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17 February, 04:41

McCue Inc.'s bonds currently sell for $1,175. They pay a $90 annual coupon, have a 25-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between this bond's YTM and its YTC

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  1. 17 February, 05:00
    0
    YTC is 0.2% more than YTM

    Explanation:

    The actual return that an investor earn on a bond until its maturity is called the Yield to maturity.

    The actual return that an investor earn on a callable bond until call of bond is called the Yield to call.

    Yield to Maturity

    Yield to maturity = [ C + (F - P) / n ] / [ (F + P) / 2 ]

    Coupon Payment = C = $90

    Number of years to mature = n = 25 years

    Current Market price = MV = $1,175

    Yield to maturity = [ $90 + ($1,000 - $1,175) / 25 ] / [ ($1,000 + $1,175) / 2 ]

    Yield to maturity = $83 / $1,087.5 = 0.076 = 7.6%

    Yield to call

    Coupon Payment = C = $90

    Number of years to call = n = 5 years

    Callable price = CP = $1,050

    Yield to maturity = [ $90 + ($1,000 - $1,050) / 5 ] / [ ($1,000 + $1,050) / 2 ]

    Yield to maturity = $80 / $1,025 = 0.078 = 7.8%

    Difference between YTM and YTC = 7.8% - 7.6% = 0.2%
  2. 17 February, 06:34
    0
    YTM - YTC = 7.63% - 5.84% = 1.79%

    Explanation:

    Yield to maturity = [C + (F - P) / n] / [ (F + P) / 2]

    C = coupon = $90 F = face value = $1,000 P = market value = $1,175 n = 25 years

    YTM = [ $90 + ($1,000 - $1,175) / 25] / [ ($1,000 + $1,175) / 2 ] = ($90 - 7) / $1,087.50 = 7.63%

    Yield to call = [C + (Cv - P) / n] / [ (Cv + P) / 2]

    C = coupon = $90 Cv = call value = $1,050 P = market value = $1,175 n = 5 years

    YTC = [ $90 + ($1,050 - $1,175) / 5] / [ ($1,050 + $1,175) / 2 ] = ($90 - 25) / $1,112.50 = 5.84%

    YTM - YTC = 7.63% - 5.84% = 1.79%
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