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1 FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial str/ For more course tutorials visit Which of the following statements is CORRECT? 1) A time line is not meaningful unless all cash flows occur annually 2) Time lines are useful for visualizing complex problems prior to doing actual calculations 3) Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly 4) Time lines can only be constructed for annuities where the payments occur at the ends of the periods, i.e., for ordinary annuities 5) 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 2. Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT? 1) The monthly payments will decline over time.

2 2) A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment 3) The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity 4) The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%. 5) Exactly 10% of the first monthly payment represents interest 3. A Treasury bond promises to 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? 1) The periodic interest rate is greater than 3% 2) The periodic rate is less than 3% 3) The present value would be greater if the lump sum were discounted back for more periods 4) The present value of the \$1,000 would be smaller if interest were compounded monthly rather than semiannually 5) The PV of the \$1,000 lump sum has a higher present value than the PV of a 3-year, \$ ordinary annuity 4. You are analyzing 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? 1) 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 2) The discount rate increases 3) The riskiness of the investment s cash flows decreases

3 4) 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 5) The discount rate decreases 5. 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? 1) A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ. 2) 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. 3) The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE. 4) The present value of ORD exceeds the present value of DUE, while the future value of DUE exceeds the future value of ORD. 5) 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. 6. Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT? 1) The monthly payments will decline over time 2) A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment 3) The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity. 4) The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%

4 5) Exactly 10% of the first monthly payment represents interest 7. A \$150,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT? 1) The annual payments would be larger if the interest rate were lower. 2) If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan. 3) The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were lower. 4) The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher. 5) The proportion of interest versus principal repayment would be the same for each of the 7 payments. 8. Which of the following statements is CORRECT? 1) A time line is not meaningful unless all cash flows occur annually. 2) Time lines are not useful for visualizing complex problems prior to doing actual calculations. 3) Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. 4) Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities. 5) Time lines can be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity.

5 9. Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero. 1) Investment A pays \$250 at the beginning of every year for the next 10 years (a total of 10 payments). 2) Investment B pays \$125 at the end of every 6-month period for the next 10 years (a total of 20 payments). 3) Investment C pays \$125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments). 4) Investment D pays \$2,500 at the end of 10 years (just one payment). 5) Investment E pays \$250 at the end of every year for the next 10 years (a total of 10 payments). 10. Which of the following statements is CORRECT? The present value of a 3-year, \$150 annuity due will exceed the present value of a 3-year, \$150 ordinary annuity. If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%. If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different. The proportion of the payment that goes toward interest on a fully amortized loan increases over time. An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6% 11. Which of the following statements regarding a 15-year (180- month) \$125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.) 1) The remaining balance after three years will be \$125,000 less one third of the interest paid during the first three years. 2) Because the outstanding balance declines over time, the monthly payments will also decline over time.

6 3) Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant. 4) 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. 5) The outstanding balance declines at a faster rate in the later years of the loan s life 12. Which of the following bank accounts has the highest effective annual return? 1) An account that pays 8% nominal interest with monthly compounding 2) An account that pays 8% nominal interest with annual compounding. 3) An account that pays 7% nominal interest with daily (365-day) compounding 4) An account that pays 7% nominal interest with monthly compounding 5) An account that pays 8% nominal interest with daily (365-day) compounding 13. 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? 1) The periodic interest rate is greater than 3%. 2) The periodic rate is less than 3%. 3) The present value would be greater if the lump sum were discounted back for more periods. 4) The present value of the \$1,000 would be smaller if interest were compounded monthly rather than semiannually. 5) The PV of the \$1,000 lump sum has a higher present value than the PV of a 3-year, \$ ordinary annuity.

7 14. Which of the following statements is CORRECT? 1) If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0. 2) If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost. 3) To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the PV of the negative CFs. This is, essentially, a trial-and-error procedure that is easy with a computer or financial calculator but quite difficult otherwise. 4) If you solve for I and get a negative number, then you must have made a mistake. 5) If CF0 is positive and all the other CFs are negative, then you cannot solve for I. 15. 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? 1) 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. 2) 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. 3) The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE. 4) The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD. 5) 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.

8 16. Amram Inc. can issue a 20-year bond with a 6% annual coupon. This bond is not convertible, is not callable, and has no sinking fund. Alternatively, Amram could issue a 20-year bond that is convertible into common equity, may be called, and has a sinking fund. Which of the following most accurately describes the coupon rate that Amram would have to pay on the convertible, callable bond? 1. Exactly equal to 6%. 2. It could be less than, equal to, or greater than 6%. 3. Greater than 6%. 4. Exactly equal to 8%. 5. Less than 6%. 17. A Treasury bond has an 8% annual coupon and a 7.5% yield to maturity. Which of the following statements is CORRECT? 1 The bond has a current yield greater than 8 percent. 2 The bond sells at a price above par. 3. If the yield to maturity remains constant, the price of the bond is expected to fall over time. 4. Statements b and c are correct. 5 All of the statements above are correct. 18. Which of the following bonds has the greatest interest rate price risk? 1) A 10-year \$100 annuity. 2) All 10-year bonds have the same price risk since they have the same maturity. 3) A 10-year, \$1,000 face value, zero coupon bond. 4) A 10-year, \$1,000 face value, 10% coupon bond with annual interest payments. 5) A 10-year, \$1,000 face value, 10% coupon bond with semiannual interest payments

9 19. Which of the following statements is CORRECT? A time line is not meaningful unless all cash flows occur annually. Time lines are not useful for visualizing complex problems prior to doing actual calculations. Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities. 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. 20. Which of the following statements is CORRECT? All else equal, senior debt generally has a lower yield to maturity than subordinated debt. An indenture is a bond that is less risky than a mortgage bond. The expected return on a corporate bond will generally exceed the bond's yield to maturity. If a bond s coupon rate exceeds its yield to maturity, then its expected return to investors exceeds the yield to maturity. Under our bankruptcy laws, any firm that is in financial distress will be forced to declare bankruptcy and then be liquidated. 21. A 15-year bond with a face value of \$1,000 currently sells for \$850. Which of the following statements is CORRECT? 1. The bond's yield to maturity is greater than its coupon rate. 2. If the yield to maturity stays constant until the bond matures, the bond's price will remain at \$ The bond's current yield is equal to its coupon rate. 4. The bond's current yield exceeds its yield to maturity. 5. The bond's coupon rate exceeds its current yield. 22. Which of the following statements is CORRECT?

10 1) Sinking fund provisions never require companies to retire their debt; they only establish targets for the company to reduce its debt over time. 2) A sinking fund provision makes a bond more risky to investors at the time of issuance. 3) 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. 4) Most sinking funds require the issuer to provide funds to a trustee, who holds the money so that it will be available to pay off bondholders when the bonds mature. 5) If interest rates increase after a company has issued bonds with a sinking fund, the company will be less likely to buy bonds on the open market to meet its sinking fund obligation and more likely to call them in at the sinking fund call price. 23. 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? 1. A 10-year bond with a 10 percent coupon. 2. An 8-year bond with a 9 percent coupon. 3. A 10-year zero coupon bond. 4. A 1-year bond with a 15 percent coupon. 24. A 12-year bond has an annual coupon rate of 9%. The coupon rate will remain fixed until the bond matures. The bond has a yield to maturity of 7%. Which of the following statements is CORRECT? 1. The bond is currently selling at a price below its par value. 2. If market interest rates decline today, the price of the bond will also decline today. 3. If market interest rates remain unchanged, the bond s price one year from now will be lower than it is today. 4. All of the statements above are correct.

11 5. None of the statements above is correct. 25. A 10-year bond pays an annual coupon. The bond has a yield to maturity of 8 percent. The bond currently trades at a premium--its price is above the par value of \$1,000. Which of the following statements is CORRECT? 1. If the yield to maturity remains at 8 percent, then the bond s price will decline over the next year. 2. The bond s current yield is less than 8 percent. 3. If the yield to maturity remains at 8 percent, then the bond s price will remain the same over the next year. 4. The bond s coupon rate is less than 8 percent. 5. If the yield to maturity increases, then the bond s price will increase. 26. Which of the following statements is CORRECT? One advantage of a zero coupon Treasury bond is that no one who owns the bond has to pay any taxes on it until it matures or is sold. Long-term bonds have less interest rate price risk but more reinvestment rate risk than short-term bonds. If interest rates increase, all bond prices will increase, but the increase will be greater for bonds that have less interest rate risk. Relative to a coupon-bearing bond with the same maturity, a zero coupon bond has more interest rate price risk but less reinvestment rate risk. Long-term bonds have less interest rate price risk and also less reinvestment rate risk than short-term bonds. 27. Which of the following statements is CORRECT? A zero coupon bond's current yield is equal to its yield to maturity.

12 If a bond s yield to maturity exceeds its coupon rate, the bond will sell at par. All else equal, if a bond s yield to maturity increases, its price will fall. If a bond s yield to maturity exceeds its coupon rate, the bond will sell at a premium over par. All else equal, if a bond s yield to maturity increases, its current yield will fall. 28. A 10-year bond with a 9% annual coupon has a yield to maturity of 8%. Which of the following statements is CORRECT? 1. If the yield to maturity remains constant, the bond's price one year from now will be higher than its current price. 2. The bond is selling below its par value. 3. The bond is selling at a discount. 4. If the yield to maturity remains constant, the bond's price one year from now will be lower than its current price. 5. The bond's current yield is greater than 9%. 29. A 10-year corporate bond has an annual coupon of 9%. The bond is currently selling at par (\$1,000). Which of the following statements is CORRECT? a. The bond s expected capital gains yield is zero. b. The bond s yield to maturity is above 9%. c. The bond s current yield is above 9%. d. If the bond s yield to maturity declines, the bond will sell at a discount. e. The bond s current yield is less than its expected capital gains yield. 30. If the Federal Reserve unexpectedly announces that it expects inflation to increase, then we would probably observe an immediate increase in bond prices.

13 The total yield on a bond is derived from dividends plus changes in the price of the bond. Bonds are riskier than common stocks and therefore have higher required returns. Bonds issued by larger companies always have lower yields to maturity (less risk) than bonds issued by smaller companies. The market value of a bond will always approach its par value as its maturity date approaches, provided the bond s required return remains constant.

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