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

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%

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%