Question

It is 2018. You decided to purchase a US treasury bond now. It matures in 8 years (in 2026), has a face value of $100,000, a coupon rate of 6 percent (as usually, you get the first coupon in a year, i.e. 2019) and a yield of 7 percent.

a) Even before proceeding to calculations, you refresh what you learnt in the M&B class and immediately realize that you would have to pay … rather than the face value of this bond. (choose: more or less)

b) Based on this information, you quickly calculate that you would have to pay $____ for this bond.

c) You purchased the bond back in 2017. It is 2018 now, and you’ve received the first coupon payment. Shortly after this, FED’s actions led to an unexpected change in yield of all bonds. The yield for your bond now is 9 percent. What is the price of your bond now?

d) but, if you actually feel completely indifferent to any changes in the bond price (even if it drops a lot) and yield, it must be the case that you planned originally to... (write a sentence or two explaining the reason when you feel not affected by this at all).

Answer 1

(a) As the bond's yield of 7 % is higher than the coupon rate of 6 %, the bond's market price will be at a discount (less than) the bond's face value of $ 100000.

(b) Annual Coupon = 0.06 x 100000 = $ 6000, Bond Tenure = 6 years, Let the bond's market price be Pm

Therefore, Pm = 6000 x (1/0.07) x [1-{1/(1.07)^(8)}] + 100000 / (1.07)^(8) = $ 94028.7 approximately.

(c) As the interest rate becomes 9 % per annum, the new yield becomes equal to this value. The maturity of the bond is in 2026, thereby implying a time to maturity of 6 years.

Therefore, new bond price = 6000 x (1/0.09) x [1-{1/(1.09)^(8)}] + 100000 / (1.09)^(8) = $ 83395.54

(d) If the investor is unnerved or not impacted by a change in yields and subsequent bond price changes, it simply implies that the investor planned to hold the bond to maturity. At maturity, the investor would receive the fixed face value of $ 100000 irrespective of what the intermediate yield. Further, the annual coupons are also a fixed percentage of the face value and not the market value, thereby ensuring an annual income immune to yield changes.