Added problem 19 so u can get an overview 21. Assuming that the bond in problem

Question

Added problem 19 so u can get an overview

21. Assuming that the bond in problem 19 matures in 5 years, what would be the market prices under the various required market interest rate changes? (Hint: see Appendix G.)

19. A tax-exempt bond was recently issued at an annual 10 percent coupon rate and matures 15 years from today. The par value of the bond is $1,000. (Hint: see Appendix G.) a. If required market rates are 10 percent, what is the market price of the bond? b. If required market rates fall to 5 percent, what is the market price of the bond? c. If required market rates rise to 14 percent, what is the market price of the bond? d. At what required market rate (10 percent, 5 percent, or 14 percent) does the above bond sell at a discount? At a premium?

Explanation / Answer

19)

a) Since the coupon rate and the market rate are the same, the price of the bond will equal the face value = $ 1000

b) If the required market rate falls to 5%, the price of the bond will be the PV of the cash inflows arising from holding the bond:

ie: 1000 * 0.481 + 100 * 10.380 = 481+1038= $ 1519.6

c) If the rates rise to 14%, the price of the bond will be = 1000*0.140 + 100* 6.142 = 140 + 614.2 = $ 754.2

d) Since bond prices move inversely with changes in interest rates,

    the bond sells at a discount, when the market interest rate is greater than the coupon rate of 10%

    and, the bond sells at a premium, when the market interest rate is less than the coupon rate of 10%

    So, the bond sells at a discount when the market rate is 14% and at a premium when the market rate is 5%.

21) If the bond matures in 5 years the price of the bond would be:

     when the market rate is 10%   = $ 1000

     when the market rate is 5%   = 1000*0.784 + 100*4.329 = 784+432.9 = $ 1216.9

     when the market rate is 14% = 1000*0.519 + 100*3.433 = 519+343.3 = $ 862.3

     when the market rate is

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