Deck 29: Basic Financial Tools: A review

Question 1

The market value of any real or financial asset, including stocks, bonds, or art work purchased in hope of selling it at a profit, may be estimated by determining future cash flows and then discounting them back to the present.

Answer 1

True

Question 2

Diversification will normally reduce the riskiness of a portfolio of stocks.

Answer 2

True

Question 3

The tighter the probability distribution of its expected future returns, the greater the risk of a given investment as measured by its standard deviation.

Answer 3

False

Question 4

According to the Capital Asset Pricing Model, investors are primarily concerned with portfolio risk, not the risks of individual stocks held in isolation. Thus, the relevant risk of a stock is the stock's contribution to the riskiness of a well-diversified portfolio.

Question 5

Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.

Question 6

For bonds, price sensitivity to a given change in interest rates is generally greater the longer before the bond matures.

Question 7

An individual stock's diversifiable risk, which is measured by its beta, can be lowered by adding more stocks to the portfolio in which the stock is held.

Question 8

If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate.

Question 9

Managers should under no conditions take actions that increase their firm's risk relative to the market, regardless of how much those actions would increase the firm's expected rate of return.

Question 10

One key conclusion of the Capital Asset Pricing Model is that the value of an asset should be measured by considering both the risk and the expected return of the asset, assuming that the asset is held in a well-diversified portfolio. The risk of the asset held in isolation is not relevant under the CAPM.

Question 11

Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.

Question 12

Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.

Question 13

If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series.

Question 14

According to the nonconstant growth model discussed in the textbook, the discount rate used to find the present value of the expected cash flows during the initial growth period is the same as the discount rate used to find the PVs of cash flows during the subsequent constant growth period.

Question 15

The coefficient of variation, calculated as the standard deviation of expected returns divided by the expected return, is a standardized measure of the risk per unit of expected return.

Question 16

When adding a randomly chosen new stock to an existing portfolio, the higher (or more positive) the degree of correlation between the new stock and stocks already in the portfolio, the less the additional stock will reduce the portfolio's risk.

Question 17

A zero coupon bond is a bond that pays no interest and is offered (and subsequently sells initially) at par. These bonds provide compensation to investors in the form of capital appreciation.

Question 18

Because short-term interest rates are much more volatile than long-term rates, you would, in the real world, generally be subject to much more interest rate price risk if you purchased a 30-day bond than if you bought a 30-year bond.

Question 19

A "growing annuity" is a cash flow stream that grows at a constant rate for a specified number of periods.

Question 20

A bond that had a 20-year original maturity with 1 year left to maturity has more interest rate price risk than a 10-year original maturity bond with 1 year left to maturity. (Assume that the bonds have equal default risk and equal coupon rates, and they cannot be called.)

Question 21

A stock's beta is more relevant as a measure of risk to an investor who holds only one stock than to an investor who holds a well-diversified portfolio.

Question 22

A bond has a $1,000 par value, makes annual interest payments of $100, has 5 years to maturity, cannot be called, and is not expected to default. The bond should sell at a premium if interest rates are below 10% and at a discount if interest rates are greater than 10%.

Question 23

When a loan is amortized, a relatively low percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage increases in the loan's later years.

Question 24

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal.

Question 25

Variance is a measure of the variability of returns, and since it involves squaring the deviation of each actual return from the expected return, it is always larger than its square root, its standard deviation.

Question 26

All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases.

Question 27

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

Question 28

You have funds that you want to invest in bonds, and you just noticed in the financial pages of the local newspaper that you can buy a $1,000 par value bond for $800. The coupon rate is 10% (with annual payments), and there are 10 years before the bond will mature and pay off its $1,000 par value. You should buy the bond if your required return on bonds with this risk is 12%.

Question 29

If the returns of two firms are negatively correlated, then one of them must have a negative beta.

Question 30

Portfolio A has but one stock, while Portfolio B consists of all stocks that trade in the market, each held in proportion to its market value. Because of its diversification, Portfolio B will by definition be riskless.

Question 31

Portfolio A has but one security, while Portfolio B has 100 securities. Because of diversification effects, we would expect Portfolio B to have the lower risk. However, it is possible for Portfolio A to be less risky.

Question 32

It is possible for a firm to have a positive beta, even if the correlation between its returns and those of another firm is negative.

Question 33

The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant.

Question 34

Because of differences in the expected returns on different investments, the standard deviation is not always an adequate measure of risk. However, the coefficient of variation adjusts for differences in expected returns and thus allows investors to make better comparisons of investments' stand-alone risk.

Question 35

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan).

Question 36

A stock's beta measures its diversifiable risk relative to the diversifiable risks of other firms.

Question 37

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date.

Question 38

The prices of high-coupon bonds tend to be less sensitive to a given change in interest rates than low-coupon bonds, other things held constant.

Question 39

A portfolio's risk is measured by the weighted average of the standard deviations of the securities in the portfolio. It is this aspect of portfolios that allows investors to combine stocks and thus reduce the riskiness of their portfolios.

Question 40

Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Question 41

Midway through the life of an amortized loan, the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal. This is true regardless of the original life of the loan or the interest rate on the loan.

Question 42

If you plotted the returns of a company against those of the market and found that the slope of your line was negative, the CAPM would indicate that the required rate of return on the stock should be less than the risk-free rate for a well-diversified investor, assuming that the observed relationship is expected to continue in the future.

Question 43

Any change in its beta is likely to affect the required rate of return on a stock, which implies that a change in beta will likely have an impact on the stock's price, other things held constant.

Question 44

Which of the following statements is CORRECT?

A) time lines cannot be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity.
B) a time line is not meaningful unless all cash flows occur annually.
C) time lines are not useful for visualizing complex problems prior to doing actual calculations.
D) time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly.
E) time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities.

Question 45

Which of the following bonds would have the greatest percentage increase in value if all interest rates fall by 1%?

A) 20-year, 10% coupon bond.
B) 20-year, 5% coupon bond.
C) 1-year, 10% coupon bond.
D) 20-year, zero coupon bond.
E) 10-year, zero coupon bond.

Question 46

The CAPM is built on historic conditions, although in most cases we use expected future data in applying it. Because betas used in the CAPM are calculated using expected future data, they are not subject to changes in future volatility. This is one of the strengths of the CAPM.

Question 47

If an investor buys enough stocks, he or she can, through diversification, eliminate all of the market risk inherent in owning stocks, but as a general rule it will not be possible to eliminate all diversifiable risk.

Question 48

The slope of the SML is determined by the value of beta.

Question 49

The Y-axis intercept of the SML indicates the required return on an individual asset whenever the realized return on an average (b = 1) stock is zero.

Question 50

You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?

A) the discount rate decreases.
B) the cash flows are in the form of a deferred annuity, and they total to $100,000. you learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000.
C) the discount rate increases.
D) the riskiness of the investment's cash flows decreases.
E) the total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.

Question 51

If its yield to maturity declined by 1%, which of the following bonds would have the largest percentage increase in value?

A) a 1-year bond with an 8% coupon.
B) a 10-year bond with an 8% coupon.
C) a 10-year bond with a 12% coupon.
D) a 10-year zero coupon bond.
E) a 1-year zero coupon bond.

Question 52

Under the CAPM, the required rate of return on a firm's common stock is determined only by the firm's market risk. If its market risk is known, and if that risk is expected to remain constant, then analysts have all the information they need to calculate the firm's required rate of return.

Question 53

If you plotted the returns on a given stock against those of the market, and if you found that the slope of the regression line was negative, the CAPM would indicate that the required rate of return on the stock should be greater than the risk-free rate for a well-diversified investor, assuming that the observed relationship is expected to continue into the future.

Question 54

Which of the following bonds has the greatest interest rate price risk?

A) a 10-year, $1,000 face value, zero coupon bond.
B) a 10-year, $1,000 face value, 10% coupon bond with annual interest payments.
C) all 10-year bonds have the same price risk since they have the same maturity.
D) a 10-year, $1,000 face value, 10% coupon bond with semiannual interest payments.
E) a 10-year $100 annuity.

Question 55

Even if the correlation between the returns on two securities is +1.0, if the securities are combined in the correct proportions, the resulting 2-asset portfolio will have less risk than either security held alone.

Question 56

Which of the following statements is CORRECT?

A) if a stock has a required rate of return rs = 12% and its dividend is expected to grow at a constant rate of 5%, this implies that the stock's dividend yield is also 5%.
B) the stock valuation model, p0 = d1/(rs ? g), can be used to value firms whose dividends are expected to decline at a constant rate, i.e., to grow at a negative rate.
C) the price of a stock is the present value of all expected future dividends, discounted at the dividend growth rate.
D) the constant growth model cannot be used for a zero growth stock, where the dividend is expected to remain constant over time.
E) the constant growth model is often appropriate for evaluating start-up companies that do not have a stable history of growth but are expected to reach stable growth within the next few years.

Question 57

The Y-axis intercept of the SML represents the required return of a portfolio with a beta of zero, which is the risk-free rate.

Question 58

Assume that all interest rates in the economy decline from 10% to 9%. Which of the following bonds would have the largest percentage increase in price?

A) a 1-year bond with a 15% coupon.
B) a 3-year bond with a 10% coupon.
C) a 10-year zero coupon bond.
D) a 10-year bond with a 10% coupon.
E) an 8-year bond with a 9% coupon.

Question 59

A 10-year bond with a 9% annual coupon has a yield to maturity of 8%. Which of the following statements is CORRECT?

A) the bond is selling below its par value.
B) the bond is selling at a discount.
C) if the yield to maturity remains constant, the bond's price one year from now will be lower than its current price.
D) the bond's current yield is greater than 9%.
E) if the yield to maturity remains constant, the bond's price one year from now will be higher than its current price.

Question 60

Since the market return represents the expected return on an average stock, the market return reflects a certain amount of risk. As a result, there exists a market risk premium, which is the amount over and above the risk-free rate, that is required to compensate stock investors for assuming an average amount of risk.

Question 61

Which is the best measure of risk for a single asset held in isolation, and which is the best measure for an asset held in a diversified portfolio?

A) standard deviation; correlation coefficient.
B) beta; variance.
C) coefficient of variation; beta.
D) beta; beta.
E) variance; correlation coefficient.

Question 62

A 15-year bond has an annual coupon rate of 8%. The coupon rate will remain fixed until the bond matures. The bond has a yield to maturity of 6%. Which of the following statements is CORRECT?

A) the bond is currently selling at a price below its par value.
B) if market interest rates remain unchanged, the bond's price one year from now will be lower than it is today.
C) the bond should currently be selling at its par value.
D) if market interest rates remain unchanged, the bond's price one year from now will be higher than it is today.
E) if market interest rates decline, the price of the bond will also decline.

Question 63

You are considering two equally risky annuities, each of which pays $15,000 per year for 20 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

A) if the going rate of interest decreases from 10% to 0%, the difference between the present value of ord and the present value of due would remain constant.
B) the present value of ord must exceed the present value of due, but the future value of ord may be less than the future value of due.
C) the present value of due exceeds the present value of ord, while the future value of due is less than the future value of ord.
D) the present value of ord exceeds the present value of due, and the future value of ord also exceeds the future value of due.
E) the present value of due exceeds the present value of ord, and the future value of due also exceeds the future value of ord.

Question 64

Your friend is considering adding one additional stock to a 3-stock portfolio, to form a 4-stock portfolio. She is highly risk averse and has asked for your advice. The three stocks currently held all have b = 1.0, and they are perfectly positively correlated with the market. Potential new Stocks A and B both have expected returns of 15%, are in equilibrium, and are equally correlated with the market, with r = 0.75. However, Stock A's standard deviation of returns is 12% versus 8% for Stock B. Which stock should this investor add to his or her portfolio, or does the choice not matter?

A) stock a.
B) stock b.
C) neither a nor b, as neither has a return sufficient to compensate for risk.
D) add a, since its beta must be lower.
E) either a or b, i.e., the investor should be indifferent between the two.

Question 65

A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT?

A) the pv of the $1,000 lump sum has a higher present value than the pv of a 3-year, $333.33 ordinary annuity.
B) the periodic interest rate is greater than 3%.
C) the periodic rate is less than 3%.
D) the present value would be greater if the lump sum were discounted back for more periods.
E) the present value of the $1,000 would be smaller if interest were compounded monthly rather than semiannually.

Question 66

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 8% is CORRECT?

A) exactly 8% of the first monthly payment represents interest.
B) the monthly payments will decline over time.
C) a smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment.
D) the total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity.
E) the amount representing interest in the first payment would be higher if the nominal interest rate were 6% rather than 8%.

Question 67

Bond A has a 9% annual coupon while Bond B has a 6% annual coupon. Both bonds have a 7% yield to maturity, and the YTM is expected to remain constant. Which of the following statements is CORRECT?

A) the prices of both bonds will remain unchanged.
B) the price of bond a will decrease over time, but the price of bond b will increase over time.
C) the prices of both bonds will increase by 7% per year.
D) the prices of both bonds will increase over time, but the price of bond a will increase by more.
E) the price of bond b will decrease over time, but the price of bond a will increase over time.

Question 68

An 8-year Treasury bond has a 10% coupon, and a 10-year Treasury bond has an 8% coupon. Both bonds have the same yield to maturity. If the yield to maturity of both bonds increases by the same amount, which of the following statements would be CORRECT?

A) both bonds would decline in price, but the 10-year bond would have the greater percentage decline in price.
B) the prices of both bonds would increase by the same amount.
C) one bond's price would increase, while the other bond's price would decrease.
D) the prices of the two bonds would remain constant.
E) the prices of both bonds will decrease by the same amount.

Question 69

Stock A's beta is 1.7 and Stock B's beta is 0.7. Which of the following statements must be true about these securities? (Assume market equilibrium.)

A) stock b must be a more desirable addition to a portfolio than a.
B) stock a must be a more desirable addition to a portfolio than b.
C) the expected return on stock a should be greater than that on b.
D) the expected return on stock b should be greater than that on a.
E) when held in isolation, stock a has more risk than stock b.

Question 70

Which of the following statements is CORRECT?

A) an investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.
B) the present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.
C) if a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%.
D) if a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.
E) the proportion of the payment that goes toward interest on a fully amortized loan increases over time.

Question 71

Bonds A, B, and C all have a maturity of 15 years and a yield to maturity of 9%. Bond A's price exceeds its par value, Bond B's price equals its par value, and Bond C's price is less than its par value. Which of the following statements is CORRECT?

A) bond a has the most interest rate risk.
B) if the yield to maturity on the three bonds remains constant, the prices of the three bonds will remain the same over the next year.
C) if the yield to maturity on each bond increases to 8%, the prices of all three bonds will decline.
D) bond c sells at a premium over its par value.
E) if the yield to maturity on each bond decreases to 6%, bond a will have the largest percentage increase in its price.

Question 72

Which of the following statements regarding a 20-year (240-month) $225,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

A) the outstanding balance declines at a slower rate in the later years of the loan's life.
B) the remaining balance after three years will be $225,000 less one third of the interest paid during the first three years.
C) because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant.
D) interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.
E) the proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year.

Question 73

Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?

A) banks a and b offer the same nominal annual rate of interest, but a pays interest quarterly and b pays semiannually. deposits in bank b will provide the higher future value if you leave your funds on deposit.
B) the present value of a 5-year, $250 annuity due will be lower than the pv of a similar ordinary annuity.
C) a 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.
D) a bank loan's nominal interest rate will always be equal to or less than its effective annual rate.
E) if an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%.

Question 74

Your bank account pays a 5% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

A) the periodic rate of interest is 5% and the effective rate of interest is also 5%.
B) the periodic rate of interest is 1.25% and the effective rate of interest is 2.5%.
C) the periodic rate of interest is 5% and the effective rate of interest is greater than 5%.
D) the periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%.
E) the periodic rate of interest is 2.5% and the effective rate of interest is 5%.

Question 75

A $250,000 loan is to be amortized over 8 years, with annual end-of-year payments. Which of these statements is CORRECT?

A) the proportion of interest versus principal repayment would be the same for each of the 8 payments.
B) the annual payments would be larger if the interest rate were lower.
C) if the loan were amortized over 10 years rather than 8 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 8-year amortization plan.
D) the proportion of each payment that represents interest as opposed to repayment of principal would be lower if the interest rate were lower.
E) the last payment would have a higher proportion of interest than the first payment.

Question 76

Which of the following statements is CORRECT?

A) if some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.
B) the cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
C) if a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.
D) the cash flows for an annuity due must all occur at the ends of the periods.
E) the cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month.

Question 77

At the end of 10 years, which of the following investments would have the highest future value? Assume that the effective annual rate for all investments is the same and is greater than zero.

A) investment a pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
B) investment b pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
C) investment c pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
D) investment d pays $2,500 at the end of 10 years (just one payment).
E) investment e pays $250 at the end of every year for the next 10 years (a total of 10 payments).

Question 78

Of the following investments, which would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.

A) investment a pays $250 at the end of every year for the next 10 years (a total of 10 payments).
B) investment b pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
C) investment c pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
D) investment d pays $2,500 at the end of 10 years (just one payment).
E) investment e pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).

Question 79

The YTMs of three $1,000 face value bonds that mature in 10 years and have the same level of risk are equal. Bond A has an 8% annual coupon, Bond B has a 10% annual coupon, and Bond C has a 12% annual coupon. Bond B sells at par. Assuming interest rates remain constant for the next 10 years, which of the following statements is CORRECT?

A) since the bonds have the same ytm, they should all have the same price, and since interest rates are not expected to change, their prices should all remain at their current levels until maturity.
B) bond c sells at a premium (its price is greater than par), and its price is expected to increase over the next year.
C) bond a sells at a discount (its price is less than par), and its price is expected to increase over the next year.
D) over the next year, bond a's price is expected to decrease, bond b's price is expected to stay the same, and bond c's price is expected to increase.
E) bond a's current yield will increase each year.

Question 80

You are considering investing in one of these three stocks:
If you are a strict risk minimizer, you would choose Stock ____ if it is to be held in isolation and Stock ____ if it is to be held as part of a well-diversified portfolio.

A) a; b.
B) b; a.
C) c; a.
D) c; b.
E) a; a.