PK Software has 8.7 percent coupon bonds on the market with 22 years to maturity
ID: 2773962 • Letter: P
Question
PK Software has 8.7 percent coupon bonds on the market with 22 years to maturity. The bonds make semiannual payments and currently sell for 111 percent of par. What is the current yield on PK's bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) What is the YTM? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) What is the effective annual yield? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)Explanation / Answer
Calculation of Current Yield on Bonds:
Current Yield = Annual Interest / Current bond price
Face value of bond = $1000
Annual Interest = 1000*8.7% = 87
Current bond price = 1000*111% = $1110
Hence,
Current Yield = 87 / 1110
=0.0784
= 7.84%
Calculation of YTM of Bonds:
YTM = (C + (F-P)/n) / ((F+P)/2)
C = Semiannual Interest = 87/2 = 43.5
F= Face value = $1000
P = Price = $1110
n = number of semiannual = 22 years *2 = 44
Hence
YTM = (43.5 + (1000-1110)/44) / ((1000+1110)/2)
= (43.5 – 2.5) / 1055
= 0.0389
Annual YTM= 0.0389 * 2 = 0.0777
= 7.77%
Calculation of effective annual yield:
Semiannual yield = 7.84%/2 = 0.0392
Effective Annual yield = (1.0392)$2 – 1
= 1.0799 – 1
= 0.0799
= 7.99%
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