PK Software has 9.2 percent coupon bonds on the market with 23 years to maturity
ID: 2740243 • Letter: P
Question
PK Software has 9.2 percent coupon bonds on the market with 23 years to maturity. The bonds make semiannual payments and currently sell for 112.25 percent of par.
PK Software has 9.2 percent coupon bonds on the market with 23 years to maturity. The bonds make semiannual payments and currently sell for 112.25 percent of par. Requirement 1: 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).) answer to 2 decimal places (e.g-32.16),) Current yield 4.08 % Requirement 2 What is the YTM? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Yield to maturity Requirement 3: What is the effective annual yield? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Effective annual yieldExplanation / Answer
step-1: collect the information, here we have coupon payment = 9.2% = 1,000 * 9.2% = 92
Maturity = 23years
Par value = $1,000
Market price = 125.25% of par value = 1,000*125.25% = $1,252.5
The current yield is:
Current yield = Annual coupon payment / Price
Current yield = $92 / $1,252.5
Current yield = 0.07345 or 7.345%
Now. we will calculate the YTM (yield to maturity)
Formula, YTM = {Annual coupon + (face value - market price / years to maturity)} / (face value + market price / 2)
YTM = {92 + (1,000 - 1,252.5)23} / (1,000 - 1,252.5)2
= 92 - 252.5/23 / 1126.25 = 0.06966
YTM =6.966%
The effective annual yield is the same as the EAR,
Effective annual yield = (1+i/n)n-1
here, i = normal rate (YTM) = 6.966% and n = number of payments in an year = here its semi annual = 2 payments in one year
Effective annual yield = (1 +6.966%)2 – 1
Effective annual yield = (1 +3.483%)2 – 1
Effective annual yield = 0.07087 or 7.08%
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