Finance Final

What is the FV of $1,000 after two years at 2% compounded monthly?

$1,040.78

What is the FV of $1,000 after two years at 18% compounded monthly?

$1,429.50

What is the duration of a ten-year STRIP two years after it was issued?

8 years

As the discount rate employed in an NPV analysis rises, we generally expect the NPV to fall. T/F?

TRUE

For a project with a positive NPV, we would normally expect the IRR to be greater than the discount rate employed in the NPV analysis. T/F?

TRUE

T/F: If Amazon, Inc. has a beta of 1.3, it is possible that Amazon stock is priced such that it would appear to lie "outside" the Efficient Frontier on the CAPM.

True, and the meaning of the Efficient Frontier we described in class remains accurate/correct.

An option that is "out of the money" cannot have a significant market value as the drivers of option value (per the Black Scholes formula) are strike price and underlying asset value.

FALSE - Those are drivers, but not the sole drivers of value.

How many years will it take for $10,000 to grow to $20,000 if the interest earned is 7% compounded annually?

n = 10.2 years

An investment of $50,000 sum is earning 3% quarterly. How many years will it be until the sum grows to $100,000?

n = 23.44 Quarters or 5.86 years.

What point is Fama making when he said to Thaler, "That's an anecdote, not evidence?"

No scientist should draw a conclusion based on one data point. One data point has little statistical 'power.'

If an investment of $1,000 is earning 2% quarterly what will be the interest earned after one year?

$82.43

YTM and the IRR of a bond, where the IRR is based on the market price of the bond and all of the discounted cash flows, are the same thing. T/F?

FALSE (UNDISCOUNTED CFs)

If a gambling wheel is "fair" and has the following values: 0, 2, 3, 4, 0, 6, 7, 0, 8, & 40. What is the Ev

EV=7

T/F: Last year the S&P 500 ( a good proxy for "the market) had an annual return of 14%. The Er of the stock market is very likely not 8-10%, but something significantly closer to 14%.

FALSE. Anecdote, not evidence. A datum is not data.

The general approach to calculating the beta of a portfolio is to measure the performance of that portfolio over time vs. the market.

FALSE: We calculate beta of stocks, betas of portfolios are a function of the component stocks' betas.

If you are convinced that stocks - as an investment class - have a higher expected return than government bonds, explain why stocks may not be "the right investment for everybody."

INDIVIDUAL RISK TOLERANCE CAN AND DOES VARY

Which systematic risk is the most "inescapable?" That is, which systematic risk remains even for the investment that comes closest to being "risk free?"

PURCHASING POWER EROSION (INFLATION).

a) How much will a 15-year annuity pay you per year if it costs $600,000 and pays out based on a 3.0% rate, compounded monthly? b) What will the value of the annuity be at the end of year 16?

a) $4,143 b) ZERO, no residual value

Positive/Negative: Increase in Interest Rate: a) Effect on call option price/value b) Effect on put option price/value

a) Positive b) Negative

Positive/Negative: Increase in stock price: a) Effect on call option price/value b) Effect on put option price/value

a) Positive b) Negative

All other things being equal, if we observed a long-term increase in the so-called risk premium for stocks, the best possible explanation is: a) Investors were becoming less risk averse b) Investors were becoming more risk averse c) Inflation was increasing d) Inflation was decreasing

b)

A project who's NPV, properly calculated at the firm's WACC of 15%, is $4 million. That project likely has an IRR a) equal to 15%, b) greater than 15%, c) less than 15%, d) can't tell.

b) Greater than 15%

Your best friend tells you that they are taking a job as a security analyst at a large bank. If you believe in semi-strong EMH as taught in EC-50, you must necessarily believe which of the following: a) It is impossible for them to make positive returns by trading in one stock. b) If they make returns from trading in one stock, markets are necessarily inefficient. c) Their skill, training, and effort could not have a bearing on whether they make a return trading in one stock. d) All of the above e) None of the above

e)

A STRIP will generally trade at par. T/F?

FALSE

Define IRR. What is the "interpretation" or meaning of IRR? What is the connection between IRR and NPV?

IRR is the discount rate at which the NPV analysis yields a value of zero.

Which of the following bonds is likely to have a higher YTM? $10,000 face value, 4% coupon, maturing in 2030 $5,000 face value, 3% coupon, maturing in 2025 i. a. ii. b. iii. Can't tell

a)

A wealthy inventor has decided to endow her favorite art museum by establishing funds for an endowment which would provide $1,000,000 per year forever. She will fund the endowment upon her fiftieth birthday 10 years from today. She plans to accumulate the endowment by making annual end-of-year deposits into an account. The rate of interest is expected to be 6 percent in all future periods. How much must the scientist deposit each year to accumulate to the required amount?

$1,264,465.97 per year

You want to buy a Tesla in seven years. The car is currently selling for $50,000, and the price will increase at a compound rate of 10% per year. You can presently invest in high-yield bonds earning a compound annual rate 14% per year. How much must you invest at the end of each of the next seven years to be able to purchase your dream car in seven years?

$38,939 per year

What down payment would they have to put down to afford the $360,000 house under a 15-year, 2.7% compounded monthly mortgage if they can only afford $2,100 per month?

$49,462

Determine the future value at the end of two years of an investment of $3,000 made now and an additional $3,000 investment made one year from now if the compound annual interest rate is 4 percent.

$6,364.80

Find the present value of $7,000 to be received one year from now assuming a 3 percent annual discount interest rate. Also calculate the present value if the $7,000 is received after two years.

$6,796.12; $6,598.17

Find the future value one year from now of a $7,000 investment at a 3 percent annual compound interest rate.

$7,210

Calculate the future value if the investment is made for two years.

$7,426.3

Determine the present value if $15,000 is to be received at the end of eight years and the discount rate is 9 percent.

$7,528

You have some savings you'd like to invest. You can invest it in a bank account paying fixed 6% compounded monthly. Your plan is to leave the principal, but take out the interest at the end of every year to help cover expenses. If you wanted to be sure that your savings invested at the bank earned $5,000 per year, how much savings would you have to have? If you follow your plan for 10 years, but then decide to switch banks and you go to the bank to collect your money, how much will the bank owe you?

$81,066.43 is the answer to both questions

You have some savings you'd like to invest. You can invest it in a bank account paying fixed 5% compounded monthly. Your plan is to leave the principal but take out the interest at the end of every year to help cover expenses. If you wanted to be sure that your savings invested at the bank allowed you to take out $5,000 per year for as long as you wanted to, how much savings would you have to have?

$97,656

1. As inflation increases, we generally expect that bond YTMs will increase to account for the increased risk of "price erosion" or "purchasing power risk." Assuming that is true, as inflation increased we would likely see prices for bonds that are trading in the market to: a) Rise b) Fall c) Can't tell The best explanation for your answer above is: a) YTMs are IRRs and for IRRs to change, at least one cash flow or the timing of one cash flow must change. b) Investors become more risk averse during times of increasing inflation c) Real interest rates are assumed to change only slowly d) The NPV of the bond is unchanged e) We don't have enough information to draw a conclusion

1. b) Fall 2. a)

When does a principle-only STRIP mature if its YTM is 4.0% and it is "trading at 87" (par value)?

3.55 years

f you sit down with your stockbroker for your yearly review and she begins to review the sales, new products, and recent news for each of your portfolio companies, what should your reaction be?

Ans: I hope she isn't charging me by the hour for this! She is describing firm-specific risks. Who cares? You don't care about firm specific risk.

Your friend is double-majoring in Computer Science and Economics with a minor in Finance. He says the following, "I just read about this amazing study that just came out about peoples' aversions to particular letters in the alphabet. It was a very clever study, the researchers showed subjects a bunch of fictional product names for a new soap (this was all made up but the subjects didn't know that) and the subjects were asked which product they were most likely to buy. Well, it turns out that names starting with 'A,' 'L' and 'T' were highly preferred over product names that started with 'V' 'Z' or 'E.' While there was a range, these were the extremes. So here is my idea: we buy stocks whose company names begin with V, Z, or E and avoid companies whose names start with A, L, or T. Reality is what reality is, and eventually these companies stock price will reflect their earnings, but we can profit from the insight that investors will 'undervalue' stocks whose names start with V, Z, or E." Assume you have access to any data you'd like - including the CRSP tapes, design a study to test your friend's thesis.

Assess the firms' values

Tom Vu deposited $5,000 in a savings account that paid 8% interest compounded quarterly. What is the effective rate of interest?

EAR=8.24%

We have said that investors care about Risk and Return. Explain how the concept of an "investor's time horizon" relates to one or both of those concepts.

Expectations are based on statistical outcomes, or averages over time. The likelihood that the average will come close to the expectation increases as the number of 'iterations' increases. In the case of annual returns, each year is an iteration. To get a 'reasonable' sample size, we have to wait a 'reasonable' number of years. If we can't wait, we shouldn't invest in highly variable (risky) assets. Single iterations can (and DO) deviate widely from the expected value.

A project whose IRR is above the firm's WACC should not be undertaken. T/F?

FALSE

For every set of cash flows there is an IRR that is positive. T/F?

FALSE

For most conventional bonds, the years to maturity and the duration are the same thing. T/F?

FALSE

The expected value of a "fair" wheel with 50 "slots" is 25. The number 25 must appear somewhere on the wheel.

FALSE

"Markets cannot be efficient as it is clear that some individuals beat the market many years in a row - way more than we would expect if beating the market were a matter of 'chance.' Critique that statement.

FALSE - you can flip a coin 5 times in a row and land on heads - this is a statistically possible event even though the underlying event is a random process. This is why it is difficult to prove that stock markets are like coin flips - of course there are times when stock market prices don't look anything like coin flips (i.e., his made-up stock chart using a random number generator seemed to generate "trends" - they are trends in the sense that if you have a random sequence of numbers, patterns will emerge, These patterns aren't predicted they are accidental. The problem with stocks is that most of the time we don't interpret them as an accident: it all comes back to who ar you going to believe - your lying eyes or your math? Stock investors tend to believe their lying eyes.

What systematic risk factor are you inevitably exposed to when you make a foreign investment?

FOREIGN EXCHANGE RISK

T/F: PVs of perpetuities increase with increasing interest rates.

False

T/F: The price of perpetuities increase with increasing interest rates.

False

What principle underlies Harry Markopolous's statement (paraphrased), "When others see outperformance, I suspect fraud"?

In line with the 'teachings' of the CAPM: with return comes risk. There is no 'free lunch' of getting return while avoiding risk. If that disparity between risk and return is large, Harry thinks the explanation is (likely) fraud.

As an adherent to the teachings of EMH, why do you support the effort that was made several years ago to have the Fed be more explicit in their announcements about what they planned to do, but were not yet actually doing? If the Fed consistently failed to do what they told the markets they planned to do, what do you imagine would be the effect of the Fed's announcements?

In order to calm people's expectations...

"Markets cannot be efficient as it is clear that stock prices are very often 'wrong'. If the price of Amazon was $380/share yesterday and today it is $280, ONE of those prices must have been wrong. If one of them was wrong, then the market was not efficient." Critique that statement.

It doesn't matter if one of them is wrong - I will concede one of them is wrong, unless you can tell me which one of them is wrong before it is announced then EMH still holds. Fama goes further and argues that it is possible that both of these prices is right. He may be right, but he might be to the right of the majority view. There is a majority view that says so what - sure, one of them is wrong, but so what? Prices may deviate temporarily from their correct prices, but unless you can tell me when and in what direction the price is inccorect, then you haven't proven wrong the EMH. The only way to prove the EMH is to beat the market. If you only have the ability to look backwards at stock prices, this isn't what investors do.

Your friend from EC 50 tells you, "I purchased $100k worth of Buford Ultra Tuff Tarpaulin, Inc. stock, a company with a beta of 1.8! I'm likely going to kick butt vs the S&P over the next 10 years with BUTT, Inc.!" Has your friend correctly understood the concepts?

NO: Beta is calculated on a company level, but it is used (and only meaningful) when the stock is held in a portfolio, otherwise beta is describing only part of the risk of the stock. There was enough ambiguity in how this question was phrased that I gave everyone 10 points, regardless of their response. If you didn't get 10 points, on this question, write to me.

our friend says, "I can diversify away all non-systematic risk in my portfolio, therefore investing in stocks - if done correctly - is nearly a risk-free proposition! has your friend correctly understood the concepts?

NO: The goal of a rational investor is to minimize risk to the extent possible - or better stated - maximize return for whatever level of unavoidable risk the investor will tolerate. Optimal stock investing involves minimizing risk through diversification. The residual risk of a well-diversified portfolio is still 'high' compared to other asset classes (like US Treasury Securities) so investing in stocks is never "risk free" no matter how well done. That's why Markopolous 'knew' Madoff was a fraud. Too much return over 25 years with too little risk. Strong statistical evidence of fraud. A die can come up 6 on a single roll. Even twice (or three times!) in a row. The average of a hundred rolls of that die cannot be 6. Power of statistics.

Explain the relationship between the concept of diversification and the concepts of systematic risk and non-systematic risk.

NON-SYSTEMATIC RISK CAN BE 'AVERAGED' OR DIVERSIFIED AWAY. SYSTEMATIC RISK CANNOT.

A project has the following cash flows (by year, starting now): -$100, -$200, $200, $10, $20, $30, $30. You do not know your firm's WACC. Despite that, what can you conclude about this project? a) it should be undertaken, b) it should not be undertaken, c) you can't tell yet, d) Tampa Bay will win the Superbowl.

Not undertaken, the undiscounted sum of cash flows is negative

Explain in what sense an investor who purchases a single stock is behaving irrationally. Has she overpaid or underpaid for the stock? How do you reconcile your answer to the last question with the fact that she paid exactly the same price for the stock as thousands of other people who purchased the stock at the same time she did?

OVERPAID. CARRYING MORE RISK THAN THEY NEED TO FOR THE EXPECTED RETURN

15-year, fixed-rate mortgage of 2.7% annual, compounded monthly. How much house they can afford if they can afford to pay $2,100 a month on their mortgage?

PV=$310,538

30-year, fixed-rate mortgage of 4.7% annual, compounded monthly. How much house they can afford if they can afford to pay $2,100 a month on their mortgage?

PV=$404,906

Which is more valuable to you: a perpetuity that initially pays $100 per year, then has the payment grow by 1.5% per year, or a 20-year annuity paying $225 per year? Assume you are able to invest your money at a local bank and earn 5.0% per year.

Perpetuity ($2,857.14>$2,803.99)

They kept looking and found a house for $345,000. Assuming they put 10% of the purchase price down and finance the balance, a) what will their monthly payment be under the 30-year, 4.7% monthly mortgage? b) What is the total amount of interest paid?

Pmt = $1,610 Total Interest Paid=$269,260

The couple finds a home they love. It costs $360,000. They can scrape together a down payment of 10% of the purchase price. What is their monthly payment under 15-year, 2.7% compounded monthly?

Pmt = $2,191.03 / Mo.

Assume you have $25,000 in savings that you are going to set aside in a 15-year 5% CD (pays principal and interest at maturity and compounds quarterly). When the CD matures you plan to take the total and purchase an annuity. You want to buy a 10 year ordinary annuity. You assume that in 15 years annuities will be paying 5% annual interest. What will your annuity pay you per year?

Pmt = $6,823

NPVs generally increase with decreasing discount rates. T/F?

TRUE

T/F: It is unlikely that any individual stock lies on the SML.

TRUE

When comparing bonds from the same issuer, we generally expect to find that duration and YTM are positively correlated. T/F?

TRUE

The NPV of a capital project, using a discount rate of 11% is $1.2 million. If the company's WACC is 10%, we can be sure (according to financial theory) that the firm should undertake this project in order to increase the value of the firm? Assume the project is of "average risk" compared to the business of the company.

TRUE: NPV AT 10% WILL BE POSITIVE.

What is Malkiel's ultimate test of market efficiency (as described in his paper The Efficient Market and Its Critics?

The ability of investors to consistently earn 'abnormal' returns (returns that are on average higher than an appropriate risk-matched benchmark portfolio, net of taxes, net of transactions costs).

If you randomly choose 50 stocks from the universe of stocks that makes up the US stock market, which of the following statements is likely the best description of the portfolio you now own?

The average stock has a beta of 1 (by definition) so if you randomly choose 50 stocks it is "likely" that your portfolio is both well-diversified and has a beta 'close' to 1. So, "It is a well-diversified portfolio regarding systematic risk and it has a beta close to 1."

If you were setting up an experiment to test whether so-called "market timers" can 'beat' the market, what benchmark would you compare the results of a specific market timer to? Assume that market timers make only the following recommendations (but may do so many times a year), either "hold cash" or "hold the S&P 500."

The complexity here is what is the right benchmark for comparison. It is not the S&P, because some of the time you are not in the S&P and therefore do not have S&P-type risk. The 'right' benchmark is the S&P for the amount of time the market timer says to be in the S&P (not the exact times, but the total time) and a cash portfolio for the amount of time (not the exact times, but the total time) that the newsletter says to be in cash.

You analyze a capital project and conclude that it has an NPV of $(500,000) and an IRR of 12%. What is likely true about the discount rate you used to calculate the NPV? What most likely will be true of the NPV if you recalculate it using a discount rate of 11.8%?

The discount rate is greater than the IRR of 12%. because the NPV yielded is negative. Using a rate of 11.8% will likely yield a positive NPV.

T/F: A portfolio that maintains an average beta of 1.3 over a 10 year period is likely to have an annual average return higher than a broad market index during the same time. Therefore all stock investors should prefer this portfolio over a portfolio with a beta of 1.0, the beta of the broad market.

The premise is true and the conclusion is false. The amount of an individual's risk tolerance is a matter of choice, not a requirement or rule.

You are talking to your doctor about investments. She says that she owns only one stock. You explain to her the benefits of diversification. She says, "I get it! Diversification works like sample size in a medical trial. The more patients we treat, the more certain we can be that the observed results are attributable to the treatment." Does she "get it?"

YES

If the broad market index increased by 16% last year, and you held a well-diversified portfolio who weighted average beta was 1.2, which of the following is true?

Your expectation should be that your portfolio increased by about 19% last year.

All other things being equal, if the nominal risk-free rate of return were to increase significantly, we should expect the nominal "stock market rate of return" would: a) Increase, if we assume that the risk premium remains relatively constant. b) Decrease c) Not change d) Can't predict

a)

So-called "Event Studies" are most relevant to answering which question? a) Whether markets process information quickly b) Whether 'good' managers are able to repeat their performance more than attributable to chance. c) Whether 'professional' managers do, on average, better than a naïve investor. d) What number of randomly chosen stocks result in a well-diversified portfolio.

a)

So-called "Event Studies" contribute most directly to what areas of understanding regarding markets? a) The speed and completeness with which markets incorporate new information into security prices. b) A stock's beta. c) The number of stocks it takes to create a well-diversified portfolio d) The size of the "risk premium." e) The appropriate measure of market risk.

a)

Consider someone who purchases a large number of puts and calls on the same stock (and doesn't own the stock) there are: a) No circumstances under which this strategy will payoff (positive overall return) b) No circumstances under which this strategy could payoff (positive overall return)

a) False b) False

Positive/Negative: Increase in Exercise price: a) Effect on call option price/value b) Effect on put option price/value

a) Negative b) Positive

Positive/Negative: Increase in Time to Expiration: a) Effect on call option price/value b) Effect on put option price/value

a) Positive b) Positive

Positive/Negative: Increase in Volatility of Stock: a) Effect on call option price/value b) Effect on put option price/value

a) Positive b) Positive (Bell Curve is wider/more evenly distributed - higher possibility that you will be "in the money")

Calculate the monthly payment of a five year loan of $10,000 if the annual percentage rate is 12%, compounded monthly. a) What is the total interest paid on this loan (the undiscounted amount of interest paid over the life of the loan)? b) What is the total principal paid over the life of the loan? c) What is the total of all the payments made over the life of the loan (undiscounted)?

a) Total Interest Paid=$3,346.67 b) Total Principal Paid=$10,000 c) Total Paid=$13,346.67

If you believe that markets are efficient, and the day after Tim Cook announced the new iPhone 32 can not only make phone calls, but clean your house as well, however, the stock price doesn't change a bit, you might conclude which of the following? More than one may be true. a) The market does not believe the iPhone 32 will meaningfully change Apple's earnings. b) The market believes that the iPhone 32 will meaningfully change Apple's earnings, but they have thought that for a long time. c) The experts who follow Apple believe that the iPhone 32 will meaningfully change Apple's earnings, but the market hasn't caught up to the news yet. d) Neither the experts nor the market believes Tim Cook is telling the truth.

a), b), & d)

Which of the following statements are generally true? a) YTM and duration are negatively correlated. b) If you know a bond's YTM, you can calculate the current market price by discounting each of the bond's cash flows using the YTM rate. c) If you know a bond's stated terms (coupon amount, maturity date and face amount or principal amount) you have all the information you need to calculate the bond's market price. d) If the yield curve were to become "steeper" across all time periods covered by the curve, it is likely that bond prices also rose. e) STRIPs are useful because the stated coupon rate tells us important information about current market conditions that we need to discount cash flows from conventional bonds. f) If we knew the face amount of a STRIP and its time to maturity, we have everything we need to calculate the STRIP rate for that number of years until it matures. g) As interest rates fall, bond prices rise.

b and g

Assume it is generally true that the Federal Reserve bank can, through the actions of its open market committee, change expectations about inflation in future periods. You are driving home and hear on the radio that the Fed met yesterday and made an important announcement. Just then someone honks at you and you miss the next few words of the report. When you return to paying attention, you hear the announcer say, "....and bond prices fell dramatically today." What can you assume about the Fed's actions? a) They changed perceptions about future inflation, making the market believe inflation would be less than expected. b) They changed perceptions about future inflation, making the market believe inflation would be more than expected. c) Can't conclude anything from the facts given

b)

Consider two call options that are identical in every respect EXCEPT that Option A has a higher call (strike) price than Option B. We can reasonably conclude that: a) Option A is more valuable than Option B b) Option B is more valuable than Option A c) We cannot reasonably conclude anything regarding the relative values of Options A and B.

b)

If a friend told you she followed one company very closely in her spare time and "went in and out of the stock" based on the news of the day and her feeling as to the impact that news would have on the short-term price movement of that stock, which one of the following articles do you think she should read and understand and why? a) The Million Dollar Microsecond b) "Forget Market Timing" c) The study regarding the performance of fund managers over time d) The study regarding the average performance of fund managers vs a benchmark portfolio.

b)

If you owned a substantial amount of Apple stock and if you wrote put options on Apple stock, in the event that Apple stock price declined very substantially during the option period, you would be: a) Better off than you would have been had you not written the options. b) Worse off than you would have been had you not written the options. c) In roughly the same position you would have been in had you not written the options.

b)

An insurance company offers two retirement products, each is an annuity. The first one pays a guaranteed annual amount for as long as the annuity holder is alive. The second product is a "variable annuity" that pays a guaranteed minimum annual amount (which is less than the first product), but in addition, it pays a variable payment tied to changes in the S&P 500 index. When the market goes up, the payment will increase. When the market declines, the payment will decrease. You are told that the price to purchase either annuity is $100,000. Assuming the annuities are "fairly priced," what can you expect regarding the amount of money you will receive over the course of your life? a) The fixed annuity will pay you more. b) The variable annuity will pay you more. c) Both annuities will pay you the same. Can't tell

b) only because the time horizon is specified to be very long (retirement)

As discussed in EC-50, what is the best description of the "Warren Buffet Problem"? a) Buffet's success as an investor is an irrefutable contradiction to market efficiency. b) Buffet's success as an investor says nothing about market efficiency as data points like that are completely irrelevant to any discussion of EMH. c) Buffet's success as an investor, along with others who have achieved "abnormal returns" for a long period of time is data that must be considered and explained, but is not, as such, an irrefutable contradiction to market efficiency.

c)

Duration" as applied to bonds can best be described as: a) A measure of the risk of the bond b)A measure of the YTM of the bond c) A measure of the "average life" of the bond d) A measure of the expected level of inflation

c)

Your portfolio contains a large amount of stock from a company you once worked for. You have not rebalanced your portfolio to better ensure diversification as you are concerned about the taxes that will be due when you sell the stock. As a result you follow the price of this stock - Company X - fairly closely. Driving home from work one day you were wondering how Company X's stock did that day as you knew they were going to announce their quarterly sales and earnings that morning before the market opened. Unfortunately you missed the announcement and your iPhone was dead. As you were thinking these thoughts a genie magically appeared and said, "You can ask me two questions to help you figure out if Company X's stock price rose or fell today, but you cannot ask me anything about the stock price specifically." Which of the following two questions would be the most useful for you to ask? a) What were Company X's earnings? b) What were Company X's sales? c) Did the overall market go up or down today? d) What happened in the bond market today? e) Were Company X's earnings above or below expectations? f) Were Company X's sales above or below expectations? g) Were any management changes at Company X announced today with the earnings report?

c) & e)

Which of the following statements is/are generally true as a theoretical point if you adopt the general teachings of CAPM and market efficiency? More than one may be true. a) Beta is a measure of firm-specific risk and it is measured at a firm level. b) Beta is a measure of total risk and it is measured at a portfolio level. c) Beta is a measure of systematic risk and it is measured at the firm level. d) All investors should be equity investors as expected returns are higher for equity portfolios than for less risky asset classes. e) An investor's time horizon is important when making investment decisions in the real world because all investments carry risk as measured by variance in annual returns. f) All firms carry both firm-specific risk and market (systematic risk).

c, e, & f

If serial price changes for stocks, or stock indices followed a true random walk, then which of the following would be true? a) It is just as likely for any sequential price change (return) to be positive as negative. b) No fund manager could consistently outperform an appropriate portfolio benchmark c) Purchasing stocks would not be an investment, but a gamble d) a. & c. e) a, b and c.

d)

If you observed that on the day that a company announced its quarterly results, that the stock price declined significantly, what is the likely explanation(s)? a) Earnings declined versus the previous quarter b) Earnings increased versus the previous quarter c) Sales declined versus the previous quarter d) Earnings increased versus the previous quarter, but not as much as expected e) a. & c.

d)

The fact that price changes for both individual stocks and market indices can be well modeled as a random walk; that is, successive price changes are nearly as likely to be "up" as "down," implies that investment in the stock market is essentially a gamble, not an investment. a) True, because if prices move randomly with regard to "sign" (up vs. down) the expected return from such an investment must be close to zero, indicating the investment is actually a gamble. b) False, because while it is generally true that stock prices follow a random walk, investors can choose to invest in quality stocks whose price changes are not random and therefore represent an actual investment. c) False, because while the overall changes in price are well modeled as random walks, professionals have a much better than average ability to find "growth stocks" whose prices do not follow a random walk. Therefore investing with professional advice is not a gamble, but an investment. d) False, because although price changes are well modeled as a random walk, there is a slight positive bias towards increases in stock prices over time which match investors' expected return.

d)

Which concept is most closely connected to the "Million Dollar Microsecond" and to the concept of market efficiency? a) That nothing travels faster than light. b) Most stock trading is done by computers, not humans. c) Markets are rigged in favor of those with the costliest equipment. d) It is unlikely you will find $100 bills lying around on the streets of New York.

d)

Which of the following is a reasonable restatement of some feature of financial markets if you are an adherent of the CAPM view of the world and also believe that markets are semi-strong efficient? Circle all that apply. a) Risk and return are negatively correlated. b) All risks matter. c) The existence of insider trading is evidence against EMH d) There is no such thing as a free lunch, with expected return comes expected risk. d) Current stock prices are the "best" predictor of future stock prices. e)Financial assets are priced based on their expected return and their diversifiable risk factors.

d) & e)

Which of the following questions is not answered, in principle, by calculating the PV of a series of cash flows? a) The value of a share of Apple. b) The advisability of undertaking a major capital project within a firm. c) The market price of a bond. d) The value of a call option.

d) - (although you could make an argument even for this choice.If "none of the above" had been a choice, that would have been the best choice.

Three years after graduation you are at a cocktail party with many successful professionals. You are speaking to someone you do not know and they tell you they are an independent investor, you ask about her investment strategy and she says that she has developed an algorithmic trading model that she developed (she was a CS major at Tufts) and she uses that model to make short-term investment decisions including which stocks to buy, when to "get out of the market," and depending on the "strength of the buy/sell signal" whether to buy put or call options on particular stocks. She says that while her returns are not spectacular when compared to returns that other investors achieve with stock portfolios, maximizing return was not her goal, rather she was focused on the risk side and the beauty of her program is that it reduces investment risk considerably. She offers to use the algorithm to manage your stock portfolio for an annual fee of 1.5% of your portfolio value. You agree that risk is an important part of any investment strategy and reducing risk is a valuable goal. You promise to think about her offer. As you do, which 'voice' and which message/line of thinking should be foremost in your mind? a) Markowitz: "An equity investor can minimize risk for a given level of expected return by creating a well-diversified portfolio of securities." b) Farmer Brown: "I can sell you an individual-acre contract, but that's not how I do it and the price will be the same as for a whole-farm-average acre." c) Brealey & Myers: "If you can't remember that any other way, tattoo it on your forehead." d) Jesus: "It is harder for a rich man to enter the kingdom of heaven than for a camel to pass through the eye of a needle." (Paraphrasing perhaps). e) Markopolous: "When I see abnormal returns, I suspect fraud." f) Roosevelt: "We have nothing to fear, but fear itself." g) None of the above.

e)

If you were discussing EC-50 and EMH with your mother and she said the following, "Well, I never studied EMH, but I can tell you it seems like a lot of egg-headed nonsense to me and let me tell you why. I generally buy three companies I understand really well and I have done just fine with my strategy. In fact, I purchased Yum Brands 10 years ago and it has done great! Portfolio investing is for people who aren't smart enough too find good investments." Which of the following thoughts/questions should run through your mind even as you are saying, "Mom, you are the best, nicest, smartest person in the whole world! Thank you for being my Mom!" a) I wonder what the annual variance in her returns has been? b) I wonder what a comparable portfolio has done over the same time period? c) I wonder whether she is accounting for her after-tax returns from buying and selling? d) I wonder whether she is filtering out from her memory some of her poor investments and fooling herself by focusing on the successes? e) I wonder whether maybe she got lucky, but luck isn't an investment strategy, that's my inheritance she's gambling with! f) I wonder if her investment strategy will work for the next twenty years? g) All of the above.

g)

How long will it be until a silo filled with 50 tons of grain is half empty if the silo is emptying at the rate of 4% per hour?

n=16.9 hours

You receive an inheritance of $100,000. However the terms of the bequest specify that you cannot take possession of the cash until the sum has grown to $250,000. The money is being held in trust for you in an account that is currently paying 10%, compounded quarterly. The bank where the account is held guarantees the rate is fixed for the first five years, but thereafter may increase, but will not decrease. If the interest rate increases, the increase will not be more than 200 basis points (2%) above the current rate (total, ever). What is a) the soonest, and b) the latest you will be able to claim your inheritance?

n=8.57 years (soonest) n=9.28 years (latest)

What annual interest rate will result in $10,000 growing to $15,000 in five years?

r=8.45%

The couple finds a home they love. It costs $360,000. They can scrape together a down payment of 10% of the purchase price. What is their monthly payment under 30-year, 4.7% compounded monthly?

Pmt = $1,680.46 / Mo.

How much would you need to save at the end of every year for the next 30 years if you wanted to have $1.0 million at the end? Assume you could earn 5% annually on any funds saved.

Pmt = $15,051

How much do you have to save at the end of every year, for the next ten years (ten payments) in order to have enough money to buy an annuity that will give you 20 payments of $40,000 each? Assume you can earn 4.0%, compounded quarterly on your savings and assume that annuities will pay out based on a 3% rate.

Pmt=$49.4k per year

If you purchase a 20-year annuity for $100,000, and if it is "fairly priced" and if the payments are based on 5% per year, how much will the annuity pay you per year for each of the next 20 years?

Pmt=$8,024

Assume that a borrower is willing to pay you $2,000 at the end of three years in return for a sum of money now. To receive an annual return of 10%, how much are you willing to lend now?

$1,502.63

Find the future value of $10,000 invested now after five years if the annual interest rate is 8 percent (compounded annually).

$14,693.28

Find the future value of $10,000 invested now after five years is the annual interest rate is 8%, compounded quarterly.

$14,859.47

If you have a credit card balance of $2,000 that is being charged 18%, compounded monthly, and you make no payments on that card for two years, and then want to pay it off in two more years by way of equal monthly payments (24 of them), what will those monthly payments be?

$142.73 per month

According to CAPM, what is the expected annual return on a security with a beta of 0.9 assuming the following facts to be true: The expected return on short-term US obligations is 0.5%, and the expected return on the stock market is 8%.

Ans: 7.2% Er = Erf + beta (E(rm)-rf)

When we say that investors do not care about non-systematic risk, that implies that a major positive, firm-specific (non-systematic) event at a company has no effect on the stock price of that company.

FALSE

T/F: Assume the board of directors of a public company was meeting and one of the directors made the following statement: "I've been taking the online version of Ec-50 and I've leaned something important regarding what we might do to increase our stock price. If we can make our company significantly more risky - meaning we can find a way to make the present value of our earnings less consistent or predictable - we will increase the beta of our company's stock. The higher beta implies to investors that they will earn a higher rate of return if they group our stock in their portfolio with other companies of similar beta. Therefore, investors will pay more for our stock and the stock price should increase - all other things the same."

The director is generally correct in his premise, but incorrect regarding his conclusion.

Your employee has done an extensive analysis of a capital project your company is proposing. The project is an investment in a new production line that will increase capacity. The employee had access to all of the capital costs, incremental sales, margins, maintenance expenses, etc. She concluded that the NPV of the project is $1 million. She presents that conclusion to you in a memo stating, "I have analyzed the project and concluded it has an NPV of $1 million. I recommend we proceed with the project." What is the first question you should ask your employee?

WHAT DISCOUNT RATE DID YOU USE?

Calculate the present values of each of the following, then express those PVs as a percentage of the PV of the perpetuity. In all cases use a discount rate of 15%: a)An annuity paying $1.0 million per year for 10 years. b) An annuity paying $1.0 million per year for 15 years. c) An annuity paying $1.0 million per year for 20 years. d) A perpetuity paying $1.0 million per year.

a) $5,018,768.625; 75.28% b) $5,847,370.10; 87.71% c) $6,259,331.47; 93.89% d) $6,666,666,67

Considering the same facts as above, which of the following is likely to approximate the change in the value of the portfolio (ignore sign, just think about magnitude of the change). a) The PV of 0.5% of $100k b)The PV of 2.5% of $100k c) The PV of 3% of $100k d) None of the above

a)

If two bonds mature on the same date, and were issued by the same borrower and we observe that the YTM for the two bonds are meaningfully different, the most likely explanation is: a) The bonds were issued at dates that were far apart b) The bonds have different credit risks c) The bonds have different maturity dates d) The durations are the same None of the above

a)

Suppose a company "earns" $1.5 million a year. Assume that those earnings are reasonably equal to "cash flow." What is the value of a firm to an investor under the following assumptions: a) Earnings will grow by 3% per year b) Earnings will grow by 5% per year In both cases assume that the investor doing the analysis has a "base rate" of required return of 15% annually on all her investments.

a) $12.5 M b) $15 M

You have $10,000 in savings. Assume you earn 2.5% compounded quarterly on it for three years, then you earn 5% annually for the next two years, then you withdraw $1,000 to buy a new phone, then you earn 7% per year on the remaining balance for 10 more years. a) How much savings will you have at the end of the entire time? b) How much would you have had if you had not purchased the phone?

a) $21,404 b) $23,371

a) What is the NPV of the following cash flows? (discount at 10%). Year 1: ($10,000) Year 2: ($1,000) Year 3: 4,000 Year 4: 5,000 Year 5: 6,000 b) If the firm's WACC is 11%, this company should (assuming project is of average risk): i. Do the project ii. Not do the project iii. Can't tell without further calculation c) What would the CF in year 5 have to be in order for this project to have an IRR of 10%? (calculations required).

a) $252 b) Can't tell without further calcs c) $5,631

Determine the future values if $5,000 is invested a) 5 percent for ten years, compounded quarterly; b) 7 percent for seven years, compounded semi-annually; c) 9 percent for four years, compounded monthly

a) $8,218.10 b)8,093.27 c)$7,157.03

Bond A: Coupon rate=2%; Maturity Date=2022; Par value=99.5 Bond B: Coupon rate=3%; Maturity Date=2021 Bond C: Coupon rate=1%; Maturity Date=2023 a) Which Bond is most likely trading below par? b) Which Bond is most likely trading above par? c) If interest rates were to suddenly "spike up" in the market most relevant to these bonds, which of the following statements is true? i. The par values for all would fall ii. The par values for all would rise iii. It is not possible to predict what would happen to the par values under these circumstances. d) Which of these bonds could be a STRIP? i. A ii. B iii. C iv. A&C v. Can't Tell vi. None

a) Bond C b) Bond B c) Par values for all would fall

If a car dealer says he will finance your purchase of a car at 14%, compounded monthly for 60 months, and your payments will be a "low, low $250/month." a) What price car could you purchase if you had $10,000 for a down-payment on that car? How much would you have paid in interest over the life of that loan? b) If you didn't buy that car, but found a wreck instead for $10,000 and took the money you would have used for car payments and instead paid those monthly amounts into an account paying 4%, compounded monthly, how much money would you have in that account at the end of five years?

a) Can afford $20,744.25; total interest paid=$4,255.75 b) $13,574.77

Assume you own a home and have an existing mortgage (loan) outstanding on that home. You are paying a rate of 5.5% on that mortgage and, while it was a 30 year loan when you first took out the loan, it is now exactly 15 years until the mortgage will be due. You read that mortgage rates have fallen and are considering taking out a new mortgage in an amount to pay off the existing loan, but you also want to pay off the mortgage on the original date, when your youngest child will be entering Tufts. The house you bought cost $500,000 and you put down 10%. You call your mortgage company to ask what you owe on the mortgage. The banker says, "You know you can calculate that outstanding balance using Excel or your HP12C." To which you reply, "Yes, I know that, but we didn't cover that in EC 50 and I'm a character in an exam question, so I have to ask you." She replies, "Oh, I understand. $310,000." You thank her and hang up. a) What are you currently paying monthly on your mortgage? b) If you keep this mortgage, how much interest will you pay over the next 15 years of the loan? c) If you take out a new mortgage at the new terms, how much will you be paying monthly? d) How much will you pay in interest over the life of the new loan? e) Under these conditions, assuming you want to be rational (and ignoring any questions around taxes or fees, or costs) is it enough to compare your answers to questions a. and c and choose the one with the lower payment? i. Yes ii. No iii. Maybe so

a) Current Pmt=$2,555 b) Total interest paid in last 15 years=$149,909 c) New Pmt=$2,216 d) Total Interest New=$88,904.46 e) Yes

You analyze a capital project and conclude that it has an NPV of $(500,000) and an IRR of 12%. a) What is likely true about the discount rate you used to calculate the NPV? b) What most likely will be true of the NPV if you recalculate it using a discount rate of 11.8%?

a) Discount rate you used to calculate the NPV is MORE THAN 12% b) POSITIVE NPV w discount rate of 11.8%

A firm's management met to review a capital investment. The CFO provided a DCF analysis that showed the project's IRR of 13% was below the firm's WAAC. The participants agreed not to proceed and were heading for the door when the head of engineering spoke up and said, "I think we could re-engineer the main neutron flux regulator to reduce its cost significantly." The CFO scoffed and said, "The capital cost occurs in year "zero" and is undiscounted, so your suggestion could not change our conclusion, even if you were able to do what you propose." Who is thinking clearly? a) Engineer b) CFO c) Neither d) Both

a) Engineer

They kept looking and found a house for $345,000. Assuming they put 10% of the purchase price down and finance the balance, a) what will their monthly payment be under the 15-year, 2.7% monthly mortgage? b) What is the total amount of interest paid?

a) Pmt = $2,100 b) Total Interest Paid=$67,453

You are considering taking out a $500,000 mortgage in order to purchase a home. You are considering the following two offers. For each offer, calculate the monthly payment, the total (undiscounted) dollars paid to the lender over the life of the loan, and the total interest (undiscounted) paid to the lender. a) 30 years, 4.8% annual interest rate, paid monthly. b) 15 years, 3.6% annual interest rate, paid monthly.

a) Pmt = $2623 Total amount paid=$944,397 Total interest paid=$444,397 b) Pmt = $3,599 Total amount paid=$647,823 Total interest paid=$147,823

You inherited $225,000 from a rich uncle. You have set yourself the objective of retiring in 30 years with at least $500,000 in savings. a) What is the minimum average annual rate you must earn to achieve that goal? b) After 20 years you are pleasantly surprised to find that your savings have grown into $400,000. What average rate did you earn for the first 20 years?

a) r=2.69% b) r=2.92%

Assume an investor purchased $100k worth of bonds two years ago when yields on that portfolio averaged out to 3% and had an average duration of 5.0 years. Assume yields fell overnight to 2.5%. What happened to the value of the investor's portfolio? The average coupon rate of the bonds is 1%. a) It went down b) It went up c) It remained unchanged d) Can't tell from the facts given

b) (?)

Assume that a decade ago inflation was significantly higher than it is today, when looking at bonds issued during that time, but that have not yet matured, you would expect to see that they are generally trading: a) At par b) Above par c) Below par d) Can't tell

b) Above Par

What "inputs" are necessary to calculate the YTM of a bond? a) Price and discounted cash flows by year b) Price and undiscounted cash flows by year c) Price and duration None of the above would suffice

b) Price and undiscounted cash flows by year

If a five year US G'ment bond with a 1% coupon rate is trading significantly above par, it is reasonable to conclude: a) Investors, on average, expect inflation to be above 1% over the next five years. b) Investors, on average, expect inflation to be below 1% over the next five years. c) We cannot conclude anything regarding investors' expectations regarding inflation.

b) b) Investors, on average, expect inflation to be below 1% over the next five years.

Which of the following statements best describes the situation an investor -- who carefully constructed a portfolio with an average beta of 1.2 - would face? a)The expected return on that portfolio would not likely stay constant over the years b) Keeping the beta of the portfolio stable might require buying and selling shares in the portfolio c) Even assuming nothing else in the world changed one bit from the time the portfolio was assembled, if betas of stocks in the portfolio changed, then the prices for those stocks might change, even absent any other changes (for example a change in earnings). d) All of the above

d) All of the above

You get an email from a friend telling you about a fundraiser her charity is doing. They are "selling" rubber ducks. Each duck is numbered and each is associated with its owner. All the ducks will be put into a local stream at the same time. The first duck to cross the finish line gets $100, the second duck to cross the line gets $75, the third duck gets $50 and the fourth gets $25. The prize money has been donated by an anonymous donor. Each duck costs a $1.00. You ask your friend how many ducks are being sold and she says, "We limit it to 100, but we seldom manage to sell that many. I'm on the fundraising committee so I'm expected to find buyers for the ducks; I really hope we can sell them all this year." You pause for a few minutes, and then make an offer to your friend. Assuming you are a cold-hearted capitalist who hates to part with a nickel, let alone a dollar, which of the following offers is the most logical? Why? a) Offer to buy a duck for a dollar and hope you win. b) Offer to buy 10 ducks for $10 dollars and hope you win. c) Find an excuse to not buy a duck. d) Offer to make your friend's day by buying all the ducks for $100.

d) Positive Er=$150!, no risk.

According to financial theory, which of the following is true/logical? a) As interest rates rise, a firm's WACC generally decreases, spurring capital investment. b) As interest rates fall, a firm's WACC generally decreases, raising the IRR of some capital projects. c) As interest rates rise, a firm's WACC generally increases, lowering the IRR of some capital projects. d) As interest rates fall, a firm's WACC generally decreases, choking or slowing capital investments. e) None of the above.

e); d would be true if WACC was increasing

You meet with your investment advisor and she says, "You can expect your investment in this portfolio to double in only 15 years!" What annual return is she promising?

r=4.73%

In 1990, the average tuition for one year in the MBA program at a university was $3,600. Thirty years later, in 2020, the average tuition was $27,400. What is the compound annual growth rate in tuition over the 30-year period?

r=6.999%