Assume you purchased a high-yield corporate bond at its current market price of
ID: 2777470 • Letter: A
Question
Assume you purchased a high-yield corporate bond at its current market price of $910 on January 2, 2004. It pays 11.75 percent interest and it will mature on December 31, 2013, at which time the corporation will pay you the face value of $1,000.
Determine the current yield on your bond investment at the time of purchase. (Round your intermediate calculations and final answer to 2 decimal places.)
Determine the yield-to-maturity on your bond investment. (Round your intermediate calculations and final answer to 2 decimal places.)
Assume you purchased a high-yield corporate bond at its current market price of $910 on January 2, 2004. It pays 11.75 percent interest and it will mature on December 31, 2013, at which time the corporation will pay you the face value of $1,000.
Explanation / Answer
Answer (a)
Current Yield = 12.91 %
working
Coupon Rate = 11.75%
Annual Coupon Payment = 1000 * 11.75% = $ 117.50
Market Price = $ 910
Current Yield = Annual Cash Flow / Market Price = $ 117.50 / $ 910 = 0.1291 or 12.91%
Answer (b)
Yield to maturity = 12.77%
working
Coupon Payment = $ 117.50
Par Value = $ 1000
Purchase Price = $ 910
Time to Maturity = 10 years
Let r be the yield to maturity
$ 910 = $ 117.50 * [(1-(1/(1+r)^10)/r] + $ 1000 /(1+r)^10
Re-arranging the equation
$ 910 - $ 117.50 * [(1-(1/(1+r)^10)/r] - $ 1000 /(1+r)^10 = 0
Let r = 13%, then RHS of the equation is
= $ 910 - $ 117.50 * [(1-(1/(1.13)^10)/0.13] - $ 1000 /(1.13)^10
= $ 910 - $ 117.50 * [(1-1/3.394567)/0.13 - $ 1000 / 3.394567
= $ 910 - $ 117.50 * (0.705412/0.13) – $ 294.59
= $ 910 - $ 637.58 - $ 294.59
= - $ 22.17
Let r = 12%, then RHS of the equation is
= $ 910 - $ 117.50 * [(1-(1/(1.12)^10)/0.12] - $ 1000 /(1.12)^10
= $ 910 - $ 117.50 * [(1-1/3.10585)/0.12 - $ 1000 / 3.10585
= $ 910 - $ 117.50 * (0.67803/0.12) - $ 321.97
= $ 910 - $ 663.90 - $ 321.97
= $ 75.87
r should be between 12% and 13%
r = 0.12 + [((75.87) * (0.12-0.13))/ (-22.17-75.87)]
r = 0.12 + (0.7587/98.04)
r = 0.12 + 0.007739
r = 0.127739 or 12.77% (rounded off)
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