Practice Flashcards
Elise Corrs, hedge fund manager and avid downhill skier, was recently granted permission to take a 4 month sabbatical. During the sabbatical, (scheduled to start in 11 months), Corrs will ski at approximately 12 resorts located in the Austrian, Italian, and Swiss Alps. Corrs estimates that she will need $6,000 at the beginning of each month for expenses that month. (She has already financed her initial travel and equipment costs.) Her financial planner estimates that she will earn an annual rate of 8.5% during her savings period and an annual rate of return during her sabbatical of 9.5%. How much does she need to put in her savings account at the end of each month for the next 11 months to ensure the cash flow she needs over her sabbatical? Each month, Corrs should save approximately:
Be careful with the Y/M and the end and bgn mode.
This is a two-step problem. First, we need to calculate the present value of the amount she needs over her sabbatical. (This amount will be in the form of an annuity due since she requires the payment at the beginning of the month.) Then, we will use future value formulas to determine how much she needs to save each month.
Step 1: Calculate present value of amount required during the sabbatical
Using a financial calculator: Set to BEGIN Mode, then N = 4; I/Y = 9.5 / 12 = 0.79167; PMT = 6,000; FV = 0; CPT → PV = -23,719.
Step 2: Calculate amount to save each month
Using a financial calculator: Make sure it is set to END mode, then N = 11; I/Y = 8.5 / 12.0 = 0.70833; PV = 0; FV = 23,719; CPT → PMT= -2,081, or approximately $2,080.
(Module 1.3, LOS 1.d)
If 10 equal annual deposits of $1,000 are made into an investment account earning 9% starting today, how much will you have in 20 years?
Switch to BGN mode. PMT = –1,000; N = 10, I/Y = 9, PV = 0; CPT → FV = 16,560.29. Remember the answer will be one year after the last payment in annuity due FV problems. Now PV10 = 16,560.29; N = 10; I/Y = 9; PMT = 0; CPT → FV = 39,204.23. Switch back to END mode.
(Module 1.2, LOS 1.c)
A recent ad for a Roth IRA includes the statement that if a person invests $500 at the beginning of each month for 35 years, they could have $1,000,000 for retirement. Assuming monthly compounding, what annual interest rate is implied in this statement?
Make sure to distinguish month to yearly.
Solve for an annuity due with a future value of $1,000,000, a number of periods equal to (35 × 12) = 420, payments = -500, and present value = 0. Solve for i. i = 0.61761 × 12 = 7.411% stated annually. Don’t forget to set your calculator for payments at the beginning of the periods. If you don’t, you’ll get 7.437%.
Which of the following tools best captures the distribution of returns for a particular stock?
A histogram depicts the shape and range of a distribution of numerical data.
A frequency polygon is best suited to summarizing:
A frequency polygon depicts the shape and range of a distribution.
return on the portfolio
it is asking about the arithmetic mean
An investor will receive an annuity of $5,000 a year for seven years. The first payment is to be received 5 years from today. If the annual interest rate is 11.5%, what is the present value of the annuity?
be careful with the T.
With PMT = 5,000; N = 7; I/Y = 11.5; value (at t = 4) = 23,185.175. Therefore, PV (at t = 0) = 23,185.175 / (1.115)4 = $15,000.68.
(Module 1.2, LOS 1.c)
A firm is evaluating an investment that promises to generate the following annual cash flows:
End of Year Cash Flows
1 $5,000
2 $5,000
3 $5,000
4 $5,000
5 $5,000
6 -0-
7 -0-
8 $2,000
9 $2,000
Given BBC uses an 8% discount rate, this investment should be valued at:
PV(1 - 5): N = 5; I/Y = 8; PMT = -5,000; FV = 0; CPT → PV = 19,963
PV(6 - 7): 0
PV(8): N = 8; I/Y = 8; FV = -2,000; PMT = 0; CPT → PV = 1,080
PV(9): N = 9; I/Y = 8; FV = -2,000; PMT = 0; CPT → PV = 1,000
Total PV = 19,963 + 0 + 1,080 + 1,000 = 22,043.
(Module 1.2, LOS 1.c)
A recent study indicates that the probability that a company’s earnings will exceed consensus expectations equals 50%. From this analysis, the odds that the company’s earnings exceed expectations are:
Odds for an event equals the ratio of the probability of success to the probability of failure. If the probability of success is 50%, then there are equal probabilities of success and failure, and the odds for success are 1 to 1.
(Module 3.1, LOS 3.c)
An economist estimates a 60% probability that the economy will expand next year. The technology sector has a 70% probability of outperforming the market if the economy expands and a 10% probability of outperforming the market if the economy does not expand. Given the new information that the technology sector will not outperform the market, the probability that the economy will not expand is closest to:
Build the decision tree and calculate the P(x).
P(tech does not outperform) = P(tech does not outperform and economy does not expand) + P(tech does not outperform and economy does expand) = 0.36 + 0.18 = 0.54.
P(economy does not expand | tech does not outperform) = P(economy does not expand and tech does not outperform) / P(tech does not outperform) = 0.36 / 0.54 = 0.67.
If the odds against an event occurring are twelve to one, what is the probability that it will occur?
If the probability against the event occurring is twelve to one, this means that in thirteen occurrences of the event, it is expected that it will occur once and not occur twelve times. The probability that the event will occur is then: 1/13 = 0.0769.
Joe Mayer, CFA, projects that XYZ Company’s return on equity varies with the state of the economy in the following way:
State of Economy Probability of Occurrence Company Returns
Good .20 20%
Normal .50 15%
Poor .30 10%
The standard deviation of XYZ’s expected return on equity is closest to:
In order to calculate the standard deviation of the company returns, first calculate the expected return, then the variance, and the standard deviation is the square root of the variance.
The expected value of the company return is the probability weighted average of the possible outcomes: (0.20)(0.20) + (0.50)(0.15) + (0.30)(0.10) = 0.145.
The variance is the sum of the probability of each outcome multiplied by the squared deviation of each outcome from the expected return: (0.2)(0.20 - 0.145)^2 + (0.5)(0.15 - 0.145)^2 + (0.3)(0.1-0.145)^2 = 0.000605 + 0.0000125 + 0.0006075 = 0.001225.
The standard deviation is the square root of 0.001225 = 0.035 or 3.5%.;
(Module 3.3, LOS 3.l)
Consider the following set of stock returns: 12%, 23%, 27%, 10%, 7%, 20%,15%. The third quartile is:
The third quartile is calculated as: Ly = (7 + 1) (75/100) = 6. When we order the observations in ascending order: 7%, 10%, 12%, 15%, 20%, 23%, 27%, “23%” is the sixth observation from the left.
A parking lot has 100 red and blue cars in it.
40% of the cars are red.
70% of the red cars have radios.
80% of the blue cars have radios.
What is the probability that the car is red given that it has a radio?
Decision tree. Be careful with the question. It is asking about the reverse probability.
Given a set of prior probabilities for an event of interest, Bayes’ formula is used to update the probability of the event, in this case that the car we already know has a radio is red. Bayes’ formula says to divide the Probability of New Information given Event by the Unconditional Probability of New Information and multiply that result by the Prior Probability of the Event. In this case, P(red car has a radio) = 0.70 is divided by 0.76 (which is the Unconditional Probability of a car having a radio (40% are red of which 70% have radios) plus (60% are blue of which 80% have radios) or ((0.40) × (0.70)) + ((0.60) × (0.80)) = 0.76.) This result is then multiplied by the Prior Probability of a car being red, 0.40. The result is (0.70 / 0.76) × (0.40) = 0.37 or 37%.
(Module 3.3, LOS 3.m)
In addition to the usual parameters that describe a normal distribution, to completely describe 10 random variables, a multivariate normal distribution requires knowing the:
The number of correlations in a multivariate normal distribution of n variables is computed by the formula ((n) × (n-1)) / 2, in this case (10 × 9) / 2 = 45.
(Module 4.2, LOS 4.g)
