Consider a 6 15year semiannual payment bond with a par value

Consider a 6%, 15-year, semi-annual payment bond with a par value of $1000. Compute the current yield if the yield to maturity is 7% (round answer to two decimal points.)

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Solution

Semi-annual coupon payment = $1,000 x 6% x (1/2) = $30

Semi-annual yield to maturity = 7% x (1/2) = 3.5%

Number of coupon payments = 2 x 15 = 30

Bond price ($) = Present value of coupon payments + Present value of redemption price (face value)

= 30 x P/A(3.5%, 30) + 1,000 x P/F(3.5%, 30)

= 30 x 18.3920** + 1,000 x 0.3563**

= 551.76 + 356.3

= 908.06

Current yield = Annual coupon / Bond price = ($30 x 2) / $908.06 = 0.0661

= 6.61%

**P/A(r%, N) = [1 - (1 + r)^-N] / r

P/A(.5%, 30) = [1 - (1.035)^-30] / 0.035 = (1 - 0.3563) / 0.035 = 0.6437 / 0.035 = 18.3920

**P/F(r%, N) = (1 + r)^-N

P/F(3.5%, 30) = (1.035)^-30 = 0.3563