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The Harrison Company’s bonds currently sell for $1,275\$1,275. They pay a $120\$120 annual coupon, have a 2020-year maturity, and a par value of $1,000\$1,000, but they can be called in 55 years at $1,120\$1,120. What is their YTC?

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Q. The Harrison Company’s bonds currently sell for $1,275\$1,275. They pay a $120\$120 annual coupon, have a 2020-year maturity, and a par value of $1,000\$1,000, but they can be called in 55 years at $1,120\$1,120. What is their YTC?
  1. Identify variables for YTC: Identify the variables needed to calculate the yield to call (YTC).
    Current bond price (P) = $1,275\$1,275
    Annual coupon payment (C) = $120\$120
    Years to call (N) = 55 years
    Call price (FV) = $1,120\$1,120
  2. Calculate annual interest: Calculate the annual interest received until the bond is called.\newlineInterest received per year = Annual coupon payment\newlineInterest received per year = $120\$120
  3. Calculate total amount at call: Calculate the total amount received at the call date.\newlineTotal amount received at call = Call price + (Annual coupon payment * Years to call)\newlineTotal amount received at call = $1,120\$1,120 + ($120\$120 * 55)\newlineTotal amount received at call = $1,120\$1,120 + $600\$600\newlineTotal amount received at call = $1,720\$1,720
  4. Calculate net profit: Calculate the net profit if the bond is called.\newlineNet profit = Total amount received at call - Current bond price\newlineNet profit = $1,720\$1,720 - $1,275\$1,275\newlineNet profit = $445\$445
  5. Calculate average annual profit: Calculate the average annual profit.\newlineAverage annual profit = Net profit / Years to call\newlineAverage annual profit = $445/5\$445 / 5\newlineAverage annual profit = $89\$89
  6. Calculate YTC approximation: Calculate the yield to call (YTC) as an approximation.\newlineYTC=Annual coupon payment+Average annual profit(Current bond price+Call price2)YTC = \frac{\text{Annual coupon payment} + \text{Average annual profit}}{\left(\frac{\text{Current bond price} + \text{Call price}}{2}\right)}\newlineYTC=($120+$89)(($1,275+$1,120)/2)YTC = \frac{(\$120 + \$89)}{((\$1,275 + \$1,120) / 2)}\newlineYTC=$209(($1,275+$1,120)/2)YTC = \frac{\$209}{((\$1,275 + \$1,120) / 2)}\newlineYTC=$209($2,395/2)YTC = \frac{\$209}{(\$2,395 / 2)}\newlineYTC=$209$1,197.50YTC = \frac{\$209}{\$1,197.50}\newlineYTC=0.1745YTC = 0.1745 or 17.45%17.45\%

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