Question

13

A bond pays a semi-annual coupon at an APR of 9.75%. The bond will mature in 6.00 years and has a face value of $1,000.00. The bond has a yield-to-maturity of 11.84% APR. What is the current yield for the bond? What is the current yield for the bond? Submit Answer format: Percentage Round to: 2 decimal places (Example: 9.24%, % sign required. Will accept decimal format rounded to 4 decimal places (ex: 0.0924))

Answer 1

Face Value = $1,000.00

Annual Coupon Rate = 9.75%
Semiannual Coupon Rate = 4.875%
Semiannual Coupon = 4.875% * $1,000.00
Semiannual Coupon = $48.75

Time to Maturity = 6.00 years
Semiannual Period = 12

Annual YTM = 11.84%
Semiannual YTM = 5.92%

Current Price = $48.75 * PVIFA(5.92%, 12) + $1,000 * PVIF(5.92%, 12)
Current Price = $48.75 * (1 - (1/1.0592)^12) / 0.0592 + $1,000 / 1.0592^12
Current Price = $912.00

Current Yield = Annual Coupon / Current Price
Current Yield = (2 * $48.75) / $912.00
Current Yield = $97.50 / $912.00
Current Yield = 0.1069 or 10.69%