Unit 7.5 Quantitative Evaluation Measurements (Series 65)

If the Consumer Price Index (CPI) rose 5% during the last year, during which time your client held a 6% municipal bond, what would be the approximate annualized inflation- adjusted return? A) 1%. B) 0%. C) 5%. D) 6%.

Answer: A Because inflation, as measured by the CPI, rose by 5% each year and the client's bonds returned 6% annually, inflation would have reduced the client's purchasing power by 5%, leaving an inflation-adjusted return of 1% each year. Reference: 7.5.2.6 in the License Exam Manual.

If a client in the 30% marginal income tax bracket can earn an after-tax rate of return of 7% when the estimated inflation rate during the holding period of an investment is 4%, the client's real rate of return is A) 10%. B) 7%. C) more than 7%. D) less than 7%.

Answer: D Real return reduces nominal return by an inflation factor. Thus, the client's real return must be less than 7%. Reference: 7.5.2.6 in the License Exam Manual.

If an investor wished to compute the mean return of her portfolio, she is going to: A) find the median. B) compute using straight-line averaging. C) compute the standard deviation. D) find the arithmetic mean.

Answer: D Unless something else is specified, whenever the mean return is referenced, it is always the arithmetic mean (the simple average). Reference: 7.5.2.11.1 in the License Exam Manual.

An analyst uses the Dividend Growth Model to assist in determining appropriate stocks to recommend. This analyst would consider all of the following factors EXCEPT: A) dividend payout ratio. B) current dividend. C) growth of the dividend. D) required rate of return.

Answer: A The classic definition of the Dividend Growth Model is "a stock valuation model that deals with dividends and their growth, discounted to today". The payout ratio has nothing to do with this, it is strictly the amount of the dividend that counts. Reference: 7.5.2.10.2 in the License Exam Manual.

Over the past 5 years, a stock has had returns of +16%, +5%, -4%, +12% and +8%, The median of the returns is: A) 8.0%. B) 7.4%. C) 8.2%. D) 9.0%.

Answer: A The median of a series of returns is that number that has an equal number of occurrences below as above. In this case, that number is 8% because there are 2 returns less than 8% (-4% and +5%) and 2 above (+12% and +16%). Reference: 7.5.2.11.2 in the License Exam Manual.

In order to compute a client's realized holding period return, it is not necessary to know A) paper profits B) value at the end of the holding period C) income received during the holding period D) original investment

Answer: A ​​​The question is asking for realized return. That means that we ignore paper profits, (just another term for unrealized gain). Reference: 7.5.2.3 in the License Exam Manual.

There are several measures of central tendency used by investment analysts. Included would be all of the following EXCEPT: A) median. B) mean. C) moving averages. D) mode.

Answer: C Moving averages are used to smooth out the fluctuations in a stock price over a period of time. The other three are the most popular measures of central tendency. Reference: 7.5.2.11 in the License Exam Manual.

Which of the following has the highest real return? A) A bond that yields 10% when inflation is 7%. B) A bond that yields 8% when inflation is 5%. C) A bond that yields 6% when inflation is 4%. D) A bond that yields 5% when inflation is 1%.

Answer: D Subtracting the inflation rate from the bond yield will result in a real return of 4% on the 5% bond, the highest of the choices offered. Reference: 7.5.2.6 in the License Exam Manual.

If an adviser wished to report a security's average performance over the past five years, he would be showing the? A) mean. B) mode. C) median. D) standard deviation.

Answer: A Mean, or arithmetic mean, is obtained by simply averaging the results. Reference: 7.5.2.11.1 in the License Exam Manual.

A client is meeting with you to discuss the best way to invest today to meet the goal of funding their child's college expenses. The least important information needed to determine the amount to deposit is: A) age of the child. B) parent's salary. C) current college costs. D) expected inflation rate.

Answer: B Because this question is looking for the initial deposit, salary is not as important a factor as the other three. Reference: 7.5.1 in the License Exam Manual.

An investor buys 100 shares of KAPCO stock for $120 per share. During the year he receives $260 in dividends and, at the end of the year, the stock is worth $13,000. The investor's holding period return is: A) 2.17%. B) 10.50%. C) 9.69%. D) 8.33%.

Answer: B Holding period return is computed by dividing the total return from income (dividends or interest) plus appreciation (or minus depreciation), by the original cost. In this example, the investor received $260 in income and has $1,000 of appreciation. That is a total return of $1,260 divided by $12,000 or 10.50% Reference: 7.5.2.3 in the License Exam Manual.

To make a quantitative evaluation using the present value computation, which of the following is NOT needed? A) Account value at the end of the period. B) Account value at the beginning of the period. C) Anticipated rate of return of the portfolio. D) Time period involved.

Answer: B Present value is calculated to determine the amount required now to have a specified value at some time in the future. It is what we are looking for so we don't have it now. Reference: 7.5.1.2 in the License Exam Manual.

In an effort to find a suitable security for a client's portfolio, an investment adviser representative reviews the performance of a particular common stock over the past 7 years. The annual returns over that period have been 6%, 22%, 16%, -8%, 11%, 12%, and -3%. It would be correct for the IAR to report to the client that the range of returns has been A) 14% B) 30% C) 8% D) 11%

Answer: B The range is the difference between the highest and lowest returns. In this case, the highest return is +22% and the lowest is -8%. That is a difference of 30. The mean (or average) is 8% and the median is 11%. Reference: 7.5.2.11 in the License Exam Manual.

To calculate the future value of an investment, which of the following must be known? I. Assumed interest rate. II. Guaranteed interest rate. III. Duration of investment. IV. Time horizon of investor. A) II and IV. B) III and IV. C) I and III. D) I and II.

Answer: C Future value calculations are based on an assumed, not guaranteed, interest rate and the time period over which the funds are invested. In addition, we must know the amount available for investment. Reference: 7.5.1.1 in the License Exam Manual.

The present value of a dollar: A) is the amount of goods and services it will buy in the future at today's rate price level. B) is equal to its future value if the level of interest rates stays the same. C) cannot be calculated without knowing the level of inflation. D) indicates how much must be invested today at a given interest rate, to equal a specific cash value in the future.

Answer: D The present value of a dollar will indicate how much must be invested today at a given interest rate, to equal a cash amount required in the future. Reference: 7.5.1.2 in the License Exam Manual.

An investor is reviewing his portfolio. To compute the real rate of return on an investment, it would be necessary to know I.the gain (or loss) recognized on the asset II.the income received from holding the asset III.the rate of inflation IV.the tax bracket of the investor A) I, II and III B) I, II and IV C) I and IV D) II and III

Answer: A An investor's real rate of return is computed by dividing the total return received by the cost and then subtracting the inflation rate. If there is no realized gain, it is simply the nominal return based on the income minus the inflation rate. The investor's tax bracket is needed to compute after-tax returns. Reference: 7.5.2.6 in the License Exam Manual.

It is better to receive a dollar today and invest it rather than receive a dollar in the future because of the A) time value of money. B) discounted future value. C) effect of inflation. D) effect of deflation.

Answer: A Because of the time value of money, it is better to receive a dollar today and invest it rather than receive a dollar in the future; thus the importance of present value and future value calculations. Reference: 7.5.1 in the License Exam Manual.

One of your clients is viewing a stock held in her portfolio and wishes to know how to calculate the holding period return for that security. In order to do that, she must know the: I.date the stock was purchased and the date it was sold. II.dividends received during the holding period. III.purchase price. IV.current market price. A) II, III and IV. B) I, II and III. C) I, II, III and IV. D) III and IV.

Answer: A Holding period return is the total return on an investment over the period it was held. In order to compute this, one must know the income received (dividends) plus any capital appreciation (the difference between the purchase price and the sale price if sold, or current market price if still held). If you read the question carefully, it refers to a security "held" in her portfolio. Therefore, we don't have a sale date. Reference: 7.5.2.3 in the License Exam Manual.

Which of the following statements regarding internal rate of return (IRR) is TRUE? A) IRR is a discount rate at which the net present value (NPV) of an investment is equal to zero. B) IRR cannot be used effectively to measure return on investments with even cash flows, such as bonds. C) IRR ignores the time value of money. D) If the IRR is higher than the cost of borrowing to fund an investment, the investment is likely to be unprofitable.

Answer: A Internal rate of return (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 because of their even cash flows and on those stocks that pay stable dividends for the same reason. IRR accounts for the time value of money. If the IRR is higher than the cost of borrowing to fund the investment, the investment should be profitable. Reference: 7.5.2.9 in the License Exam Manual.

The time value of money is part of the computation for the: A) internal rate of return. B) after-tax return. C) real rate of return. D) risk-adjusted return.

Answer: A One of the unique features of IRR is that it is a compounded rate using the time value of money. Reference: 7.5.2.9 in the License Exam Manual.

Present value is a computation that is frequently used to determine the amount of a 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 10%, the future value will be A) higher than anticipated B) lower than anticipated C) the same as anticipated D) too varying to tell

Answer: A Present value is the amount deposited to meet a future goal based on an expected rate of return. If the return is higher than expected, the ending result will be greater (a good thing). Reference: 7.5.1 in the License Exam Manual.

A bond with a par value of $1,000 and a coupon rate of 8% paid semi-annually, is currently selling for $1,150. The bond is callable in 10 years at $1,100. In the computation of the bond's yield to call, which of these would be a factor? A) Interest payments of $40. B) 60 payment periods. C) Present value of $1,100. D) Future value of $1,150.

Answer: A The YTC computation involves knowing the amount of interest payments to be received, the length of time to the call, the current price and the call price. A bond with an 8% coupon will make $40 semi-annual interest payments. With a 10-year call, there are only 20 payment periods, not 60. The present value is $1,150 and the future value is $1,100, the reverse of the numbers indicated in the answer choices. Reference: 7.5.2.1.4 in the License Exam Manual.

In order to compute an investor's after-tax return on a corporate bond, all of the following are necessary EXCEPT: A) inflation rate. B) interest payments. C) appreciation. D) marginal tax bracket.

Answer: A The after-tax return is computed by taking the total return (appreciation plus income) and taking the investor's tax rate into consideration. The inflation rate is necessary for the inflation-adjusted or real rate of return. Reference: 7.5.2.5 in the License Exam Manual.

Over the past 5 years, a stock has had returns of +16%, + 5%, -4%, +12% and +8%. This results in an arithmetic mean of: A) 7.4%. B) 8.0%. C) 8.2%. D) 9.0%.

Answer: A The arithmetic mean is the simple average of all of the numbers. When adding them together (remembering to subtract the one year of negative returns, we arrive at a total of 37 divided by 5 which is equal to 7.4%. Reference: 7.5.2.11.1 in the License Exam Manual.

One method used by some analysts to estimate the future value of a stock is the dividend growth model. This model would probably be most useful in the case of a: A) large-cap stock. B) small-cap stock. C) AAA corporate bond. D) cumulative preferred stock.

Answer: A The dividend growth model is a method to value the common stock of a company on the basis of assumed constant growth of dividends in the future. Therefore, it can only be applied to a corporation whose dividends might be expected to increase. It is far more likely that a large-cap stock will be paying dividends than a small-cap. Bonds don't pay any dividends and, in any event, their interest, just like the dividends on preferred stock, is fixed; there is no growth possible. Reference: 7.5.2.10.2 in the License Exam Manual.

If you knew a given stock had a 40% chance of earning a 10% return, a 40% chance of earning 20%, and a 20% chance of earning -10%, the stock would have a(n): A) expected rate of return of 10%. B) total return of 10%. C) annualized return of 10%. D) real rate of return of 10%.

Answer: A The expected return is computed by taking the probability of each possible return outcome and multiplying it by the return outcome itself. In this example, if you knew a given stock had a 40% chance of earning a 10% return, a 40% chance of earning 20%, and a 20% chance of earning -10%, the expected return would be equal to 10%: = (0.4 × 0.1) + (0.4 × 0.2) + (0.2 × -0.1), = .04 + .08 = .12 − .02, = 0.10, = 10%. You will not have to do this calculation on the exam, but you should know the concept. Reference: 7.5.2.7 in the License Exam Manual.

An investor purchases 100 shares of RIF common stock. In the year following the purchase, the RIF shares appreciated by 12% and paid a 2% dividend. If inflation, as measured by the CPI, was at a 4% rate, the investor's total return on the RIF shares is closest to: A) 14%. B) 8%. C) 10%. D) 12%.

Answer: A This question is asking for the total return which is 14% (12% appreciation + 2% dividend). Had the question asked for the inflation-adjusted return, (which it doesn't), that is 14% minus the 4% CPI. Reference: 7.5.2.6 in the License Exam Manual.

The holding period return (HPR) on a share of stock is equal to: A) the capital appreciation plus the dividend yield over the period. B) the capital appreciation minus the inflation rate over the period. C) the current yield plus the dividend yield. D) the dividend yield plus the risk premium.

Answer: A To compute holding period return, you calculate the total return for that holding period. Total return combines any dividend income plus appreciation (or minus depreciation). Reference: 7.5.2.3 in the License Exam Manual.

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 the: A) future value of the $25,000. B) internal rate of the return on the $25,000. C) present value of $25,000. D) net present value of the $25,000.

Answer: A 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. Reference: 7.5.1.1 in the License Exam Manual.

Your client has $10,000 to invest and expects to earn an after-tax return of 8% to send his daughter to college in 12 years. Which of the following items will help determine whether the investment is likely to satisfy the client's goal? A) Expected cost of college. B) Present value. C) Consumer Price Index. D) Client's marginal federal income tax bracket.

Answer: A To determine whether the investment will satisfy the goal, the investment adviser representative needs to know the amount needed to pay for college. While the investment will be worth $25,181.70, this may not be enough to pay for even one year of college 12 years from now. Reference: 7.5.1.1 in the License Exam Manual.

During your annual review with a client, you go over all of the year's transactions. The beginning of the year balance in the account was $3,000. The client purchased 100 shares of ABC on February 1st at $30 per share and sold it on June 1st at $33 per share. During that period, ABC paid one quarterly dividend of $.30. The client used the proceeds of the ABC sale to purchase 66 shares of DEF on June 15th at $50 per share and sold it on December 15th at $60 per share. DEF pays quarterly dividends of $.25 on the first of each month on a cycle beginning with February. Based on this information, you would inform the client that the account's total return is: A) 34.10%. B) 46%. C) 100%. D) 102.70%.

Answer: A Total return in an account is computed by taking all income plus capital gains and dividing that by the original investment. In this example, the client received a $.30 dividend on 100 shares ($30) and two $.25 dividends (August 1st and November 1st) on 66 shares ($33). Add that $63 of income to the gain of $300 on the first transaction, and $660 on the second, to come up with a total of $1,023 divided by $3,000, which equals a total return of 34.1%. Reference: 7.5.2.2 in the License Exam Manual.

An investor buys a 5% AA-rated corporate bond. After 1 year, if his total return on the position is 4%, the most likely explanation for this is: A) interest rates increased causing the bond price to decrease. B) the bond rating was downgraded. C) interest rates decreased causing the bond price to increase. D) the investor paid accrued interest when he bought the bond diminishing his first year's return.

Answer: A Total return is computed by adding together the income received plus any capital gain or loss. Since the bond is purchased at par, selling the bond at a loss is the only way the investor's total return could be less than the coupon rate. When interest rates go up, bond prices go down. Reference: 7.5.2.2 in the License Exam Manual.

If the required rate of return is less than anticipated in a present value calculation, the effect would be that the: A) present value would be higher. B) present value would be lower. C) future value would be lower. D) yield to maturity would decrease.

Answer: A Try to follow me on this one. The present value computation is used to determine how much money must be deposited NOW (present) to reach a specified future goal when you know how many years you have to reach that goal. One critical component of the formula is the rate of return used in the formula. As a simple example, if you need $100,000 eighteen years from now for your newborn's college education and you expect to earn 8%, you'll have to deposit $25,000 now (present value) to reach the goal. However, if it turns out that the earnings rate is less than anticipated, say only 4%, then you would have to deposit twice as much presently. Therefore, we answer this question by indicating that a lower rate of return will require a higher present value. Reference: 7.5.1.2 in the License Exam Manual.

An investor is looking at the past performance of a security over the past five years. The chart looks like this: 2006-10% 2007-15% 2008-3% 2009-11% 2010-6% The average return over this period is 9%. This would be properly referred to as the: A) arithmetic mean. B) geometric mean. C) internal rate of return. D) median return.

Answer: A When a true average return is shown, that is the arithmetic mean. The median return (the number in the middle of the group of five) is 10%. Reference: 7.5.2.11.1 in the License Exam Manual.

When it comes to computing market returns, it is TRUE to state that A) the median is always higher than the geometric mean B) the geometric mean could never be greater than the arithmetic mean C) the median is always lower than the average D) the mode is always higher than the mean

Answer: B Because the geometric mean always involves taking a "root" of the product of the numbers rather than an average, it is either the same or lower (can never be higher) than the arithmetic (average) mean. Here it is very simply: 1 + 2 = 3. The arithmetic mean is 3/2 = 1.5. For the geometric mean, we multiply 1 × 2, and then take the square root of the product (the square root of 2), which is 1.414. If we took returns of 1%, 2%, and 4%, we would have 1 + 2 + 4 = 7/3, for an average of 2.34%. However, the geometric mean would be the cube root of 1 × 2 × 4. That product is 8, and its cube root is 2%. You will not have to compute a geometric mean; just know how it compares to the arithmetic mean. As far as the others, the median could be the same (higher or lower than the average), and the same is true of the mode. There is no statistical relationship between the median and the geometric mean. That is, the median could be higher or lower, but not generally the same. Reference: 7.5.2.11 in the License Exam Manual.

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 the initial investment. 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 interest.

Answer: B 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. Reference: 7.5.1.1 in the License Exam Manual.

An investor purchased stock for $50 per share at the beginning of the year. In December, the investor liquidated his stock for $55 per share, while also receiving dividends of $2 per share during the year. Assuming an inflation rate of 3%, what is the investor's real rate of return? A) 14%. B) 11%. C) 4%. D) 10%.

Answer: B Given the fact the client liquidated his shares at a price of $55, we can conclude that he attained a 10% ($5 profit ÷ $50 initial investment) return based on capital appreciation of the stock. He also received dividends of $2 per share giving him an additional return of 4% ($2 ÷ $50). By adding these two percentages together, we can conclude that his total return is 14%, less an inflation rate of 3%, which would give a real rate of return of 11%. Reference: 7.5.2.6 in the License Exam Manual.

In the formula for determining the real rate of return, the: A) marginal tax bracket is subtracted from the investment return. B) inflation rate is subtracted from the investment return. C) investment return is divided by the inflation rate. D) inflation rate is divided by the investment return.

Answer: B In computing the real rate of return, which represents inflation-adjusted compounding (or discounting), a formula is applied in which the rate of inflation (usually as measured by the CPI) is subtracted from the investor's rate of return. Reference: 7.5.2.6 in the License Exam Manual.

Using the net present value method, a potential investment should be undertaken if the present value of all cash inflows minus the present value of all cash outflows (which equals the net present value) is: A) positively correlated. B) greater than zero. C) less than zero. D) equal to zero.

Answer: B NPV compares the value of a dollar today to the value of that same dollar in the future, taking inflation and returns into account. If the NPV of a proposed investment is positive, it should be accepted. However, if NPV is negative, the investment should probably be rejected because cash flows will also be negative. Reference: 7.5.2.8 in the License Exam Manual.

Which of the following best describes net present value? A) The amount of money that must be invested today at some specified rate of return to equal a targeted value in a specified number of years. B) The difference between the sum of the discounted cash flows that are expected from an investment and its initial cost. C) The discount rate that results in a return of zero for a series of future cash flows. D) It is the true interest yield expected from an investment expressed as a percentage.

Answer: B Net present value is a computation taking into consideration future cash flows, discounted to the present, and comparing that to the capital investment necessary to obtain those flows. It is always expressed in monetary units and, if positive, indicates a potentially worthwhile investment. Reference: 7.5.2.8 in the License Exam Manual.

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 future value will not be able to be computed B) the present value was insufficient to meet the objective C) the accumulated value will meet the objectives D) the yield to maturity will be lower than anticipated

Answer: B 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). Reference: 7.5.1 in the License Exam Manual.

A bond with a par value of $1,000 and a nominal yield of 6% paid semi-annually is currently selling for $1,300. The bond matures in 25 years and is callable in 15 years at $1,080. In the computation of the bond's yield to call, which of these would be a factor? A) Future value of $1,300 B) Interest payments of $30 C) 50 payment periods D) Present value of $1,080

Answer: B The YTC computation involves knowing the amount of interest payments to be received, the length of time to the call, the current price, and the call price. With a 15-year call, there are only 30 semiannual interest payment periods, not 50. The present value is $1,300 and the future value is $1,080; the reverse of the numbers indicated in the answer choices. Reference: 7.5.2.1.4 in the License Exam Manual.

A customer purchases stock for $40 per share and holds it for one year, selling it for $50 per share exactly 12 months after the date of purchase. Four quarterly qualifying dividends of $.50 were paid during the year. If the customer's tax bracket is 30%, what is the after-tax rate of return? A) 17.5%. B) 21.75%. C) 21%. D) 18.40%.

Answer: B The customer's return on the stock includes the $10 per share short-term capital gain ($50 − $40) plus the $2 qualifying dividend (quarterly dividend of $.50 × 4). After-tax rate of return is found by computing the total after-tax earnings. Short-term gains are taxed at the same rate as ordinary income, and qualifying dividends are taxed at a maximum rate of 15% (except for very high income earners - not tested). The tax on the $10 gain is $3, and the tax on the $2 dividend is $.30. The investor's total return is the $12 total minus the $3.30 in taxes, or $8.70; $8.70 divided by the original investment of $40 results in an after-tax return of 21.75%. Reference: 7.5.2.5 in the License Exam Manual.

Which of the following is a method for determining the appropriate market price of a common stock based on the present value of all future dividends to be paid on that stock? A) Net present value. B) Dividend discount model. C) Dividend payout ratio. D) Price/earnings ratio.

Answer: B The dividend discount model (DDM) calculates the present value of the future dividends that a company is expected to pay its shareholders. It uses that calculation to arrive at a projected market value of the common stock. Reference: 7.5.2.10.1 in the License Exam Manual.

Expected return is: A) the one discount rate that equates the future value of an investment with its net present value. B) an estimate of probable returns an investment may yield. C) the difference between an investment's present value and its cost. D) the worth of future income discounted to reflect what that income is worth today.

Answer: B The expected return is the estimate of probable returns that an investment may yield when taking the sum of all probabilities. Reference: 7.5.2.7 in the License Exam Manual.

If an investor buys a utility stock with a stable 5% dividend, and after a year the investor's total return in the stock is 10%, the most likely reason for this is the: A) stock price declined. B) the stock appreciated by 5%. C) company doubled its dividend payment. D) investor reinvested the quarterly dividends.

Answer: B The most likely cause for the total return was an increase in the stock price. Reference: 7.5.2.2 in the License Exam Manual.

An investment is made of $10,000. At the end of the year, $500 in non-qualifying dividends has been received and the value of the investment is $10,500. If the investor is in the 30% tax bracket, the after-tax yield is: A) 8.5% B) 3.5% C) 5.0% D) 6.5%

Answer: B The only return (as far as yield is concerned) is the $500 of dividends. Remember, non-qualifying dividends do not "qualify" for the 15% rate. Subtracting 30% for taxes leaves $350 which, when divided by the $10,000 initial cost, is an after-tax yield of 3.5%. If the question had asked about total return, then the $500 unrealized profit would have been included, although there would have been no tax on it. Reference: 7.5.2.5 in the License Exam Manual.

The real interest rate of a fixed income investment is the: A) interest earned adjusted for the investment's premium or discount price. B) interest earned after inflation. C) coupon interest payment. D) interest earned after taxes.

Answer: B The real interest rate is the interest received minus the inflation rate. Reference: 7.5.2.6 in the License Exam Manual.

In order to compute an investor's real rate of return on a common stock holding, all of the following are necessary EXCEPT: A) appreciation. B) marginal tax bracket. C) dividends. D) inflation rate.

Answer: B The real rate of return is another term for inflation-adjusted return. It is the total return, which is appreciation plus income adjusted for the inflation rate as expressed by the CPI. Tax bracket is necessary to compute after-tax return. Reference: 7.5.2.6 in the License Exam Manual.

In order to compute the real rate of return for a security, it would be necessary to know all of the following EXCEPT A) the purchase price. B) the beta of the security. C) the CPI. D) the annual dividend.

Answer: B The real rate of return is the actual return less the inflation rate as measured by the CPI. Reference: 7.5.2.6 in the License Exam Manual.

The formula for real rate of return would most likely be used when the adviser wishes to: A) analyze investment returns in terms of uneven cash flows. B) measure inflation-adjusted performance. C) measure after-tax investment performance. D) measure risk-adjusted performance.

Answer: B The real return formula measures inflation-adjusted performance. Reference: 7.5.2.6 in the License Exam Manual.

A client purchased a security for $60 and sold it one year later for $59. If he received 4 quarterly dividends of $.50 each during the period, his total percentage return would be: A) 3.30% B) 1.67%. C) 0%. D) 2%.

Answer: B The total return on an investment is the sum of the capital gains/losses plus any income distribution such as dividends or interest. In this case, the client had a capital loss of $1 ($60 − $59 = $1) which was offset by $2 (4 × $.50 = $2) in dividend distributions for a total dollar return of $1. In percentage terms, the return is calculated by dividing the dollar return amount by the total invested or $1 divided by $60 = 1.67%. Reference: 7.5.2.2 in the License Exam Manual.

The true rate of return on a bond is the nominal rate minus: A) the margin rate. B) the inflation rate. C) the prime rate. D) the discount rate.

Answer: B The true rate of return on a bond considers the inflation rate because inflation reduces the purchasing power of the interest payments. Reference: 7.5.2.6 in the License Exam Manual.

An investment of $1,000 made 10 years ago is now worth $4,000. Using the Rule of 72, the approximate compounded annual rate of return is A) 40%. B) 14.4%. C) 7.2%. D) 25%.

Answer: B This investment has quadrupled in 10 years. Using the Rule of 72, we know how to compute the rate of return when an investment doubles. This one has doubled every 5 years. Dividing 72 by 5 years gives us an approximate rate of 14.4%. Reference: 7.5.1.3 in the License Exam Manual.

When using the Dividend Discount Model, A) best results are obtained from stocks that pay irregular dividends B) future expected dividends are discounted to compute the present value of the stock C) the discount rate is generally lower than the expected rate of return D) a higher degree of accuracy in forecasting stock prices is obtained with preferred stock

Answer: B This method of common stock valuation takes the investor's expected future dividend returns and then discounts that amount by the expected rate of return to arrive at the supposed present value. Expected (or required) rate of return is a component of both the Dividend Discount Model and the Dividend Growth Model, and neither Model is used for preferred stocks because the dividend can never increase. When using any dividend model, the greater the regularity of dividends, the more accurate the forecast. Reference: 7.5.2.10.1 in the License Exam Manual.

What is the total return on a 1-year, newly issued (365 days to maturity) zero-coupon bond priced at 950? A) 5.26% plus the implied coupon rate. B) 5.26% C) The return cannot be determined without knowing current interest rates. D) 5.00%

Answer: B To determine the total return on this zero-coupon bond, the $50 capital appreciation is divided by the cost of the bond (in this case, $50 divided by $950 equals a total return of 5.26%). Total return of a zero-coupon bond is made up entirely of the difference between the cost of the bond and the sale or maturity price of the bond. Reference: 7.5.2.2 in the License Exam Manual.

Which of the following methods of calculating investment returns are discounted cash flow (DCF) techniques? I. Net present value (NPV). II. Holding period return (HPR). III. Internal rate of return (IRR). A) II and III. B) I, II and III. C) I and III. D) I and II.

Answer: C A discounted cash flow (DCF) technique is one that takes into account the time value of money. Holding period return (HPR) is the total of the income cash flows and capital growth earned by an investment during the period for which it is held. It does not take into account the time value of money. Both net present value (NPV) and internal rate of return (IRR) take the time value of money into account. Reference: 7.5.2.9 in the License Exam Manual.

Early in the year, an investor purchased 100 shares of KAP common stock at a price of $60 per share. Just before the end of the year, after receiving three quarterly dividends of $1, the investor liquidated all of the KAP at a price of $59 per share. If the CPI increased by 3%, the investor's total return over the holding period was: A) 2%. B) 5%. C) 3.33%. D) 0.33%.

Answer: C An investor's total return is computed by adding together income plus capital gain (loss). In this case, the investor received $3 in dividends and lost $1. That resulted in a total return of $2, which, when divided by the $60 cost, results in a percentage return of 3.33%. Even though the CPI is given, the question is not asking for inflation adjusted or real rate of return. Reference: 7.5.2.2 in the License Exam Manual.

An IAR is comparing an investment in two securities by computing the net present value of each. The available funds for investment are $20,000, and the NPV of choice A is $21,223, while that of choice B is $18,946. Based on this information, it would be correct to state that A) choice A would result in a capital loss B) choice B would result in a capital gain C) choice A would be the more attractive choice D) choice B would result in an increase in present wealth if held to maturity

Answer: C Anytime the NPV is higher than the cost of the investment, you will have made a profitable investment. Therefore, purchasing choice A would result in an increase to the investor's present wealth. Reference: 7.5.2.8 in the License Exam Manual.

All of the following statements regarding an investment's internal rate of return (IRR) are true EXCEPT: A) investments are acceptable when their internal rates of return exceed the investor's required rate of return. B) IRR is the one rate of return that results in an investment having a net present value (NPV) of zero. C) IRR can easily be calculated for investments with uneven cash flows. D) IRR expresses the rate of interest that matches the initial investment with the present value of future cash flows.

Answer: C IRR is the rate of interest that equates the initial investment with the present value of future cash flows; it is the rate of return that results in an investment having a net present value of zero. It is possible, although difficult, to calculate IRR for investments with uneven cash flows. That is why it is used primarily with debt securities and common stocks with stable dividends. Reference: 7.5.2.9 in the License Exam Manual.

One measure of an investor's total return is called holding period return. The computation includes both income and appreciation and is used for both debt and equity securities. An investor's holding period return would exceed the bond's yield to maturity if: A) the investor purchased a put option on the bond. B) the bond was redeemed at a discount. C) the coupons were reinvested at a rate exceeding the yield to maturity. D) the bond was called at a premium.

Answer: C The calculation of yield to maturity assumes reinvestment of the bond's interest at the coupon rate. Therefore, if the investor were able to do better than that, the holding period return would be increased. This is part of the concept of internal rate of return (IRR) which takes into consideration the time value of money (compounding). It is tempting to answer a call at a premium and that might, in fact, increase the total return, but we have no idea when the call takes place, at what price and the original purchase price of the bond. Just keep it simple - if the question says you can earn more than the YTM, your return will be higher than the quoted YTM. Reference: 7.5.2 in the License Exam Manual.

When analyzing a specific common stock, the expected return is: A) computed using the Sharpe ratio. B) the extent to which the net present value exceeds the internal rate of return. C) the sum of a probability distribution of possible returns. D) the projected annual dividend divided by the current market price.

Answer: C The expected return is computed by taking the probability of each possible return outcome, multiplying it by the return outcome itself, and then adding them all together. For example, if you knew a given stock had a 40% chance of earning a 10% return, a 40% chance of earning 20%, and a 20% chance of earning -10%, the expected return would be equal to 10%, as illustrated below: = (0.4) (0.1) + (0.4) (0.2) + (0.2) (-0.1); = .04 + .08 = .12 − .02; = 0.10; and = 10%. If you were trying to compute the expected return for a portfolio (more than one security), then you would take the average of the individual results to get an overall expected return. You will not have to do this calculation on the exam, but you should know the concept. Reference: 7.5.2.7 in the License Exam Manual.

The future value of an invested dollar is dependent upon I. the exchange rate of the dollar at the beginning and end of the period. II. interest rate at maturity. III. the rate of return it earns. IV. the time period over which it is invested. A) I and III. B) II and III. C) III and IV. D) I and II.

Answer: C The future value of a dollar reflects the interest rate it earns over a period of time. The rate of foreign exchange is not related to or used in the calculation of the future value of a dollar. Reference: 7.5.1.1 in the License Exam Manual.

A measurement of investment return that takes the time value of money into consideration is A) real rate of return B) risk-adjusted rate of return C) internal rate of return (IRR) D) holding period return

Answer: C The internal rate of return compounds returns and takes into consideration the time value of money. Real rate of return considers the inflation rate and risk-adjusted return is another way of stating the Sharpe Ratio. Reference: 7.5.2.9 in the License Exam Manual.

One way in which internal rate of return (IRR) differs from most return computations is that A) it is always an annualized rate of return B) its application to debt securities is limited C) it takes into consideration the time value of money D) it takes into consideration the rate of inflation

Answer: C The internal rate of return compounds returns and takes into consideration the time value of money. Real rate of return considers the inflation rate. Reference: 7.5.2.9 in the License Exam Manual.

Over the past five years, an investor's portfolio has shown returns of 6%, 4%, 11%, 10%, and 4%. Which of the following statements is correct? I.The mean return is 7% II.The median return is 6% III.The mode is 4% IV.The range is 7% A) I and II B) III and IV C) I, II, III, and IV D) I, II, and III

Answer: C The mean is the average return. Add these five numbers together and the total is 35% over a five-year period. That is an average (or mean) return of 7% (35 divided by 5). The median is the return that has as many above as below and, in this case, would be 6% (4, 4 below and 10, 11 above). The mode is the return that appears the most often and, with two of the five at 4%, that is the mode. The range is the difference between the highest and lowest returns. In this case, from the high of 11% to the low of 4% is a range of 7%. Reference: 7.5.2.11 in the License Exam Manual.

An analyst has been charting previous 9 year's returns for a stock and displays the following results: 5%, 5%, 8%, -3%, 10%, 12%, 5%, 17% and 22%. If you were asked the mode of these returns, you would reply: A) 9%. B) 10%. C) 5%. D) 8%.

Answer: C The mode of a series of number is that number that has the largest number of occurrences. In this case, 5% appears three times, more than any other number. Note that the mode is not similar to the mean (in this example 9%) or the median (in this case 8%). Reference: 7.5.2.11.3 in the License Exam Manual.

Which of the following securities has an easily determinable internal rate of return? A) 5% municipal bond. B) 6% Ginnie Mae. C) Zero-coupon bond. D) 7% corporate bond.

Answer: C The only security that does not have reinvestment risk (the risk that periodic interest payments cannot be reinvested at the same yield as the bond providing the interest payments) is a zero-coupon bond such as Treasury STRIPS. With a zero-coupon bond, there are no periodic interest payments to reinvest, so a yield can be locked in. The interest rate that discounts the redemption price (par) to the discounted purchase price is the locked-in yield, which is the same as the internal rate of return, also referred to as the yield to maturity. Reference: 7.5.2.9 in the License Exam Manual.

Over the past 5 years, a stock has had returns of +16%, +5%, -4%, +12% and +8%. The mid-range value of this stock's returns is: A) +8.2%. B) +9.0%. C) +6.0%. D) +7.4%.

Answer: C The range of a stock's performance is the low to the high, in this case, -4% to +16%. The mid-range is that number that is exactly in the middle of the range. With a range of 20 points, the midpoint is going to be the high minus 10 or the low plus 10. +6.0% is 10 points higher than the low and 10 points lower than the high. Reference: 7.5.2.11.5 in the License Exam Manual.

Using the following information, compute the real rate of return for an investor holding the ABC Corporation's 20-year bond: Coupon rate 5%, paid semi-annually Rating Aa Maturity date December 1, 2026 CPI 2% Par value $1,000 Purchase price 90 Call date December 1, 2023 Call price 101 A) 4.50%. B) 5.00%. C) 3.56%. D) 2.50%.

Answer: C The real rate of return is the actual return (income received divided by the purchase price) less the inflation rate as measured by the CPI. In this example, the bond pays $50 per year on an investment of $900. That is an actual return of 5.56%. Subtracting the CPI of 2% gives us an inflation-adjusted, or real, rate of return of 3.56%. Reference: 7.5.2.6 in the License Exam Manual.

An analytical tool used to predict the future price of a common stock using projected dividends is the: A) future value computation. B) dividend payout ratio. C) dividend discount model. D) price/earnings ratio.

Answer: C There are two widely accepted forms of common stock price projection using dividends - the dividend discount model and the dividend growth model. Reference: 7.5.2.10 in the License Exam Manual.

An investor purchases 100 shares of Kapco stock at $50 per share. At the time of the purchase, the stock is paying a quarterly dividend of $.25. The dividend increases 5% each year over the next five years. The purchaser sells the 100 shares five years after purchase for $82 per share. What is the total return for the investor over the five years holding period? A) 11%. B) 74%. C) 75%. D) 10%.

Answer: C Total return includes capital appreciation plus income. The capital gain realized was $32 per share. The income was $1.00 per share (four quarterly dividends of $.25) the first year, 5% higher the second year ($1.05) and 5% higher each successive year. The total of the dividends received is $5.53. Adding that to the $32, we compute by dividing $37.53 by $50 resulting in a 75% total return. Reference: 7.5.2.3 in the License Exam Manual.

On June 20, 2003, an investor in the 30% marginal federal tax bracket acquired a growth stock paying no dividend for $10 per share. On June 22, 2004, the investor sold the stock for $20 per share. Presuming capital gains rates are 15%, the investor's after-tax rate of return is closest to: A) 70%. B) 100%. C) 200%. D) 85%.

Answer: D Although the stock grew at a 100% rate of return (by doubling), the investor must pay capital gains tax on the investment at 15%, and the investor realizes an after-tax rate of return of approximately 85%. Because the investor held the stock for more than one year, the sale is taxed at a favorable capital gains rate rather than at the investor's ordinary income tax rate. Reference: 7.5.2.5 in the License Exam Manual.

In order to calculate an investor's holding period return, it is necessary to know: I.value of the portfolio at the beginning of the period. II.value of the portfolio at the end of the period. III.income received during the period. IV.capital appreciation or depreciation over the period. A) I and II. B) I, II, III and IV. C) III and IV. D) I, II and III.

Answer: D An investor's holding period return is the total return received over the specified holding period. That return includes any income plus or minus any gain or loss. In terms of calculating, when you know the beginning and ending values, that tells you the capital appreciation or depreciation. Reference: 7.5.2.3. in the License Exam Manual.

An investor owns a common stock that has been paying a $2.00 annual dividend. If the investor buys 100 shares of the stock at $50 and sells it 3 months later for $52, the approximate annualized rate of return is: A) 12%. B) 4%. C) 5%. D) 20%.

Answer: D Annualized rate of return is computed by taking the investor's total return and annualizing it. In this case, the investor had $2 of appreciation and $.50 (one quarter) in dividends. Total return of $2.50 divided by the $50 cost is 5%. But, that is for three months - one quarter. Multiply that by 4 to get the annual rate. Reference: 7.5.2.4 in the License Exam Manual.

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 and no maturity. C) Common stock does not have a net present value. D) Uneven cash flows, no maturity date and price.

Answer: D 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. Reference: 7.5.2.9 in the License Exam Manual.

Which of the following is NOT related to the variability of a portfolio's returns? A) Asset allocation. B) Market timing. C) Security selection. D) Total return.

Answer: D Let's analyze the question. A portfolio's future returns can vary, that is, fluctuate based on investment decisions made by the investor or adviser. The way the portfolio assets are allocated between different classes of securities will have an impact on the returns. Same is true with the timing of purchases or sales (buying stock when bad economic news is announced is probably not a good time). Finally, the specific securities selected will certainly impact the returns of the portfolio. That leaves total return. Total return is a measurement of the investor's past return on the portfolio. It measures what has happened and has no effect on future variability. Reference: 7.5.2.2 in the License Exam Manual.

Which of the following statements is NOT correct? A) Internal rate of return (IRR) is a method of determining the exact discount rate to equalize cash inflows and outflows, thus allowing comparison of rates of return on alternative investments of unequal size and investment amounts. B) Net present value analysis (NPV) is a commonly used time value of money technique employed by businesses and investors to evaluate the cash flows associated with capital projects and capital expenditures. C) Time-weighted returns show performance without the influences of additional investor deposits or withdrawals from the account. D) Net present value (NPV) is the difference between the initial cash outflow (investment) and the future value of discounted cash flows.

Answer: D Net present value (NPV) is the difference between the initial cash outflow (investment) and the present value of discounted cash flows (NPV = PV of CF − cost of investment). That is why it is called Net Present Value instead of Net Future Value. Reference: 7.5.2.8 in the License Exam Manual.

Those who place bonds in client's portfolios usually focus their attention on yields. For which of the following bonds would the yield to maturity be lower than the yield to call? A) A high-yield bond. B) A municipal bond. C) A bond selling at a premium. D) A bond selling at a discount.

Answer: D One of the contributing factors to the yield to maturity on a discounted bond is the realization of that discount. If a bond is called prior to maturity, that discount is realized sooner, thus increasing the yield. When the bond is selling at a premium, the reverse is generally true. Reference: 7.5.2.1.4 in the License Exam Manual.

One measure of an investor's total return is called holding period return. The computation includes both income and appreciation and is used for both debt and equity securities. An investor's holding period return would be less than the bond's yield to maturity if A) the bond was called at a discount B) the investor purchased a put option on the bond C) the bond was redeemed at a premium D) the coupons were reinvested at a rate below the yield to maturity

Answer: D The calculation of yield to maturity assumes reinvestment of the bond's interest at the coupon rate. Therefore, if the investor was only able to do less than that, the holding period return would be decreased. This is part of the concept of internal rate of return (IRR), which takes into consideration the time value of money (compounding). It is tempting to choose the answer "a call at a discount," but bonds are never called at a price below par. Just keep it simple: If the question says you can earn less than the YTM, your return will be lower than the quoted YTM. Reference: 7.5.2 in the License Exam Manual.

An analyst using the dividend growth model would take into account all of the following factors EXCEPT: A) the current dividend. B) the growth of the dividend. C) the investor's required rate of return. D) the current earnings per share.

Answer: D The dividend growth model is a stock valuation model that deals with dividends and their growth, discounted to today. The value of the stock equals next year's dividends divided by the difference between the required rate of return and the assumed constant growth rate in dividends. Reference: 7.5.2.10.2 in the License Exam Manual.

An investor purchases shares of ABC stock at $50 per share. One year later, ABC is selling for $54 per share and, at the end of the second year, the price is $52 per share. ABC has paid dividends of $2 per year. Upon liquidation, the investor would have earned a return of: A) $2 per share. B) $4 per share. C) $8 per share. D) $6 per share.

Answer: D The investor paid $50 and sold it for $52 for a $2 per share gain. During the two year holding period, $4 in dividends were paid. That is a total return of $6 per share. Reference: 7.5.2.2 in the License Exam Manual.

An investor purchased 100 shares of ABC at $50 per share and sold them exactly four months later at $52 per share. The investor's holding period return was: A) 2%. B) 12%. C) 16%. D) 4%.

Answer: D The investor's return was a profit of $2 on an investment of $50. This is a return for the period held of 4%. Reference: 7.5.2.3 in the License Exam Manual.

A corporation is considering a substantial capital expenditure for new equipment. Using the net present value (NPV) technique, the corporation will consider this investment to be acceptable if the net present value of the investment is: A) less than zero. B) equal to zero. C) less than its after-tax return. D) greater than zero.

Answer: D The net present value (NPV) of an investment is the difference between the present value of the investment's cash inflows and the amount of the investment outlay. An investment is acceptable only if the net present value is greater than zero-that is, if the present value of the expected returns is greater than the amount of the investment outlay. Reference: 7.5.2.8 in the License Exam Manual.

When an investor's original value is subtracted from the ending value, and then has the income received over that time period added to it which is then divided by the original cost, the result is: A) expected return. B) internal rate of return. C) annualized return. D) holding period return.

Answer: D This is the method of computing holding period return. Reference: 7.5.2.3 in the License Exam Manual.

An investor invests a total of $30,000 and creates a portfolio of three different stocks placing one third of his investment into each security. From his holding in Company A, he receives a dividend of $600; from Company B, a dividend of $500 and from Company C, no dividend. One year later, A has increased by 20%, B by 10% and C has remained the same. What is this investor's total return on this portfolio? A) 3.67% B) 10% C) 4.56% D) 13.67%

Answer: D Total return includes both income (dividends) and appreciation. In this case, the total income was $1,100 and the appreciation was $3,000 (20% of $10,000 = $2,000 and 10% of $10,000 = $1,000). That is a total return of $4,100 on an investment of $30,000, or 13.67% Reference: 7.5.2.2 in the License Exam Manual.

What is the total return on a bond that cost an investor $950, was sold for $1,000, and paid $50 in interest payments? A) 5%. B) 10%. C) The return cannot be determined from the information supplied. D) 10.50%

Answer: D Total return is the sum of all payments ($50) plus the capital gains ($50) divided by the cost ($950). In this case, $50 + $50 ÷ $950 = .10526 or 10.5%. Reference: 7.5.2.2 in the License Exam Manual.

One of the important roles of an investment adviser representative is assisting clients in analyzing the performance of securities held in their portfolios. Which of the following is the best measurement of a security's performance? A) Yield B) Beta C) Standard deviation D) Total return

Answer: D Total return reflects the entirety of a security's performance because it includes both income and capital appreciation. Beta and standard deviation are risk measurements and, while they may be used to evaluate a security's performance when compared to the risk taken, they don't truly provide a measurement as does total return. Reference: 7.5.2.2 in the License Exam Manual.

Under the net present value (NPV) method of evaluating investments, an investment is acceptable if the net present value of the expected returns is A) less than zero B) equal to zero C) greater than the risk-adjusted return D) greater than zero

Answer: D Under the net present value (NPV) approach, an investment is acceptable only if the net present value of the expected returns is greater than the amount of the investment outlay. In other words, an investment is acceptable (it will add value) if the net present value is greater than zero. On the other hand, if the NPV is negative (less than zero), it would not be acceptable (it will subtract value) and should not be undertaken. Reference: 7.5.2.8 in the License Exam Manual.

Mr. and Mrs. Rose, advisory clients of yours, request a meeting with you to discuss the options available if they wish to deposit a lump sum to save for college tuition for their child. All of these would be factors to consider EXCEPT: A) current college costs. B) the expected inflation rate. C) the age of the child. D) the Rose's salary.

Answer: D When making a lump sum investment, salary is not a factor. The funds will have to come out of savings or investments. This is basically a present value computation. In order to project how much will be needed, we need to know what the current tuition is, the rate at which it is expected to inflate, and the number of years we have until the child starts college. That will give us the three components of present value: total amount needed, earnings rate, and length of investment. Reference: 7.5.1.2 in the License Exam Manual.

A bond's yield to maturity reflects its A) nominal return. B) return based on annual interest as a percentage of current price. C) taxable equivalent return. D) internal rate of return.

Answer: D Yield to maturity reflects the internal rate of return on a bond. Internal rate of return (IRR) equates the cost of an investment to the cash flows produced by that investment. Reference: 7.5.2.9 in the License Exam Manual.