Question

Aziz works for a broker. One of his clients is offered to buy a bond at $1,050. It is a 10%, 15-year bond with a par value of $1,000 and a call price of $1,100. (The bonds first call date is in five years). Coupon payments are made semiannually.

Find the current yield, YTM and YTC on this issue. Which of these yields is the highest? Which is the lowest? Which yield would Aziz use to value this bond? Explain.  
              
Assume that the price of the bond declines to $875. Now which yield is the highest? Which is the lowest? Which yield would Aziz use to value this bond? Explain.                           

Answer 1

Calculation of Yield to Maturity

YTM = {Annual Interest + (Face value - Market Price)/Maturity date} / (Face value + Market Price)/2

= {100 + (1000 - 1050)/15} / (1000 + 1050)/2 = 9.43 %

Calculation of Yield to Call

YTC = {Annual Interest + (Call Price - Market Price)/First call date} / (Call Price + Market Price)/2

= {100 + (1100 - 1050)/5} / (1100+1050)/2 = 10.23%

Yield to call is highest and Yield to maturity is Lowest.

If market price declines to $875

YTM = {100 + (1000 - 875)/15} / (1000 + 875)/2 = 11.56%

YTC = {100 + (1100 - 875)/5} / (1100+875)/2 = 14.68%

Yield to call is highest and Yield to maturity is Lowest.

Aziz would use Yield to call to value this bond. As the buyer of a bond usually focuses on its yield to maturity (the total return that will be paid out by a bond's expiration date). But the buyer of a callable bond also wants to estimate its yield to call.

A callable bond can be redeemed by its issuer before it reaches its stated maturity date. Callable bonds usually offer a more attractive yield to maturity, along with the proviso that the issuer may "call" it if overall interest rates change and it finds it can borrow money less expensively in another way.