation This is a present value question. Selmer needs to figure out how much the trip will cost in one year, and use the 5% as a discount rate to convert the future cost to a present value. Thus, in this context the rate is best viewed as a discount rate. Although you would never have to compute it, for each $1,000 Selmer needs, he would have to put away $952.38 (the present value of $1,000 at 5% in 1 year).
Twelve years ago, an investor placed $2,500 into an account. The account is now worth $10,000. Using the Rule of 72, you can determine that the approximate annual return was A) 400% B) 12% C) 6% D) 36%
Answer: B) Under the Rule of 72, we can determine an earnings rate by dividing 72 by the number of years it takes for money to double. In this case, the money has quadrupled. That means it has doubled twice in 12 years or, every 6 years. Divifding 12 by 6 results in an annual return of 12%?
An investor's required rate of return is 6%. If the internal rate of return of the investment offered is 6.32%, then the NPV is A) between 6% and 6.32% B) zero C) positive D) negative
Answer: C) Explanation Anytime an investment's IRR is more than the required rate of return, the NPV is positive (and should probably be selected). The NPV is expressed as a dollar amount. It is the IRR which is expressed as a percentage.
An investor places $10,000 into BCD common stock 12 years ago. Today, that stock has a market value of $20,000. Using the Rule of 72, the internal rate of return on BCD is closest to A) 6.8%. B) 5%. C) 6%. D) 8%.
Answer: C) Explanation The Rule of 72 indicates that the approximate return required for a number to double in 12 years can be determined by dividing 72 by 12. That results in a return nearest to 6%.
One of your clients has $150,000 in his 401(k) plan at work. He is assuming the portfolio will increase in value at a rate of 7% compounded annually for the next 5 years. If that is the case, the portfolio value at the end of that 5-year period will be closest to A) $160,500. B) $202,500. C) $210,383. D) $240,867.
Answer: C) Explanation This is a straightforward future value computation. The proper way to do this is to enter the beginning value ($150,000) into your calculator, and then multiply times 107% five consecutive times. We'll get you started: 150,000 x 107% = $160,500 x 107% = $171,735 x 107% = $183,756 (and do this 2 more times to get $210,383). If that is too challenging, then use the "shortcut" - it always works. Figure the answer using simple interest. The starting value is $150,000. Seven percent growth is $10,500. Do that for 5 years and it is $52,500. Add that to the initial value and you have $202,500. Then, select the next highest number because that takes into consideration the compounding effect.
A client owns an investment-grade bond with a coupon of 7%. If similarly rated bonds are being issued today with coupons of 5%, and the market is efficient, it would be expected that the client's bond A) has a negative net present value B) will be selling at a discount from par C) has a zero net present value D) has a positive net present value
Answer: C) Explanation With a discount rate of 5% (the discount rate in a present value computation is the current market interest rate), a debt instrument with a 7% coupon rate will be selling at a premium (interest rates down, prices up). If the market is efficiently pricing that bond, its market price should be equal to its present value, resulting in an NPV of zero. LO 20.a
Which of the following statements best represents a bond's present value? A) Present value is the discounted future repayment of principal. B) Present value represents the internal rate of return (IRR) of the bond. C) Present value is the sum of all the discounted future payments. D) Present value is the sum of all the discounted future interest payments.
Answer: C) The correct answer is the standard defintition. There are two future cash flows from a bond. First is the periodic interest payments and second is the repayment of the principal at maturity. The PV of the bond is the sum of the discounted value of both (all) future payments.
A corporate bond with a 6% coupon is purchased for your customer's portfolio. If current bonds of the same quality and maturity are yielding 7.25% and the net present value (NPV) of the bond is zero, the bond's internal rate of return (IRR) is A) trading at a discount. B) more than 7.25%. C) 7.25%. D) 6.00%.
Answer: C) When a bond's NPV is zero, it meeans that is is priced to provide a yield to maturity equal to the current market interest rate. In this case, that rate is 7.25%. A bond's internal rate of return is its yield to maturity. Isn't the bond selling at a discount? Yes it is, but IRR is always expressed as a percentage, not a price.
A client owns an investment-grade bond with a coupon of 5% that is priced to yield 6.7%. If similarly rated bonds are being issued today with coupons of 7%, it would be expected that the client's bond A) has a positive net present value B) will be selling at a premium over par C) has a negative net present value D) has a zero net present value
Answer: C) With a discount rate of 7% (the discount rate in a present value computation is the current market interest rate), a debt instrument with a 5% coupon rate will be selling at a discount (interest rates up, prices down). We are told that this bond is offering a yield of 6.7%, which is less than the current market rate. Because a present value computation using a 6.7% rate would reflect a higher value than a 7% rate (the higher the discount rate, the lower the value), that would mean that the bond can be purchased at a price above its present value. Anytime that occurs, the instrument has a negative net present value (the difference between the price and the present value).
If a security has an anticipated return of 8.7% and a standard deviation of 14.6%, you would expect the returns to have a 95% probability (assuming a normal distribution) of falling between A) 0 and 37.9% B) 8.7 and 23.3% C) −5.9 and +23.3% D) −20.5 and +37.9%
Answer: D) A security with a normal distribution has a 95% probability of falling within 2 standard deviations of its anticipated return. In theat case, would be -20.5% and +37.9%, which is computed by calculating return movements of 29.2% (14.6% *2) in either direction.
Plymouth Standard's common stock has an average return of 12%; its returns fall within a range of -2% to +26% approximately 68% of the time. Which one of the following numbers is closest to the standard deviation of returns of Plymouth Standard's stock? A) 28% B) 19% C) 8% D) 14%
Answer: D) Explanation A standard deviation of 14% means an investor can expect a return on an investment to vary ±14 from the average return approximately 68% of the time. A return of +26% minus the 12% average return equals 14%. Likewise, the difference between the -2% return and the average of 12% is also 14%.
One of your clients wishes to give her daughter $200,000 to start her own business. The daughter expects to be finished with graduate school and an internship in 8 years. The expected rate of return is 9%. Using the Rule of 72, calculate the amount the client must deposit today to meet that future goal. A) $144,000 B) $112,500 C) $72,000 D) $100,000
Answer: D) Explanation In this question, we are told to use the Rule of 72 to compute the present value. That is, the sum required today (present) to reach a stated future goal. With an earnings rate of 9%, the rule tells us that money will double in 8 years (72 divided by 9 = 8). With an 8-year accumulation period and a goal of $200,000, the deposit required to reach that by doubling is $100,000.
Which of the following statements regarding internal rate of return (IRR) is true? A) IRR cannot be used effectively to measure return on investments with even cash flows, such as bonds. B) IRR ignores the time value of money. C) If the IRR is higher than the cost of borrowing to fund an investment, the investment is likely to be unprofitable. D) IRR is a discount rate at which the net present value (NPV) of an investment is equal to zero.
Answer: D) IRR is a DISCOUNT RATE at which the net present value (NPV) of an investment is equal to zero. IRR can be used to measure return on bonds or stocks that pay stable dividends. It accounts for time value of Money. If the IRR is higher than cost of borrowing, it should be profitable.
If you were using the discounted cash flow method to determine the appropriate value of a security, you would want to purchase that security when A) the current market price equals the PV B) the rating of the security has just been upgraded C) the current market price is above the PV D) the current market price is below the PV
Answer: D) xplanation Those who use the DCF to value a security would recommend purchasing when the current market price is below the PV—that is, when the NPV is positive.
An investment adviser is analyzing 4 bonds of similar quality for a client. Bond A has a coupon of 6%, matures in 12 years, and is currently priced at 50. Bond B has a coupon of 8%, matures in 9 years, and is currently priced at 50. Bond C has a coupon of 4%, matures in 18 years, and is priced at 45. Bond D has a coupon of 12%, matures in 6 years, and is priced at 50. Based on NPV, which of these bonds represents the better value? A) Bond B B) Bond D C) Bond A D) Bond C
Answer: D) Explanation Because you don't have the proper calculator to do a real PV calculation, NASAA expects you to use the rule of 72. Remember, under that rule, dividing 72 by the interest rate tells you the number of years it will take for a deposit to double. Or, if you divide 72 by the number of years, it will tell you the interest rate required for a present deposit to double. Finally, a positive NPV is when you can buy the bond for less than its present value. So, let's look at all 4 choices. Bond A, at 6%, takes 12 years to double. That's exactly the time to maturity, so the PV of this bond should be approximately $500 (a quote of 50). The same is true of bonds B and D—their PV should be approximately $500 (72 ÷ 8% = 9 years; 72 ÷ 12% = 6). Because their price is the same as the PV, the NPV is zero. However, with bond C, 72 divided by 4% equals 18 years, so this bond also has a PV of approximately $500 (50), but it can be purchased for less than that: 45 ($450). Therefore, with an NPV of $50, bond C is the best value. One final point: If you are stuck and have to guess, note that 3 of the 4 bonds are selling for $500 with the other priced at $450. If they are all going to mature at $1,000, a good guess would be that the cheapest one is the best deal.
In order to perform a discounted cash flow estimation of the value of a bond, it would be necessary to know all of the following except A) the future cash flow B) the discount rate C) the number of interest payments D) the parity price of the bond
Answer: D) Explanation In its simplest iteration, discounted cash flow is nothing more than taking all the money you are scheduled to receive over a given future period and adjusting that for the time value of money (the discount rate). Parity price is only relevant to convertible bonds.
The following numbers (in %) represent the returns from an investment fund over the past seven years: 2016: 13%, 2017: 11%, 2018: 2%, 2019: 6%, 2020: 5%, 2021: 8%, 2022: 6%. Using the range measure would indicate that the seven-year returns from the fund had a range of A) 9%. B) 2%. C) 4%. D) 11%.
Answer: D) 11% Explanation Using the range measure would indicate that the seven-year returns from the fund had a range of 11 = (13 - 2). This is simply the difference between the highest and lowest returns.
One measure of a corporation's liquidation value is its book value per share. When performing this computation, the value of which of the following would normally be subtracted from the corporation's net worth? I. Cash II. Wages payable III. Patents IV. Preferred stock A) III and IV B) I and IV C) II and III D) I and II
Explanation The computation of book value per share is basically net tangible worth per share of common stock. Therefore, we subtract both the par value of the preferred stock and the value listed on the balance sheet for the intangible assets, such as patents. The key to this question is recognizing that it is looking for those items that would be subtracted from a corporation's net worth to arrive at the book value per share. Method #1: The net worth is $12 million (20 - 8). Subtract the goodwill ($1 million) and the preferred par value of $2 million to get a total of $9 million. Divide the $9 million by the 3 million common shares outstanding, which results in a book value per share of $3.
Which of the following statements is most accurate regarding the net present value (NPV) and internal rate of return (IRR) on a bond? A) NPV assumes the cash flows can be reinvested at market interest rates. B) IRR assumes the cash flows are reinvested at market interest rates. C) IRR assumes the cash flows are reinvested annually. D) NPV assumes that cash flows can be reinvested at the bond's IRR.
Explanation The first step in finding the NPV is to compute the present value (PV). The PV is computed by taking the future cash flows and discounting them by a "discount" rate. That rate is the current market interest rate. So, if NPV is based on PV and PV assumes reinvestment at the discount rate, that assumption must hold true for figuring NPV. In the case of the IRR, that is the yield to maturity of a bond and assumes that the cash flows are reinvested at that IRR. For example, a bond with a YTM of 7% assumes that all reinvestments will be made at that 7% rate. The periodic cash flow on a bond comes from the semiannual interest payments making reinvestments semiannually, not annually.
