Question

1. A bond with two years remaining until maturity offers a 3% coupon rate with interest paid annually. At a market discount rate of 4%, find the price of this bond per 1000 of par value.



2. A bond offers an annual coupon rate of 5%, with interest paid semiannually. The bond matures in seven years. At a market discount rate of 3%, find the price of this bond per 1000 of par value.



3. A zero-coupon bond matures in 15 years. At a market discount rate of 4.5% per year and assuming annual compounding, find the price of the bond per 1000 of par value.



4. A bond with 20 years remaining until maturity is currently trading for $1,110 per $1000 of par value. The bond offers a 5% coupon rate with interest paid semiannually. Find the bond’s annual yield-tomaturity (YTM).



5. (True or False) Suppose a bond’s price is expected to increase by 5% if its market discount rate decreases by 100 bps (1%). If the bond’s market discount rate increases by 100 bps (1%), the bond price is most likely to change by 5%. _________ (Provide explanations if the answer is False!)

The following information relates to Questions 6 and 7 (Assume the par value of bonds are $1,000. You do not need to provide numbers for your answer. However, explain why you picked the bond!)

Bond Price Coupon Rate Time-to-Maturity

A $1018.86 5% 2 years

B $1000.00 6% 2 years

C $973.27 5% 3 years
  
6. Which bond offers the lowest yield-to-maturity?


7. Which bond will most likely experience the smallest percent change in price if the market discount rates for all three bonds increase by 100 basis points (bps)? (100 bps is translated into 1%)

  

Answer 1

1.)  

Face value = 1000 coupon rate = 3% = PMT = Time to maturity (N) = 2 years Market rate (1/Y) = 4% Present Value = ? use financial calculator PV = 981.14 so the price of the bond is $981.14

2).

Face value = 1000 coupon rate = 5%, interest is being paid semiannually = PMT= 25 Time to maturity (N) = 7*2 = 14 (semiannual interest) Market rate (1/Y) = 3% =3/2 = 1.5 Present Value = ? use financial calculator PV = 1125.43 so the price of the bond is $1125.43

3)

zero coupon bond matures in 15 years face value of the bond = 1000 Market discount rate = 4.5% price of the bond = 1000/(1.045)^15 516.72

4)

Face value of the bond = 1000 Present value = 1110 Coupon rate = 5%, interest being paid semiannually=PMT = (0.05/2)*1000 = 25 Time to maturity (N) = 20*2 = 40 (semiannual Interest) Yield to maturity = ? Use financial calculator to get the YTM and multiply it by 2 YTM = 2.09 * 2 Annual YTM = 4.18%