FAC Module 2

If an investment of $400,000 were to grow to $5,000,000 over a period of 20 years, what is the stated annual rate at which it must be invested, given that the return is compounded semiannually?

13.04% PV = −$400,000; FV = $5,000,000; N = (20)(2) = 40; CPT I/Y: I/Y = Semiannual discount rate = 6.52% Stated annual rate = 6.52 × 2 = 13.04%

The 4th quintile for the following distribution of returns is closest to: 8%, 6%, 12%, 18%, 25%, 8%, 9%, 17%, 14%, 10%

17.8% First rearrange the data in ascending order: 6%, 8%, 8%, 9%, 10%, 12%, 14%, 17%, 18%, 25% Quintiles are fifths (1/5) so the 4th quintile is 80% of the observations. Using this formula:Ly=(n+1)y/100 Ly=(10+1)*80/100=8.8th item This means that when the data is arranged in ascending order, the 4th quintile is 8th data point from the left plus 0.8 times the distance between the 8th and 9th values: = 17 + 0.8(18 - 17) = 17.8%

A parameter is defined as:

A descriptive measure of a population characteristic.

A distribution that has a kurtosis of 3 is known as:

Mesokurtic

The geometric mean return approximately equals:

The arithmetic mean return minus half the variance of returns.

If two events are mutually exclusive:

The probability of both of them occurring equals zero.

It is Jim's birthday and he has thrown a party for his friends. Everyone except Henry has arrived. George states that the chances of Henry showing up on the party are only 10%. If Jim bets a dollar against George that Henry will show up, his expected return from the bet would be:

$0 The expected return on a bet according to the stated odds is always zero and is calculated as: (−$1)(0.9)+($9)(0.1)=0

Given a discount rate of 3%, the value as of the end of Year 5 of the following cash flow stream is closest to: Year 0−$200Year 1$150Year 2$250Year 3−$100Year 4$400Year 5−$75

$441.06 FV = [−200 × (1.03)5] + [150 × (1.03)4] + [250 × (1.03)3] − [100 × (1.03)2] + [400 × 1.03] −75 FV = $441.063

The probability function for a random variable is given as p(x) = x/100. The set of possible values that the random variable, X, can take is given by X = (10, 20, 30, 40). For other values of x, p(x) = 0. p(10) equals:

0.1 p(10) = 10/100 = 0.1

The probability function for a random variable is given as p(x) = x/100. The set of possible values that the random variable, X, can take is given by X = (10, 20, 30, 40). For other values of x, p(x) = 0. F(40) equals:

1 F(40) = p(10) + p(20) + p(30) + p(40) = 0.1 + 0.2 + 0.3 + 0.4 = 1.0

An investment of $1,000 appreciates to a value of $1,450 in 3.5 years. What is the continuously compounded annual return on this investment?

10.62% rcc = [ln(HPR + 1)]/ t. Therefore, rcc = [ln(0.45 + 1)]/ 3.5 = 10.62%

Which of the following measurement scales should most likely be used to measure cash dividends per share?

Nominal scale. Ordinal scale. Ratio scale. Cash dividends per share can be best measured on a ratio scale. Ratio scales have a true zero point as the origin. For the variable in question, zero represents the absence of dividends.

Which of the following statements is most accurate?

The longer the time period until the future amount is received, the higher its present value The higher the discount rate, the higher the present value of the amount The shorter the time period until the future amount is received, the higher its present value <-- For a given interest rate, the present value increases as the number of periods decreases. For a given number of periods, the present value decreases as the interest rate increases.

A deposit of $1 million earns a return of 5% compounded continuously for 8 years. The future value is closest to:

$1,492,000 The future value is given by:FVN=PVerS×N=$1,000,000e0.05×8=$1,491,825 Note: To find the programmed value of "e" on your CFA Institute-approved financial calculator, use the keystrokes: HP-12C 1 g ex 2.7183 BA II Plus 1 2nd [ex] 2.7183

A company takes a loan of $200,000 at an interest rate of 12%. The loan must be paid back in 7 years through equal end-of-year annual installments. The value of principal outstanding after the second payment has been made is closest to:

$157,974 PV = $200,000; N = 7; I/Y = 12; CPT PMT: PMT = $43,823.55 Amortization table YearBalanceInterestPaymentPrinciple RepaidEnd Balance1$200,000$24,000.0$43,823.55$19,823.6$180,176.52$180,176.5$21,621.2$43,823.55$22,202.4$157,974.09 An easier way to solve this question is to simply compute the PV of the remaining payments at the end of Year 2. N = 5; I/Y = 12; PMT = −$43,823.55; CPT PV; PV = $157,974.09

At a 100% annual interest rate, a rational investor would be indifferent about choosing between receiving $20 today and:

$160 after 3 years At an interest rate of 100%, $20 will be worth $40 in 1 year, $80 in 2 years, and $160 in 3 years.

An investor expects to receive $79 at the beginning of each year for 3 years. The first payment will be received 5 years from today. Given a discount rate of 6%, the present value of the annuity is closest to:

$167.26 With the calculator in BGN mode: PMT = $79; N = 3; I/Y = 6; CPT PV; PV = −$223.83 The present value of the annuity due at the end of Year 5 equals: $211.17 × 1.06 = $223.84 Finally, calculate the present value of this amount: FV = −$223.84, N = 5, I/Y = 6, CPT PV; PV = $167.26

Juan Carlos wants to save money for his son's college tuition. His son will start college after 10 years and Carlos expects to make annual payments of $12,500 at the beginning of each year for a 5-year study program, with the first payment to be made at the beginning of Year 11. Given a discount rate of 12%, the amount that Carlos must deposit at the end of each of the next 10 years is closest to:

$2,876 With the calculator in BGN mode: N = 5; I/Y = 12; PMT = −$12,500; CPT PV; PV → $50,466.867 With the calculator in END mode: N = 10; I/Y = 12; FV = −$50,466.867; CPT PMT; PMT → $2,875.81

An investment of $3,000 is made at the beginning of each of the next 7 years. Given an interest rate of 0.67%, the value of this investment 11 years from today is closest to:

$22,154 This cash flow stream is an annuity due. With the calculator in BGN mode: PMT = −$3,000; N = 7; I/Y = 0.67; CPT FV; FV = $21570.41 The future value of the cash flow stream after another 4 years (Year 11) equals: N = 4; I/Y = 0.67; PV = −$21,570.41; CPT FV; FV = $22,154.32

Brian will receive $1,000 at the end of each year for the next 21 years. Given that the interest rate is 8%, the value of these payments 43 years from today is closest to:

$274,126 N = 21; PMT = $1,000; I/Y = 8; CPT FV; FV = −$50,423 This is the future value of the cash flow stream after 21 years. Next we must determine the value of these payments after another 22 years. N = 22; PV = −$50,423; I/Y = 8; CPT FV; FV = $274,126

An annuity pays $12,000 every year for 5 years with the first payment at the end of Year 4. Given a 13% discount rate, the present value of this annuity is closest to?

$29,251 we first find the present value (at the end of Year 3) of the 5 year annuity, and then discount it for another 3 years to compute its PV today. Step 1: PMT = $12,000; N = 5; I/Y = 13; CPT PV; PV = −$42,206.77 Step 2: FV = −$42,206.77; N = 3; I/Y = 13; CPT PV; PV = $29,251.41

Bill wants to accumulate $15,000 in 4 years by making 4 equal end-of-year deposits. Given that the interest rate is 7%, what is the minimum amount that he should deposit each year?

$3,378 FV = $15,000; I/Y = 7; N = 4; CPT PMT; PMT= −$3,378 Note: Your calculator must be in END mode.

Given a discount rate of 3%, the present value of the cash flow stream presented below is closest to: Year 0−$1,100Year 1$1,500Year 2$750Year 3−$1,000Year 4$4,000Year 5−$275

$3,464.85 [CF] [2ND] [CE|C] 1,100 [+|−] [ENTER] [↓] 1,500 [ENTER] [↓] [↓] 750 [ENTER] [↓] [↓] 1,000 [+|−] [ENTER] [↓] [↓] 4,000 [ENTER] [↓] [↓] 275 [+|−] [ENTER] [NPV] 3 [ENTER] [↓] [CPT] NPV = $3,464.847

Sarah wants to start college after 5 years, for which she wants to accumulate money by making annual deposits in her bank account beginning at the end of Year 1. She estimates that she will have to make a payment of $8,000 at the beginning of each year through the 4-year study program, with the first payment to be made at the beginning of Year 6. Given a discount rate of 11%, the amount that must be deposited at the end of each year for the next 5 years to satisfy the eventual payment obligations is closest to:

$4,424 With the calculator in BGN mode: N = 4; I/Y = 11; PMT = −$8,000; CPT PV; PV → $27,549.72 (PV of obligations at the end of Year 5/ Beginning of Year 6) With the calculator in END mode: N = 5; I/Y = 11; FV = −$27,549.72 (required amount); CPT PMT; PMT → $4,423.67

A company pays a $2 per share annual dividend on its preferred stock. Given that the required rate of return is 5% and that this dividend policy will continue forever, the value of the preferred stock today is closest to:

$40 The value of preferred stock equals D/P = 2 / 0.05 = $40.

An annuity pays $50,000 annually at the beginning of each year for 15 years. If the discount rate equals 8%, the present value of the annuity is closest to:

$462,212 Switch your calculator to BGN mode. PMT = −$50,000; I/Y = 8; N = 15; CPT PV; PV = $462,211.85

Mary invested $3,000 in an account with an interest rate of 15% compounded continuously. After 5 years, the value of her investment will be closest to:

$6,351 FV= PVert PV = $3,000; r = 0.15; t = 5 FV = $6,351

An investment of $500 will be made 3 years from today. Given an interest rate of 7.25%, the value of this investment 40 years from today will be closest to:

$6,663 One year from today is t=1, so 3 years from today is t=3. Therefore, 40 years from today is t=40 and t=40-3=37 years from the time payment is made. The future value of the payment is: PV = −$500; N = 37; I/Y = 7.25; CPT FV; FV = $6,663

Sarah wants to accumulate $10,000 over the next 10 years. Given a rate of return of 10%, the fixed amount that she should deposit in the bank at the end of each year for the next 10 years is closest to:

$627.45 FV = −$10,000; I/Y = 10; N = 10; CPT PMT; PMT = $627.45

James has just inherited $100,000. His goal is to accumulate $200,000 in 15 years. How much of the inheritance can he spend on a car right now if the remainder will be invested at 12% compounded semiannually?

$65,178 FV = −200,000; I/Y = 12%/2 = 6; N = (15)(2) = 30; CPT PV: PV = $34,822.03 Amount that he can spend in the current period = $100,000 − $34,822 = $65,178

Larry purchases a car worth $20,000 by making an initial payment of $3,000. The rest of the amount is financed with a loan that requires equal monthly payments over 24 months. Assuming a 12% interest rate implicit in the loan, the monthly installment is closest to:

$800 An amount of $17,000 has to be paid back over the next 2 years. I/Y = 12/12 = 1; N = 12 × 2 = 24; PV = −$17,000, CPT PMT; PMT = $800.25

The covariance of returns of A and B is closest to:

-0.00156 The covariance is calculated as: Cov(A,B)=(0.05)(0.11 - 0.0295)(-0.09−0.082)+(0.75)(0.04 - 0.0295)(0.075 - 0.082)+(0.2)(-0.03 - 0.0295)(0.15 - 0.082)=-0.00156.

The correlation of returns of A and B is closest to:

-0.9437 The first step is to calculate the expected returns for A and B: 2.950% and 8.175% resp. Next, the variances for each asset can be calculated by summing the probability weighted, squared deviations from means. The square root of these variances will give the standard deviations of A and B returns: 0.03339 and 0.04940 resp. The covariance of A and B can then be determined by summing the probability-weighted product of deviations from the means: -0.00156. The correlation coefficient is calculated as: (−0.00156)/[(0.0334)(0.0494)]=−0.9437

The average annual return on a stock over its entire history is 10% and the standard deviation of returns equals 7.5%. Given that the stock's returns are distributed normally, calculate the 95% confidence interval for the return in any given year.

-4.7% - 24.7% The reliability factor for a 95% confidence interval equals 1.96. Therefore, the confidence interval is calculated as: 10 ± (1.96) × (7.5)

Excess kurtosis of normal distribution equals:

0 While kurtosis for the normal distribution is 3, the excess kurtosis of a normal distribution equals 0.

The probability function for a random variable is given as p(x) = x/100. The set of possible values that the random variable, X, can take is given by X = (10, 20, 30, 40). For other values of x, p(x) = 0. p(35) equals

0 p(35) = 0 because 35 is not a possible outcome for the random variable.

A board game's rules state that: 1. The game uses just one die, and players take turns rolling it. 2. If a player rolls a 6, the player MUST roll again up to a maximum of three rolls per turn. 3. If a player rolls three consecutive 6's, it results in a loss of turn and a score of zero points. 4. A player's score on any turn is the total of all roll(s) on that turn. The players are using a fair die for the game. The probability of scoring exactly 6 points on a turn is closest to:

0.00% A player cannot score 6 points on a turn. If a player rolls less than a 6, the turn will end and the player will receive that score (<6). If the player rolls a 6, they must roll again. It is impossible for a player to then score 6; as any further roll will increase the score above 6 (>6); or the player will roll 2 more 6s and score 0. Thus, a score of 6 is impossible.

The variance of A's returns is closest to:

0.00111 Var(A)=(0.05)(0.11 - 0.0295)^2+(0.75)(0.04 - 0.0295)^2+(0.2)(-0.03 - 0.0295)^2=0.00111475 or 0.00111 where 0.0295 is the expected value of A.

Use the joint probability table for returns on portfolio A and portfolio B below to answer the question The expected return on A is closest to:

0.03 E(RA)=(0.11)(0.05)+(0.04)(0.75)+(-0.03)(0.2)=0.0295 or 0.03

The standard deviation of A's returns is closest to:

0.0334 The expected return of A is the probability weighted sum of the returns = 11% × 5% + 4% × 75% + -3% × 20% = 2.95% The variance is the probability weighted sum of the squared deviations = 5% × (11% - 2.95%)2 + 75% × (4% - 2.95%)2 + 20% × (-3% - 2.95%)2 = 0.001115 The standard deviation is the positive square root of the variance. Standard deviation of A = (0.001115)0.5 = 0.0334

The standard deviation of B's returns is closest to:

0.0494 Standard deviation of B = (0.00244)^0.5 = 0.0494 E(RB) = ΣRB,ipB,i = −0.09 × 5% + 0.075 × 75% + 0.15 × 20% = 0.08175 VarB = Σ[RB,i - E(RB)]^2pB,i = (−0.09 − 0.08175)^2 × 5% + (0.075 − 0.08175)^2 × 75% + (0.15 − 0.08175)^2 × 20% = 0.00244069 σB = √VarB = 4.9403%

A job interview at an investment company attracts 100 candidates of which 60% are females and 40% are males. Twenty-five percent of both female and male candidates have less than 6 months of work experience and the other 75% have at least 6 months of work experience. If only one of them will be hired, the probability that he/she is a: Male and has less than 6 months of work experience is closest to:

0.10 The joint probability of the person hired being a male and having less than 6 months of work experience is calculated as: P(Male and Inexperienced)=P(Inexperienced/Male)*P(Male)=(0.25)(0.40)=0.1

The probability of an economic recession is 0.55 and the probability of good stock performance given a bad economy is 0.36. The probability of having a recession and good stock performance is closest to:

0.20 Using the multiplication rule, the probability of a recession and good stock performance is calculated as:(0.55)*(0.36)= 0.198 or 0.2

The probability function for a random variable is given as p(x) = x/100. The set of possible values that the random variable, X, can take is given by X = (10, 20, 30, 40). For other values of x, p(x) = 0. p(30) equals:

0.3 p(30) = 30/100 = 0.3

The following data was recorded from a sample of 500 cricket matches played by a particular team: 1. The probability that a team chooses to bat first is 0.57. 2. The probability that the team chooses not to bat first is 0.43. 3. The probability that a team wins a match given that it chose to bat first is 0.69. 4. The probability that a team wins a match given that it chose not to bat first is 0.81. All the matches resulted in one of the teams winning and the other losing the match. The conditional probability of a team not winning a match given that it chose to bat first is closest to:

0.31 The conditional probability of a team not winning a match given that it chose to bat first is given as: 1 - P(winning & chose to bat first)= 1 - 0.69=0.31

The following data was recorded from a sample of 500 cricket matches played by a particular team: 1. The probability that a team chooses to bat first is 0.57. 2. The probability that the team chooses not to bat first is 0.43. 3. The probability that a team wins a match given that it chose to bat first is 0.69. 4. The probability that a team wins a match given that it chose not to bat first is 0.81. All the matches resulted in one of the teams winning and the other losing the match. The probability that a team chooses to bat first and wins the match is closest to:

0.39 The joint probability, P(chose to bat first and wins), of a team that chose to bat first and wins that match is calculated as: P(chose to bat first)*P(wins & chose to bat first)= (0.57)(0.69)= 0.39

A board game's rules state that: 1. The game uses just one die, and players take turns rolling it. 2. If a player rolls a 6, she rolls again up to a maximum of three rolls per turn. 3. If a player rolls three consecutive 6's, she loses her turn and scores zero points. 4. A player's score on any turn is the total of her roll(s) on that turn. The players are using a fair die for the game. The probability of scoring zero points is closest to:

0.46% A player scores zero points when she rolls a 6 three times. The probability of rolling a 6 on any roll is 1/6 and the probability of rolling three consecutive 6s is (1/6)*(1/6)*(1/6)= 0.00463 or 0.46%.

A board game's rules state that: 1. The game uses just one die, and players take turns rolling it. 2. If a player rolls a 6, she rolls again upto a maximum of three rolls per turn. 3. If a player rolls three consecutive 6's, she loses her turn and scores zero points. 4. A player's score on any turn is the total of her roll(s) on that turn. The players are using a fair die for the game. The probability of scoring the highest possible score on a turn is closest to:

0.46% To score 17 points, a player will have to roll a 6 on both the first and the second roll, and a 5 on the third roll. Therefore, the probability of scoring 17 points is (1/6)(1/6)(1/6)= 0.00463 or 0.46%.

You toss a fair coin 10 times. The outcome is heads 7 times. The probability of obtaining a head on the 11th toss is closest to:

0.5 Since every toss is independent, the probability of obtaining a head on the 11th toss is 0.5.

The probability function for a random variable is given as p(x) = x/100. The set of possible values that the random variable, X, can take is given by X = (10, 20, 30, 40). For other values of x, p(x) = 0. F(35) equals:

0.6 F(35) = p(10) + p(20) + p(30) = 0.1 + 0.2 + 0.3 = 0.6

Annual Return (R)Frequency-30% ≤ R ﹤ -20%1-20% ≤ R ﹤ -10%4-10% ≤ R ﹤ 0%150% ≤ R ﹤ 10%1010% ≤ R ﹤ 20%1420% ≤ R ﹤ 30%2 The cumulative relative frequency of the 5th interval is:

0.956 Cumulative relative frequency is the cumulative frequency divided by the total frequency (44/46 = 0.956)

It is Jim's birthday and he has thrown a party for his friends. Everyone except Henry has arrived. George states that the chances of Henry showing up on the party are only 10%. According to George the odds of Henry showing up at the party are:

1 to 9 The odds for an event are stated as the probability of the event occurring to the probability of the event not occurring.

Junglelala's returns over its first 4 years of operations are -1.1%, 1.1%, 1.9%, and 2.8%, respectively. The geometric mean of its returns is closest to:

1.165% (0.989 × 1.011 × 1.019 × 1.028)^(1/4) - 1 = 1.1646%

An individual invests $1,000 in a particular security on two different dates ($2,000 total). The price of the security is $10 on the first day and $12 on the second. The investor's average purchase price is closest to:

10.91 Harmonic mean=2/((1/10) +(1/12))

The unconditional probabilities of p, q, and, r are 0.10, 0.60, and 0.30, respectively. The values and the conditional probabilities of x are given in the table below. The expected value of x is closest to: Value of x & P(x|p) & P(x|q) & P(x|r): 13, 0.3, 0.1, 0.7, 7, 0.4, 0.5, 0.1, 19, 0.3, 0.4, 0.2

12.76 The expected value of x can be calculated as: (0.1)*[(13)(0.3) + (7)(0.4) + (19)(0.3)] + (0.6)*[(13)(0.1) + (7)(0.5) + (19)(0.4)] + (0.3)*[(13)(0.7) + (7)(0.1) + (19)(0.2)] = 12.76

A board game's rules state that: 1. The game uses just one die, and players take turns rolling it. 2. If a player rolls a 6, she rolls again up to a maximum of three rolls per turn. 3. If a player rolls three consecutive 6's, she loses her turn and scores zero points. 4. A player's points on any turn is the total of the numbers obtained on her roll(s) on that turn. The players are using a fair die for the game. The probability of scoring exactly 3 points on a turn is closest to:

16.67% A player will have to roll a 3 to score 3 points. The probability of rolling a 3 on a roll of a fair die is 1/6 or 16.67%

A board game's rules state that: 1. The game uses just one die, and players take turns rolling it. 2. If a player rolls a 6, she rolls again up to a maximum of three rolls per turn. 3. If a player rolls three consecutive 6's, she loses her turn and scores zero points. 4. A player's score on any turn is the total of her roll(s) on that turn. The players are using a fair die for the game. The probability of rolling a 6 on the first roll is closest to:

16.67% The probability of rolling a 6 on the first roll equals 1/6 or 16.67%.

An oil refinery has a fire alarm system installed on its premises. The alarm is supposed to go off in case of a fire. The probability of a fire occurring on any given day is 0.25%. Unfortunately, the system that is installed is not perfect. When a fire actually occurs, the alarm goes off 99% of the time. Furthermore, the probability of the alarm going off when there is no fire is believed to be 1%. Given that the alarm went off today, the probability of there being a fire is closest to:

19.9% This question requires us to use the Bayes' Theorem for updated probability. Given a set of prior probabilities for an event, if you receive new information, the rule for updating the probability of the event is given as: Updated probability of event given the new information= (Probability of new information given event/Unconditional probability of the new information)×Prior probability of event In this question, the event is the occurrence of a fire incident. P(information|event)=P(Alarm goes off|Fire)=99% Prior probability of event=P(Fire)=0.25% Unconditional probability of information, P(Alarm goes off) is calculated using the total probability rule: P(Alarm goes off|Fire)×P(Fire)+P(Alarm goes off|No fire)×P(No fire)=(0.99)(0.0025)+(0.01)(.9975)=0.01245 P(Fire)=(0.0025)(0.99)/(0.01245)=0.1987 or 19.9%

The annual returns of the various stocks for 2008 are given in the table below: Stock & Return ABC-21% DEF-(-10%) GHI-5% JKL-13% MNO-(-19%) PQR-5% The arithmetic mean of the returns on these stocks for the year 2008 is:

2.5% The arithmetic mean is the sum of the returns divided by the total number of stocks: (21-10+5+13-19+5)/6 = 2.5%

Cool Pop Soda Corp's annual profit margins since its incorporation are presented below: Year 1-11% Year 2-9% Year 3-4% Year 4-(-2%) Year 5-1% Year 6-4% Given that the data set is only a representative sample of profit margins over the company's entire existence, the variance for Cool Pop Soda Corp's profit margins over the 6 years is closest to:

23.5 For sample variance, we must use (n - 1) in the denominator [(11 - 4.5)^2+ (9 - 4.5)^2 + (4 - 4.5)^2 + (-2 - 4.5)^2 + (1 - 4.5)^2 + (4 - 4.5)^2] / (6 - 1) = 23.5

Twelve questions have been submitted for a multiple choice exam. A computer program will randomly select any 10 out of these 12 questions for the actual exam. ii. In how many different ways can we number 10 questions out of these 12 from 1 to 10? The question selected first will be numbered "1," the next one will be numbered "2," and so on.

239,500,800 The number of ways that the set of 12 questions can be numbered from 1 to 10 (order is important) is calculated as 12P10, or 239,500,800.

The maximum percentage of observations in a data set that lies further than 1.85 standard deviations away from the mean is closest to:

29.2% Using Chebyshev's inequality: 1 - [1 / (1.85)^2] = 70.8% At least 70.8% of the data lie within 1.85 standard deviations from the mean. This implies that a maximum of 29.2% of the observations may lie more than 1.85 standard deviations away from the mean.

Over the next 5 years, MT Technologies expects to earn the following amounts: Year 1$90 million Year 2$76 million Year 3$92 million Year 4$105 million Year 5$103 million The annually compounded growth rate based on the company's forecasts is closest to:

3.43% Annual rate of return = (103 / 90)1/4 - 1 = 3.43%

Cool Pop Soda Corp's annual profit margins since its incorporation are presented below: Year 1-11% Year 2-9% Year 3-4% Year 4-(-2%) Year 5-1% Year 6-4% The mode for Cool Pop Soda Corp's profit margins over the years is closest to:

4% The mode is the value that has the highest frequency, 4% (twice).

Cool Pop Soda Corp's annual profit margins since its incorporation are presented below: Year 1-11% Year 2-9% Year 3-4% Year 4-(-2%) Year 5-1% Year 6-4% The median for Cool Pop Soda Corp's profit margins over the years is closest to:

4% There is an even number of observations in the data set so the median equals the average of the middle two numbers after the data set has been arranged in ascending order. (4+4)/2 = 4%

Cool Pop Soda Corp's annual profit margins since its incorporation are presented below: Year 1-11% Year 2-9% Year 3-4% Year 4-(-2%) Year 5-1% Year 6-4% The population standard deviation for Cool Pop Soda Corp's profit margins over these years is closest to:

4.43% The population standard deviation equals the positive square root of the variance. √19.58 = 4.425

Cool Pop Soda Corp's annual profit margins since its incorporation are presented below: Year 1-11% Year 2-9% Year 3-4% Year 4-(-2%) Year 5-1% Year 6-4% The arithmetic mean for Cool Pop Soda Corp's profit margins over the years is closest to:

4.5% [11+9+4+(−2)+1+4] /6 = 4.5%

Cool Pop Soda Corp's annual profit margins since its incorporation are presented below: Year 1-11% Year 2-9% Year 3-4% Year 4-(-2%) Year 5-1% Year 6-4% Given that the data set is only a representative sample of profit margins over the company's entire existence, the standard deviation for Cool Pop Soda Corp's profit margins over the 6 years is closest to:

4.85% The standard deviation of the sample is the root of the sample variance. √23.5=4.847%

The annual returns of the various stocks for 2008 are given in the table below: Stock & Return ABC-21% DEF-(-10%) GHI-5% JKL-13% MNO-(-19%) PQR-5% The median return of these stocks for the year 2008 is:

5% The median is the ½(n + 1)th element in the dataset. In this case, it is the 3.5th element, which lies between the 3rd and the 4th items. The average of 5% and 5% equals 5%.

Twelve questions have been submitted for a multiple choice exam. A computer program will randomly select any 10 out of these 12 questions for the actual exam. i. In how many different ways can 10 questions out of these 12 be selected for the exam if the order of selection is not important?

66 If the order is not important then the number of possible combinations is simply calculated as 12C10, or 66.

According to research, heart attack is one of the leading causes of death worldwide with about 7.6 million casualties in 2013. The research also claimed that "male smokers are likely to experience heart attack 15 times more than those who don't smoke and female smokers are likely to experience heart attack 12 times more than nonsmoking females." Furthermore, the National Statistics Office released data that 16% of females worldwide are smokers. Suppose you're in a hospital, waiting for your turn for a medical checkup, and the female beside you is having a monthly maintenance checkup following a heart attack. What are the chances that she is a smoker?

69.57% Given: P(S) = 16%, thus, P(NS) = 84% P(H/S) = 12 × P(H/NS), thus, P(H/NS) = P(H/S)/12 Also, P(H) = P(H&S) + P(H&NS) = P(H/S) × P(S) + P(H/NS) × P(NS) = P(H/S) × P(S) + (P(H/S)/12) × P(NS) We want P(S/H) which equals: P(H&S)/P(H) = (P(H/S) × P(S))/(P(H/S) × P(S) + (P(H/S)/12) × P(NS)) = P(S)/(P(S) + P(NS)/12) = 16%/(16% + 84%/12) = 69.67%

The probability that a baseball player will swing his bat on any given pitch equals 0.35. He faces 20 pitches in each batting practice session. How many times is the player expected to swing the bat at any given batting practice?

7 E(X) = (n)(p) = (20)(0.35) = 7

The effective annual rate for an automobile loan that has an interest rate of 7%, compounded monthly, is closest to:

7.23% EAY = [1 + (0.07/12)]12 - 1 = 7.23%

What is the minimum percentage of a distribution that will lie within 3 standard deviations of the mean?

89% Applying Chebyshev's inequality 1 - 1/k^2: 1-(1/3^2)

Which of the following statements is most likely?

A portfolio with a higher SF Ratio also has a higher probability of attaining returns higher than the threshold level.

You toss a fair coin 10 times. The outcome is heads 7 times. Each coin toss is:

An independent event Every toss of this coin is an independent event as the result of the toss is not affected by the result of any other toss.

Which of the following statements regarding frequency distributions is least accurate?

Any particular observation could fall into one or more intervals. <-- The set of intervals should include the entire range of values in the data set. The interval with the highest frequency is called the modal class.

Stock A has an average return of 11% and a standard deviation of 4%. Stock B has an average return of 33% and a standard deviation of 14%. Stock C has an average return of 7% and a standard deviation of 0.33%. Given a risk-free rate of 5%, which investment is most attractive based on the coefficient of variation?

C The coefficient of variation (CV) equals the standard deviation divided by the mean of the distribution and measures the risk per unit of return. It does not consider the risk-free rate. A lower CV is preferred. For Stock A, CV = 4/11 = 0.36. For Stock B, CV = 14/33 = 0.42. For Stock C, CV = 0.33/7 = 0.047.

A leptokurtic distribution most likely:

Has a positive excess kurtosis and is more peaked and has fatter tails than a normal distribution A leptokurtic distribution is more peaked and has fatter tails than a normal distribution. It also has an excess kurtosis greater than zero.

Which of the following is least likely a component of the required rate of return on a security after the nominal risk-free rate has been deducted?

Inflation risk premium

Sonia wants to invest $5,000 and is considering the following investments over a horizon of 8 years: Investment 1: Invest in a mutual fund which is expected to earn 8% for the first 3 years and 12% thereafter. Investment 2: Invest in a savings account which is expected to offer 11% a year compounded annually. Investment 3: Invest in gold whose current value is expected to double in 8 years. Which of these investments offers the highest return based on her expectations?

Investment 2 Investment 1: N = 3; I/Y = 8; PV = −$5,000; CPT FV; FV → $6,298.56 N = 5; I/Y = 12; PV = −$6,298.56; CPT FV; FV → $11,100.215 Investment 2: N = 8; I/Y = 11; PV = −$5,000; CPT FV; FV → $11,522.689 Investment 3: Value of $5,000 investment in 8 years = $5,000 × 2 = $10,000

William is evaluating the following options for investing $10,000 for 5 years: Investment A: Offers a 10% interest rate compounded monthly. Investment B: Offers a 12% interest rate compounded semi-annually. Investment C: Offers an 11% interest rate compounded quarterly. Which of the following statements is most accurate?

Investment A offers a $1,455 less return than Investment B. <-- Investment C offers a $704 greater return than Investment B. Investment A offers a $751 greater return than Investment C. Investment A: N = 5 × 12; I/Y = 10/12; PV = −$10,000; CPT FV; FV → $16,453.09 Investment B: N = 5 × 2; I/Y = 12/2; PV = −$10,000; CPT FV; FV → $17,908.48 Investment C: N = 5 × 4; I/Y = 11/4; PV = −$10,000; CPT FV; FV → $17,204.28

Which of the following is least likely regarding the correlation coefficient?

It is expressed in the same units as the data itself. The correlation coefficient has no unit.

Compared to the standard deviation, the mean absolute deviation is always:

Less than or equal to the standard deviation The MAD is always less than or equal to the standard deviation as the standard deviation attaches a heavier weight to larger deviations.

Which of the following types of measurement scales sorts data into categories that are ranked according to a certain characteristic, but does not tell us anything about the differences between categories?

Ordinal Scales

Which of the following least likely offers a finite series of cash flows?

Ordinary annuity Annuity due Perpetuity <-- Perpetuity offers a series of cash flows that go on forever.

Portfolio A has an expected return of 9% and a standard deviation of 12%, while Portfolio B has an expected return of 12% and a standard deviation of 15%. Using Roy's safety-first criterion and assuming that the target return equals 5%, which portfolio should be preferred?

Portfolio B Portfolio B has a higher SF Ratio so it is preferred. (7/15 = 0.47 versus 4/12 = 0.33).

The closing prices of various stocks are given in the table below: Stock and Price ABC-$21 DEF-$10 GHI-$5 JKL-$13 MNO-$19 PQR-$5 The geometric and harmonic means for the data are closest to: Geometric Mean &Harmonic Mean A.10.4&8.9 B.1.6&16.1 C.1.0&8.9

Row A Geometric mean = (21×10×5×13×19×5)^(1/6) = 10.4 Harmonic mean=6/[(1/21)+(1/10)+(1/5)+(1/13)+(1/19)+(1/5)]=8.9

George is thinking of taking a loan of $50,000 to buy a house. The loan will be fully amortized with equal monthly installments over 10 years. Given that the interest rate is 8% compounded monthly, the amount of each mortgage payment and the effective interest rate will be closest to: Mortgage Payment & Effective Interest Rate A.$607, 8.3% B.$615, 8.15% C.$606, 8%

Row A PV = $50,000; N = 120; I/Y = 8/12 = 0.67; CPT PMT: PMT = $606.74 Effective interest rate = [(1 + 0.006667)12] - 1 = 0.083 or 8.3% OR you could use the Interest conversion function on your BA II Plus: [2ND][2]to enter the ICONV function[2ND][CE|C]to clear memory[8][ENTER]enter the nominal interest rate[↓][↓][12][ENTER]enter the compounding periods per year C/Y[↑][CPT]compute the effective interest rate

A loan is amortized over time with equal annual payments. How do the principal and interest components of the annual payment change over time? Interest Component & Principal Repayment Component A.Decreases, Increases B.Increases, Decreases C.Decreases, Decreases

Row A The payments made over time reduce the outstanding principal amount. Therefore, the interest component decreases with each payment. Since all payments are equal, a reduction in the interest component implies an increase in the principal repayment component.

What sum should be deposited today at 8% compounded quarterly if one wants to accumulate $200,000 in 6 years? How much interest will be earned during the period? Amount Deposited Today & Interest Earned A.$124,344, $69,788 B.$124,344, $75,656 C.$130,212, $75,656

Row B I/Y = 8/4 = 2%; N = (6)(4) = 24; FV = −$200,000; CPT PV; PV = $124,344 Interest earned = FV - PV = $200,000 − $124,344 = $75,656

Alison plans to deposit $500 in her savings account at the end of each quarter for the next 10 years. The interest rate is 10% per year compounded quarterly. After 10 years, her account balance and the total amount of interest that she would have earned are closest to: Account Balance & Interest Earned A.$33,701, $13,254 B.$33,701, $13,701 C.$32,504, $13,254

Row B PMT = −$500; N= (10)(4) = 40; I/Y = 10%/4 = 2.5; PV=0; CPT FV: FV = Account balance after 10 years = $33,701.28 Over the period she will make 40 deposits worth $500 each for a total of $20,000 Therefore, total interest income = $33,701 − $20,000 = $13,701

Given the following samples of returns from Portfolio A and Portfolio B, which portfolio has the smaller range and, based on range alone, which portfolio has greater risk? Portfolio A &Portfolio B 16.2%&9.2% 20.5%&8.4% -11.1%&-1.6% 7.2%&13.2% Smaller Range & Higher Risk A.A&B B.B&A C.B&B

Row B Range of Portfolio A = 20.5% - (-11.1%) = 31.6% Range of Portfolio B = 13.2% - (-1.6%) = 14.8% Portfolio B has the smaller range and Portfolio A is riskier as it has a higher range.

The annual returns of the various stocks for 2008 are given in the table below: Stock & Return ABC-21% DEF-(-10%) GHI-5% JKL13% MNO-(-19%) PQR-5% The range and standard deviation of the stock returns, assuming that they represent a population, are: Range & Std Dev A.40&32.9 B.40&13.43 C.28.16&40

Row B The range is the difference between the highest and lowest value in the dataset [21 − (−19) = 40]. The standard deviation is the average of the square root of the sum of squared deviations from the mean: Std Dv=√(21−2.5)^2+(−10−2.5)^2+(5−2.5)^2+(13−2.5)^2+(−19−2.5)^2+(5−2.5)^2 / 6=13.43

What is the mean absolute deviation and variance of the sample investment returns given below: Year & Return 2004-8% 2005-9% 2006--7% 2007-5% MAD & Variance A.6.375%-0.004069 B.5.375%-0.005425 C.6.375%-0.005425

Row B Mean=¯x=(8%+9%+(−7%)+5%)/4=3.75% MAD=(|8−3.75|+|9−3.75|+|−7−3.75|+|5−3.75|)/4=5.375% Variance=(8%−3.75%)^2+(9%−3.75%)^2+(−7%−3.75%)^2+(5%−3.75%)^2/(4 - 1)=0.005425

An analyst gathered the following information about the required rate of return of different stocks held in a portfolio: IntervalReq. RORAbsolute Frequency15% - 6%126% - 7%337% - 8%448% - 9 %259% - 10%3 The relative frequency and cumulative relative frequency of Interval 4 are closest to: Relative FrequencyCumulative Relative FrequencyA.15%23%B.20%77%C.15%77%

Row C Relative frequency=AbsolutefrequencyofeachintervalTotalnumberofobservations×100=213=15.38%or15% Cumulative relative frequency is the cumulative frequency of 4th interval divided by the total number of observations:CRF=1+3+4+213=1013=0.7692or77%

Which of the following statements is most likely?

The cumulative frequency for an interval is the proportion of total observations that lies in that particular interval. The cumulative absolute frequency for a particular interval is the number of observations that are less than the upper bound for the interval. <-- The cumulative relative frequency for a particular interval is the number of observations that are less than the midpoint of the interval. The cumulative frequency/cumulative absolute frequency for an interval equals the number of observations that are less than the upper bound of the interval. The cumulative relative frequency for an interval is the proportion of total observations that is less than the upper bound of the interval.

Melena Anderson, an analyst, is in the process of estimating the intrinsic value of Dazzle Industrial Corporation's common stock. She is planning to estimate the value using eight different methods under three different labels. The methods to be used are as follows: Labels & Methods 1.Present value models & Gordon growth model and free-cash-flow-to-equity model 2.Multiplier models & Price-to-earnings multiple, price-to-book multiple, price-to-sales multiple, price-to-cash-flow multiple, and enterprise value multiple 3.Asset-based valuation model & Book value model Later, Melena decides that she will estimate the intrinsic value using only three methods. Assuming Melena uses one method from each of the labels, which of the following should be used to calculate the number of ways the methods can be allocated?

The multiplication rule of counting The multiplication rule of counting should be used to calculate the number of ways the methods can be allocated as per the desired criteria. Applying the rule, the methods can be allocated in 10 (2 × 5 × 1) different ways. Please note that since the purpose of this process is to ascertain a range of estimated intrinsic values, the order in which the methods are used does not matter.

What does an observation's z-score essentially represent?

The number of standard deviations away from the mean the given observation actually lies.

A random variable, X, can take any of the five values, 10, 20, 30, 40, and 50. Given that this set of events is mutually exclusive and exhaustive, which of the following is most likely?

The probabilities of the five outcomes are 0.2, 0.2, 0.2, 0.2, and 0.2, respectively. The sum of the probabilities of any set of mutually exclusive and exhaustive events equals 1.