holdy Inc's bonds currently sell for $1,275. They pay a $120 annual coupon and have a 20-year maturity, but they can be called in 5 years at $1,120. 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 the bond's YTM and its YTC?

Yield to maturity (YTM) is 1.91% higher than yield to call (YTC).

Explanation:

YTM = {coupon + [(face value - market value)/n]} / [(face value + market value)/2]

YTM = {$120 + [($1,000 - $1,275)/20]} / [($1,000 + $1,275)/2] = $106.25 / $1,137.50 = 9.34%

YTC = {coupon + [(call price - market value)/n]} / [(call price + market value)/2]

YTC = {$120 + [($1,120 - $1,275)/5]} / [($1,120 + $1,275)/2] = $89 / $1,197.50 = 7.43%

9.34% - 7.43% = 1.91%

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