Question

A bond that settles on June 7, 2016, matures on July 1, 2036, and may be called at any time after July 1, 2026, at a price of 170. The coupon rate on the bond is 6 percent and the price is 187.00. What are the yield to maturity and yield to call on this bond? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

yield to maturity and yield to call?

Answer 1

A bond that settles on June 7, 2016, matures on July 1, 2036, and may be called at any time after July 1, 2026, at a price of 170. The coupon rate on the bond is 6 percent and the price is 187.00. What are the yield to maturity and yield to call on this bond?

Yield to maturity

The formula for YTM = (C+ ((P-M) / n)) / ((p+m) / 2)

Here,

YTM = Yield to maturity

C (coupon interest) = coupon rate * Par value =  6% * $100   =   $ 6

P (Par Value ) = $100

M (Market Price) = $ 187

n (years to maturity) = 20 years  ( 2036 - 2016 )

By applying values into the formula we get,

YTM = ($6 + (($100 - $ 187) / 20 )) / (($100 + $187 ) /   2  )

YTM = ( $6 +  - $ 4.35 ) / $ 143.5

YTM = 0.01152 or   1.15%

Yield to Call

The formula for YTC = (C + ( CP - P ) / n) / ( ( CP + P ) / 2 )

Here,

YTC = Yield to Call

C (coupon interest) = coupon rate * Par value =  6% * $100   =   $ 6

P (Current price) = $187

CP (Call Price) = $ 170

n (years to Call) = 10 years  ( 2026 - 2016 )

By applying values into the formula we get,

YTC = ($6 + (($170 - $ 187 ) / 10 )) / ( ( $170 +  $187 ) /   2  )

YTM = ( $6 +  -1.7 ) / 178.5

YTM = 0.0240 or   2.40%