Question

Marco Verratti's bonds currently sell for $1,175.89 with par value of $1,000.00. The bonds pay 13.00 percent coupon rate and have a 17-year maturity, but they can be called in 6 years at $1,097.00. There are no costs but the call premium and refund the bonds. In addition, assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the bonds’ yield to maturity? What is the bonds’ yield to call?

Answer 1

Assumption: Bond pays annual coupon

Yield to maturity is the discount rate at which the sum of all future cash flows from the bond (coupons and principal) is equal to the current price of the bond.

Yield to call is the yield of a bond or note if you were to buy and hold the security until the call date, but this yield is valid only if the security is called prior to maturity.

Manually, it is almost impossible to calculate YTM or YTC. In order to calculate exact YTM or YTC, we need to use either financial calculator or Excel (Excel calculations shown in snapshot at end).

We will use approximation formula for YTM and YTC.

Mathematical relation for approximate YTM is as below:

C = 130 (13% of par value), F = $1,000, P = $1,175.89, n = 17

Substituting these values in mathematical relation above:

Approx YTM = 119.6535/1087.9450

Approx YTM = 10.998%

Similaryly, mathematical relation for approximate Yield to Call is as below:

Call price = $1,097, Number of years to call = 6 years

Approx YTC = 10.86%

Now, the above calculations are only aprroximate. Exact calculations need to use Excel or Financial Calculators, for which snapshots are below:

Exact YTM and YTC are hence 10.71% and 10.19%, respectively