Consider the following data on various bonds trading at t = 0. Bond Coupon Rate
ID: 2623577 • Letter: C
Question
Consider the following data on various bonds trading at t = 0.
Bond Coupon Rate Payment Frequency Face Value Time to Maturity Price at t = 0 (per $1000 in face value)
A 7% 4 times a year 1000 8 years ?
B 12% once a year 1000 2 years 1100
C 0 2 times a year 1000 5 years 700
The prices are all ex-coupon. That is, they are the price you would pay immediately after the coupon has been paid. Thus, when you pay that price, you will receive the next coupon one period later.
Answer the following questions.
a. What is the yield to maturity on Bond B?
b. If the yield curve were flat at 5 percent effective annual yield, what should the price of Bond A equal? (Note: given all of the data above, it may not be flat.)
c. If in one year (i.e., at t = 1), the yield curve is flat at 6% (i.e., the yield to maturity on zero-coupon bonds of all maturities is 6%), what will be the holding period yield for Bond B if you bought Bond B at t = 0?
Explanation / Answer
a. The yield to maturity of bond B can be calculated in Excel as =RATE(2,-12%*1000,1100,-1000). This is equal to 6.51%
b. Quarterly yield = (1+5%)^(1/4)-1 = 1.2272%
Bond price of A can be calculated in Excel as =PV(1.2272%,8*4,-1000*7%/4,-1000). This is equal to 1137.67
c. After one year, the remaining payments left for Bond B is coupon payment of 1000*12% = 120 in one year, along with par value of 1000 in one year, i.e. a total of 120+1000 = 1120 in one year.
Value of bond B in one year at 6% yield = 1120 / (1+6%) = 1056.60
So total holding period yield = (1056.60 + 120) / 1100 - 1 = 6.96%
Hope this helped ! Let me know in case of any queries.
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