Test 2
You have an interesting question: How much would $1, growing at 3.5% per year, be worth after 75 years?
$13.20 N 75 I/YR 3.5% PV $1.00 PMT $0.00 FV $13.20
Assume that you are considering the purchase of a 20-year, noncallable bond with an annual coupon rate of 9.5%. The bond has a face value of $1,000, and it makes semiannual interest payments. If you require an 8.4% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?
$1,105.69 Par value $1,000 Coupon rate 9.5% Periods/year 2 Yrs to maturity 20 Periods = Yrs to maturity × Periods/year 40 Required rate 8.4% Periodic rate = Required rate/2 = I/YR 4.20% PMT per period = Coupon rate/2 × Par value $47.50 Maturity value = FV $1,000 PV $1,105.69
Recently you open bank account that pays 3.5 percent interest compounded per year, you have deposited $500 today. How much will your account be worth at the end of 25 years?
$1,181.62 N 25 I/YR 3.5% PV $500 PMT $0 FV $1,181.62
Grossnickle Corporation issued 20-year, noncallable, 7.5% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds is 5.5%. What is the current price of the bonds, given that they now have 19 years to maturity?
$1,232.15 Par value = Maturity value = FV $1,000 Coupon rate 7.5% Years to maturity = N 19 Required rate = I/YR 5.5% (Coupon rate)(Par value) = PMT $75 PV $1,232.15
Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures?
$1,781.53 N 5 I/YR 3.5% PV $1,500 PMT $0 FV $1,781.53
Assume that Rich Filisteo company has 5 payments of $2,500 at an interest rate of 5.5%, what will be he PV of an annuity due?
$11,262.88 BEGIN ModeN 5 I/YR 5.5% PMT $2,500 FV $0.00 PV $11,262.88
Morin Company's bonds mature in 8 years, have a par value of $1,000, and make an annual coupon interest payment of $65. The market requires an interest rate of 8.2% on these bonds. What is the bond's price?
$903.04 N 8 I/YR 8.2% PMT $65 FV $1,000 PV $903.04
If a financial institution decides to compound savings accounts quarterly, the nominal rate will exceed the effective annual rate.
False
Since yield curves are based on a real risk-free rate plus the expected rate of inflation, at any given time there can be only one yield curve, and it applies to both corporate and Treasury securities.
False
Starting to invest early for retirement reduces the benefits of compound interest. Correct!
False
The four most fundamental factors that affect the cost of money are (1) production opportunities, (2) time preferences for consumption, (3) risk, and (4) weather conditions.
False
A time line is meaningful even if all cash flows do not occur annually.
a. True
You want to quit your job and go back to school for a law degree 4 years from now, and you plan to save $3,500 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these assumptions, how much will you have 4 years from today?
$16,112 BEGIN ModeN 4 I/YR 5.7% PV $0.00 PMT $3,500 FV $16,112 Alternative setup: 0 1 2 3 4 $3,500 $3,500 $3,500 $3,500 FV = $16,112
You are interested in buying a sport car when you graduate which is 2 years from now, and you plan to save $8,200 per year, beginning one year from today. You will deposit your savings in an account that pays 6.2% interest. How much will you have just after you make the 2nd deposit, 2 years from now?
$16,908 N 2 I/YR 6.2% PV $0.00 PMT $8,200 FV $16,908
You have decided to invest money and have thought about the following financial instrument: suppose a U.S. treasury bond will pay $2,500 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today?
$2,030.30 N 5 I/YR 4.25% PMT $0 FV $2,500.00 PV $2,030.30
You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?
$2,363.24 N 25 I/YR 3.5% PV $1,000 PMT $0 FV $2,363.24
Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. How much will you have when the CD matures?
$3,754.27 N 10 I/YR 6.5% PV $2,000 PMT $0 FV $3,754.27
Last year Rocco Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later?
$301.10 N 5 I/YR 6.0% PV $225.00 PMT $0.00 FV $301.10
Kelly Inc's 5-year bonds yield 7.50% and 5-year T-bonds yield 4.90%. The real risk-free rate is r* = 2.5%, the default risk premium for Kelly's bonds is DRP = 0.40%, the liquidity premium on Kelly's bonds is LP = 2.2% versus zero on T-bonds, and the inflation premium (IP) is 1.5%. What is the maturity risk premium (MRP) on all 5-year bonds?
0.90% Maturity 5 rKelly Yield 7.50% rT-bond Yield 4.90% r*Included in both bonds 2.50% LPIncluded in Kelly's only 2.20% DRPIncluded in Kelly's only 0.40% IPIncluded in both bonds 1.50% rT-bond = r* + IP + MRP + DRP + LPrKelly = r* + IP + MRP + DRP + LPMRP = rKelly − r* − IP − LP − DRP = 0.90%Or, MRP = rT-bond − r* − IP = 0.90%
Rasputin Smith has $2,500 invested in a bank that pays 4% annually. How long will it take for his funds to double?
17.67 I/YR 4.0% PV $2,500.00 PMT $0 FV $5,000.00 N 17.67
You plan to invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $30,000?
18.85 I/YR 6.0% PV $10,000.00 PMT $0 FV $30,000.00 N 18.85
Suppose the rate of return on a 10-year T-bond is 6.55%, the expected average rate of inflation over the next 10 years is 2.0%, the MRP on a 10-year T-bond is 0.9%, no MRP is required on a TIPS, and no liquidity premium is required on any Treasury security. Given this information, what should the yield be on a 10-year TIPS? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.
3.47% 10-year T-bond yield 6.55% Expected inflation 2.00% MRP, 10-year T-bond only 0.90% TIPS Yield = r* = rT10 − IP − MRP 3.65%
Suppose the real risk-free rate is 3.50% and the future rate of inflation is expected to be constant at 2.20%. What rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.
5.14% Real risk-free rate, r* 3.50% Inflation 2.20% Yield on 1-year T-bond 5.70%
Suppose the real risk-free rate is 3.00%, the average expected future inflation rate is 2.25%, and a maturity risk premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the years to maturity. What rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is NOT valid? Include the cross-product term, i.e., if averaging is required, use the geometric average.
5.42% Real risk-free rate, r* 3.00% Inflation 2.25% MRPYears: 1Per year: 0.10% 0.10% Yield on 1-year T-bond = (1 + r*)(1 + IP) − 1 + MRP5.42%
Radoski Corporation's bonds make an annual coupon interest payment of 7.35%. The bonds have a par value of $1,000, a current price of $1,130, and mature in 12 years. What is the yield to maturity on these bonds?
5.82% Coupon rate 7.35% N 12 PV = Price $1,130 PMT $73.50 FV = Par $1,000 I/YR 5.82% = YTM
Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?
6.00% N 5 PV $747.25 PMT $0 FV $1,000.00 I/YR 6.00%
Dyl Inc.'s bonds currently sell for $1,040 and have a par value of $1,000. They pay a $65 annual coupon and have a 15-year maturity, but they can be called in 5 years at $1,100. What is their yield to maturity (YTM)?
6.09%
The real risk-free rate is 3.55%, inflation is expected to be 3.15% this year, and the maturity risk premium is zero. Taking account of the cross-product term, i.e., not ignoring it, what is the equilibrium rate of return on a 1-year Treasury bond?
6.812% Real risk-free rate, r* 3.55% Inflation this year 3.15% 1-year bond yield: rRF = (1 + r*)(1 + IP) − 1 6.812% The approximation method, which ignores the cross-product, is r* + IP = 6.700%
Suppose Benito Juarez Company sells a bond, and it will pay $1,000 eight years from now. If the going interest rate on these 8-year bonds is 5.5%, how much is the bond worth today?
651.60 N 8 I/YR 5.5% PMT $0 FV $1,000.00 PV $651.60
Adams Enterprises' noncallable bonds currently sell for $1,120. They have a 15-year maturity, an annual coupon of $85, and a par value of $1,000. What is their yield to maturity?
7.17% N 15 PV $1,120 PMT $85 FV $1,000 I/YR 7.17%
You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?
7.84 I/YR 8.0% PV $5,000.00 PMT $0 FV $9,140.20 N 7.84
What's the rate of return you would earn if you paid $950 for a perpetuity that pays $85 per year?
8.95% Cost (PV) $950 PMT $85 I/YR 8.95%
Which of the following statements is CORRECT?
All else equal, if a bond's yield to maturity increases, its price will fall.
Three $1,000 face value, 10-year, noncallable, bonds have the same amount of risk, hence their YTMs are equal. Bond 8 has an 8% annual coupon, Bond 10 has a 10% annual coupon, and Bond 12 has a 12% annual coupon. Bond 10 sells at par. Assuming that interest rates remain constant for the next 10 years, which of the following statements is CORRECT?
Bond 8 sells at a discount (its price is less than par), and its price is expected to increase over the next year.
A call provision gives bondholders the right to demand, or "call for," repayment of a bond. Typically, companies call bonds if interest rates rise and do not call them if interest rates decline
False
A zero coupon bond is a bond that pays no interest and is offered (and initially sells) at par. These bonds provide compensation to investors in the form of capital appreciation.
False
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 price risk if you purchased a 30-day bond than if you bought a 30-year bond
False
One of the four most fundamental factors that affect the cost of money as discussed in the text is the expected rate of inflation. If inflation is expected to be relatively high, then interest rates will tend to be relatively low, other things held constant.
False
Which of the following statements is CORRECT? If a coupon bond is selling at par, its current yield equals its yield to maturity. If a coupon bond is selling at a discount, its price will continue to decline until it reaches its par value at maturity. If interest rates increase, the price of a 10-year coupon bond will decline by a greater percentage than the price of a 10-year zero coupon bond. If a bond's yield to maturity exceeds its annual coupon, then the bond will trade at a premium. If a coupon bond is selling at a premium, its current yield equals its yield to maturity.
If a coupon bond is selling at par, its current yield equals its yield to maturity.
Which of the following statements is CORRECT?
If inflation is expected to increase in the future, and if the maturity risk premium (MRP) is greater than zero, then the Treasury yield curve will have an upward slope.
A 10-year bond pays an annual coupon, its YTM is 8%, and it currently trades at a premium. Which of the following statements is CORRECT?
If the yield to maturity remains at 8%, then the bond's price will decline over the next year. Par $1,000 YTM 8.00% Maturity 10 Price $1,100 Payment $94.90 Coupon rate 9.49% Current yield 8.63% The current yield is greater than 8%.
An investor is considering buying one of two 10-year, $1,000 face value, noncallable bonds: Bond A has a 7% annual coupon, while Bond B has a 9% annual coupon. Both bonds have a yield to maturity of 8%, and the YTM is expected to remain constant for the next 10 years. Which of the following statements is CORRECT?
One year from now, Bond A's price will be higher than it is today.
Which of the following statements is CORRECT?
Reinvestment risk is lower, other things held constant, on long-term than on short-term bonds.
111. Which of the following statements is CORRECT? The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity. The cash flows for an annuity due must all occur at the beginning of the periods. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month. 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.
The cash flows for an annuity due must all occur at the beginning of the periods.
Which of the following statements is CORRECT?
The longer the time to maturity, the smaller the change in the value of a bond in response to a given change in interest rates.
Which of the following statements is CORRECT?
The market price of a bond will always approach its par value as its maturity date approaches, provided the bond's required return remains constant.
Which of the following statements is CORRECT?
The pure expectations theory states that the maturity risk premium for long-term Treasury bonds is zero and that differences in interest rates across different Treasury maturities are driven by expectations about future interest rates.
If the Treasury yield curve is downward sloping, how should the yield to maturity on a 10-year Treasury coupon bond compare to that on a 1-year T-bill?
The yield on a 10-year bond would be less than that on a 1-year bill.
105. Which of the following statements is CORRECT?
Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly.
If investors expect the rate of inflation to increase sharply in the future, then we should not be surprised to see an upward-sloping yield curve.
True
If the required rate of return on a bond (rd) is greater than its coupon interest rate and will remain above that rate, then the market value of the bond will always be below its par value until the bond matures, at which time its market value will equal its par value. (Accrued interest between interest payment dates should not be considered when answering this question.)
True
Restrictive covenants are designed primarily to protect bondholders by constraining the actions of managers. Such covenants are spelled out in bond indentures.
True
Sinking funds are provisions included in bond indentures that require companies to retire bonds on a scheduled basis prior to their final maturity. Many indentures allow the company to acquire bonds for sinking fund purposes by either (1) purchasing bonds on the open market at the going market price or (2) selecting the bonds to be called by a lottery administered by the trustee, in which case the price paid is the bond's face value.
True
Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.
True
The desire for floating-rate bonds, and consequently their increased usage, arose out of the experience of the early 1980s, when inflation pushed interest rates up to very high levels and thus caused sharp declines in the prices of outstanding bonds.
True
The price sensitivity of a bond to a given change in interest rates is generally greater the longer the bond's remaining maturity.
True
The risk that interest rates will decline, and that decline will lead to a decline in the income provided by a bond portfolio as interest and maturity payments are reinvested, is called "reinvestment rate risk."
True
Which of the following statements is CORRECT? Two bonds have the same maturity and the same coupon rate. However, one is callable and the other is not. The difference in prices between the bonds will be greater if the current market interest rate is below the coupon rate than if it is above the coupon rate. A callable 10-year, 10% bond should sell at a higher price than an otherwise similar noncallable bond. Corporate treasurers dislike issuing callable bonds because these bonds may require the company to raise additional funds earlier than would be true if noncallable bonds with the same maturity were used. Two bonds have the same maturity and the same coupon rate. However, one is callable and the other is not. The difference in prices between the bonds will be greater if the current market interest rate is above the coupon rate than if it is below the coupon rate. The actual life of a callable bond will always be equal to or less than the actual life of a noncallable bond with the same maturity. Therefore, if the yield curve is upward sloping, the required rate of return will be lower on the callable bond.
Two bonds have the same maturity and the same coupon rate. However, one is callable and the other is not. The difference in prices between the bonds will be greater if the current market interest rate is above the coupon rate than if it is below the coupon rate.
104. Which of the following statements is CORRECT?
a. Sinking fund provisions sometimes turn out to adversely affect bondholders, and this is most likely to occur if interest rates decline after the bond was issued.
. During periods when inflation is increasing, interest rates tend to increase, while interest rates tend to fall when inflation is declining.
a. True
An upward-sloping yield curve is often call a "normal" yield curve, while a downward-sloping yield curve is called "abnormal."
a. True
As a general rule, a company's debentures have higher required interest rates than its mortgage bonds because mortgage bonds are backed by specific assets while debentures are unsecured.
a. True
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 price risk if you purchased a 30-day bond than if you bought a 30-year bond.
a. True
Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value
a. True
Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value.
a. True
If a firm raises capital by selling new bonds, it could be called the "issuing firm," and the coupon rate is generally set equal to the required rate on bonds of equal risk.
a. True
If investors expect a zero rate of inflation, then the nominal rate of return on a very short-term U.S. Treasury bond should be equal to the real risk-free rate, r*.
a. True
If investors expect the rate of inflation to increase sharply in the future, then we should not be surprised to see an upward-sloping yield curve.
a. True
If the demand curve for funds increased but the supply curve remained constant, we would expect to see the total amount of funds supplied and demanded increase and interest rates in general also increase.
a. True
Junk bonds are high-risk, high-yield debt instruments. They are often used to finance leveraged buyouts and mergers, and to provide financing to companies of questionable financial strength.
a. True
Sinking funds are provisions included in bond indentures that require companies to retire bonds on a scheduled basis prior to their final maturity. Many indentures allow the company to acquire bonds for sinking fund purposes by either (1) purchasing bonds on the open market at the going market price or (2) selecting the bonds to be called by a lottery administered by the trustee, in which case the price paid is the bond's face value.
a. True
Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.
a. True
The four most fundamental factors that affect the cost of money are (1) production opportunities, (2) time preferences for consumption, (3) risk, and (4) inflation.
a. True
The four most fundamental factors that affect the cost of money are (1) production opportunities, (2) time preferences for consumption, (3) risk, and (4) the skill level of the economy's labor force.
a. True
The four most fundamental factors that affect the cost of money are (1) production opportunities, (2) time preferences for consumption, (3) risk, and (4) weather conditions. a. True
a. True
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.
a. True
The price sensitivity of a bond to a given change in interest rates is generally greater the longer the bond's remaining maturity.
a. True
The risk that interest rates will decline, and that decline will lead to a decline in the income provided by a bond portfolio as interest and maturity payments are reinvested, is called "reinvestment rate risk."
a. True
The risk that interest rates will increase, and that increase will lead to a decline in the prices of outstanding bonds, is called "interest rate risk," or "price risk."
a. True
Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.
a. True
Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.
a. True
Your uncle Camilo says that if you start to invest early for retirement increases the benefits of compound interest.
a. True
103. 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.)
b. False
107. All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases.
b. False
112. You are considering 2 bonds that will be issued tomorrow. Both are rated triple B (BBB, the lowest investment-grade rating), both mature in 20 years, both have a 10% coupon, neither can be called except for sinking fund purposes, and both are offered to you at their $1,000 par values. However, Bond SF has a sinking fund while Bond NSF does not. Under the sinking fund, the company must call and pay off 5% of the bonds at par each year. The yield curve at the time is upward sloping. The bond's prices, being equal, are probably not in equilibrium, as Bond SF, which has the sinking fund, would generally be expected to have a higher yield than Bond NSF.
b. False
24. One of the four most fundamental factors that affect the cost of money as discussed in the text is the risk inherent in a given security. The higher the risk, the higher the security's required return, other things held constant.
b. False
62. Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts.
b. False
A bond that had a 20-year original maturity with 1 year left to maturity has more 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.)
b. False
A call provision gives bondholders the right to demand, or "call for," repayment of a bond. Typically, companies call bonds if interest rates rise and do not call them if interest rates decline.
b. False
A zero coupon bond is a bond that pays no interest and is offered (and initially sells) at par. These bonds provide compensation to investors in the form of capital appreciation.
b. False
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).
b. False
Floating-rate debt is advantageous to investors because the interest rate moves up if market rates rise. Since floating- rate debt shifts price risk to companies, it offers no advantages to corporate issuers.
b. False
If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate.
b. False
If the Treasury yield curve were downward sloping, the yield to maturity on a 10-year Treasury coupon bond would be higher than that on a 1-year T-bill.
b. False
If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series.
b. False
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.
b. False
One of the four most fundamental factors that affect the cost of money as discussed in the text is the current state of the weather. If the weather is dark and stormy, the cost of money will be higher than if it is bright and sunny, other things held constant.
b. False
One of the four most fundamental factors that affect the cost of money as discussed in the text is the time preference for consumption. The higher the time preference, the lower the cost of money, other things held constant.
b. False
Since yield curves are based on a real risk-free rate plus the expected rate of inflation, at any given time there can be only one yield curve, and it applies to both corporate and Treasury securities.
b. False
Starting to invest early for retirement reduces the benefits of compound interest.
b. False
Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.
b. False
Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.
b. False
You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?
b. 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.
Assume that interest rates on 20-year Treasury and corporate bonds with different ratings, all of which are noncallable, are as follows: T-bond = 7.72% A = 9.64% AAA = 8.72% BBB = 10.18% The differences in rates among these issues were most probably caused primarily by:
c. Default and liquidity risk differences.
Which event would make it more likely that a company would call its outstanding callable bonds in the future?
c. Market interest rates decline sharply.
110. Which of the following statements is CORRECT? The higher the maturity risk premium, the higher the probability that the yield curve will be inverted. The most likely explanation for an inverted yield curve is that investors expect inflation to increase. The most likely explanation for an inverted yield curve is that investors expect inflation to decrease. If the yield curve is inverted, short-term bonds have lower yields than long-term bonds. Inverted yield curves can exist for Treasury bonds, but because of default premiums, the corporate yield curve can never be inverted.
c. The most likely explanation for an inverted yield curve is that investors expect inflation to decrease.
Assume that the current corporate bond yield curve is upward sloping. Under this condition, then we could be sure that
d. Maturity risk premiums could help to explain the yield curve's upward slope.
118. Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?
d. The periodic rate of interest is 2% and the effective rate of interest is greater than 8%.
97. Which of the following bonds would have the greatest percentage increase in value if all interest rates in the economy fall by 1%?
e. 20-year, zero coupon bond.
