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(1) You have a chance to buy an annuity that pays $5,000 at the beginning of each year for 5 years. You could earn 4.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?
2. You have an opportunity to purchase a perpetuity that pays $74 per year. What is the most you should pay for the perpetuity if you could earn 7.44% on your money in other investments with equal risk?
3. Your uncle has $500,000 and wants to retire. He expects to live for another 30 years and to earn 6.5% on his invested funds. How much could he withdraw at the end of each of the next 30 years and end up with zero in the account?
4. Consider a bond paying a coupon rate of 8% per year semiannually when the market interest rate is only 5% per half-year, (i.e., the YTM is 8%). The bond has three years until maturity. Assume that the face value is $1,000.
(a) Find the bond's price today and six months from now after the next coupon is paid.
(b) What is the total rate of return on the bond?
5. A 10-year maturity bond with par value $1,000 makes semiannual coupon payments at a coupon rate of 4%. Find the bond yield to maturity (YTM) of the bond if the bond price is:
(a) $950
(b) $1,000
(c) $1,050
A zero-coupon bond with face value $1,000 and maturity of ten years sells for $750.
6. What is its yield to maturity? What will happen to its yield to maturity if its price falls immediately to $700?
7. A 20-year maturity, 5% coupon bond paying coupons semiannually is callable in ten years at a call price of $1,050. The bond currently sells at a yield to maturity of 4% (2% per half-year). Assume the face value is $1,000.
(a) What is the bond price given the YTM?
(b) What is the yield to call based on the price computed in part (a)?
8. (1) ABC Enterprises' bonds currently sell for $1,050. They have a 6-year maturity, an annual coupon of $75, and a par value of $1,000. Compute their YTM, coupon rate, and current yield.
(2) Which of the following non-callable bond has the greatest interest rate risk, i.e. the greatest sensitivity of bond price to interest rate increases?
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Maturity
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Coupon Rate
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a. short-term low coupon bond
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1 year
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Zero
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b. short-term high coupon bond
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1 year
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10%
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c. long-term low coupon bond
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30 years
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Zero
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d. long-term high coupon bond
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30 years
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10%
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9. Which type of risk is most significant for bonds?
default risk
interest rate risk
reinvestment rate risk
maturity risk
10. Which of the following rates represents a bond's annual interest payment per dollar of par value?
YTM
IRR
coupon rate
holding period return