(Solved): 1. A coupon bond that pays interest annually has a par value of \( \$ 1,000 \), matures in 5 years, ...

1. A coupon bond that pays interest annually has a par value of \( \$ 1,000 \), matures in 5 years, and has a yield to maturity (market rate) of \( 10 \% \). The intrinsic value of the bond today will be if the coupon rate is \( 7 \% \). A) \( \$ 712.99 \) B) \( \$ 620.92 \) C) \( \$ 1,123.01 \) D) \( \$ 886.28 \) E) \( \$ 1,000.00 \) 2. A coupon bond that pays interest annually, has a par value of \( \$ 1,000 \), matures in 5 years, and has a yield to maturity (market rate) of \( 10 \% \). The intrinsic value of the bond today will be if the coupon rate is \( 12 \% \). A) \( \$ 922.77 \) B) \( \$ 924.16 \) C) \( \$ 1,075.82 \) D) \( \$ 1,177.20 \) E) None of the above 3. A coupon bond that pays interest semi-annually has a par value of \( \$ 1,000 \), matures in 5 years, and has a yield to maturity (market rate) of \( 10 \% \). The intrinsic value of the bond today will be if the coupon rate is \( 8 \% \). A) \( \$ 922.78 \) B) \( \$ 924.16 \) C) \( \$ 1,075.80 \) D) \( \$ 1,077.20 \) E) None of the above 4. You purchased an annual interest coupon bond one year ago that now has 6 years remaining until maturity. The coupon rate of interest was \( 10 \% \) and par value was \( \$ 1,000 \). At the time you purchased the bond, the yield to maturity (market rate) was \( 8 \% \). The amount you paid for this bond one year ago was A) \( \$ 1,057.50 \). B) \( \$ 1,075.50 \) E) None of the above 4. You purchased an annual interest coupon bond one year ago that now has 6 years remaining until maturity. The coupon rate of interest was \( 10 \% \) and par value was \( \$ 1,000 \). At the time you purchased the bond, the yield to maturity (market rate) was \( 8 \% \). The amount you paid for this bond one year ago was A) \( \$ 1,057.50 \). B) \( \$ 1,075.50 \). C) \( \$ 1,088.50 \). D) \( \$ 1.092 .46 \). E) \( \$ 1,104.13 \). 5. Consider two bonds, A and B. Both bonds presently are selling at their par value of \( \$ 1,000 \). Each pays interest of \( \$ 120 \) annually. Bond \( \mathrm{A} \) will mature in 5 years while bond \( \mathrm{B} \) will mature in 6 years. If the yields to maturity (market rate) on the two bonds change from \( 12 \% \) to \( 10 \% \) A) Both bonds will increase in value, but bond \( A \) will increase more than bond \( \mathrm{B} \) B) Both bonds will increase in value, but bond B will increase more than bond \( \mathrm{A} \) C) Both bonds will decrease in value, but bond A will decrease more than bond \( \mathrm{B} \) D) Both bonds will decrease in value, but bond B will decrease more than bond \( A \) E) None of the above 6. A zero-coupon bond has a yield to maturity (market rate) of \( 9 \% \) and a par value of \( \$ 1,000 \). If the bond matures in 8 years, the bond should sell for a price of today. A) \( 422.41 \) B) \( \$ 501.87 \) C) \( \$ 513.16 \) D) \( \$ 483.49 \) E) None of the above 7. Which one of the following statements about convertibles is true? A) The longer the call protection on a convertible, the less the security is worth. B) The more volatile the underlying stock, the greater the value of the conversion feature. C) The smaller the spread between the dividend yield on the stock and the vield-to-maturity on the bond, the 7. Which one of the following statements about convertibles is true? A) The longer the call protection on a convertible, the less the security is worth. B) The more volatile the underlying stock, the greater the value of the conversion feature. C) The smaller the spread between the dividend yield on the stock and the yield-to-maturity on the bond, the more the convertible is worth. D) The collateral that is used to secure a convertible bond is one reason convertibles are more attractive than the underlying stock. E) Convertibles are not callable. 8. The bond indenture includes A) The coupon rate of the bond. B) The par value of the bond. C) The maturity date of the bond. D) all of the above. E) None of the above. 9. Convertible bonds A) Give their holders the ability to share in price appreciation of the underlying stock. B) Offer lower coupon rates than similar nonconvertible bonds. C) Offer higher coupon rates than similar nonconvertible bonds. D) Both A and B are true. E) Both \( \mathrm{A} \) and \( \mathrm{C} \) are true. 10. Consider two bonds, F and G. Both bonds presently are selling at their par value of \( \$ 1,000 \). Each pays interest of \( \$ 90 \) annually. Bond \( F \) will mature in 15 years while bond \( G \) will mature in 26 years. If the yields to maturity on the two bonds change from \( 9 \% \) to \( 10 \% \), A) Both bonds will increase in value, but bond \( \mathrm{F} \) will increase more than bond \( G \) B) Both bonds will increase in value, but bond \( G \) will increase more than bond \( \mathrm{F} \) C) Both bonds will decrease in value, but bond \( \mathrm{F} \) will decrease more than bond \( \mathbf{G} \) D) Both bonds will decrease in value, but bond \( \mathrm{G} \) will decrease more than bond \( \mathrm{F} \) E) None of the above are selling at their par value of \( \$ 1,000 \). Each pays interest of \( \$ 90 \) annually. Bond F will mature in 15 years while bond \( \mathrm{G} \) will mature in 26 years. If the yields to maturity on the two bonds change from \( 9 \% \) to \( 10 \% \), A) Both bonds will increase in value, but bond \( \mathrm{F} \) will increase more than bond \( \mathrm{G} \) B) Both bonds will increase in value, but bond \( \mathrm{G} \) will increase more than bond \( \mathrm{F} \) C) Both bonds will decrease in value, but bond \( \mathrm{F} \) will decrease more than bond \( G \) D) Both bonds will decrease in value, but bond \( G \) will decrease more than bond \( \mathrm{F} \) E) None of the above 2. Your parents are planning to retire after 10 years. They currently have \( \$ 100000 \), and they would like to have \( \$ 236700 \) when they retire. What annual rate of interest would they have to earn on their \( \$ 100000 \) in order to reach their goal, assuming they save no more money? 3. A- You are thinking about buying a car, and a local bank is willing to lend you \( \$ 200,000 \) to buy it. Under the terms of the loan, it will be fully amortized over 2 years (24 months), and the nominal rate of interest is 12 percent with interest paid monthly. What would be the monthly payment on the loan? B- What would be the effective rate of interest on the loan? 4. Which amount is worth more at 14 percent, compounded annually: \( \$ 1,000 \) in hand today or \( \$ 2,000 \) due in 6 years or \( 5000 S \) due in 10 years? Explain your answer? 5. While you were a student in college, you borrowed \( \$ 18,000 \) in student loans at an interest rate of 3 2. Your parents are planning to retire after 10 years. They currently have \( \$ 100000 \), and they would like to have \( \$ 236700 \) when they retire. What annual rate of interest would they have to earn on their \( \$ 100000 \) in order to reach their goal, assuming they save no more money? 3. A- You are thinking about buying a car, and a local bank is willing to lend you \( \$ 200,000 \) to buy it. Under the terms of the loan, it will be fully amortized over 2 years (24 months), and the nominal rate of interest is 12 percent with interest paid monthly. What would be the monthly payment on the loan? B- What would be the effective rate of interest on the loan? 4. Which amount is worth more at 14 percent, compounded annually: \( \$ 1,000 \) in hand today or \( \$ 2,000 \) due in 6 years or \( 5000 \$ \) due in 10 years? Explain your answer? 5. While you were a student in college, you borrowed \( \$ 18,000 \) in student loans at an interest rate of 3 percent, compounded annually. If you repay \( \$ 1,500 \) per year, how long, to the nearest year, will it take you to repay the loan? 6. Your client is 40 years old and wants to begin saving for retirement. You advise the client to put \( \$ 6,000 \) a year into the stock market. You estimate that the market's return will be, on average, 12 percent a year. Assume the investment will be made at the end of each year. A) If the client follows your advice, how much will she have by age 65 ? B) if your client wants to have a pension salary (retirement salary) by age 65 and forever, how much the yearly salary is, assuming that the interest rate at that date \( =5 \% \) ? 7. Adams Company bought a piece of land in 1981 for \( \$ 200,000 \). By 2005 , its value had increased to \( \$ 1,582,200 \). Find the annual rate of appreciation during this period. 8. Your employer has promised to give you a \( \$ 5,000 \) 6. Your client is 40 years old and wants to begin saving for retirement. You advise the client to put \( \$ 6,000 \) a year into the stock market. You estimate that the market's return will be, on average, 12 percent a year. Assume the investment will be made at the end of each year. A) If the client follows your advice, how much will she have by age \( 65 ? \mathrm{~B} \) ) if your client wants to have a pension salary (retirement salary) by age 65 and forever, how much the yearly salary is, assuming that the interest rate at that date \( =5 \% \) ? 7. Adams Company bought a piece of land in 1981 for \( \$ 200,000 \). By 2005 , its value had increased to \( \$ 1,582,200 \). Find the annual rate of appreciation during this period. 8. Your employer has promised to give you a \( \$ 5,000 \) bonus after you have been working for him for 10 years. What is the present value of this bonus if the proper discount rate is \( 12 \% \) ? 9. A downtown bank is advertising that if you deposit \( \$ 1,000 \) with them, and leave it there for 60 months, you can get \( \$ 1801 \) back at the end of this period. Assuming quarterly base compounding, what is the annual rate of interest paid by the bank? 10. Cincinnati Company has decided to put \( \$ 30,000 \) per quarter in a pension fund. The fund will earn interest at the rate of \( 8 \% \) per year, compounded quarterly. Find the amount available in this fund after 10 years. 11. What is the effective interest rate for one dollar invested in the bank at a \( 9 \% \) nominal annual rate compounded on a daily basis ( use 365 days in a year )?