A 6.50 percent coupon bond with 24 years left to maturity can be called in eight

Question

A 6.50 percent coupon bond with 24 years left to maturity can be called in eight years. The call premium is one year of coupon payments. It is offered for sale at $1,127.25. What is the yield to call of the bond? (Assume interest payments are semiannual.) (Round your answer to 2 decimal places.)

A 6.50 percent coupon bond with 24 years left to maturity can be called in eight years. The call premium is one year of coupon payments. It is offered for sale at $1,127.25. What is the yield to call of the bond? (Assume interest payments are semiannual.) (Round your answer to 2 decimal places.)

Explanation / Answer

Time to Maturity = 24 years

Coupon rate = 6.5%

Coupon payments are semi annual

Semi Annual Coupon Rate = (6.5%/2) * 1000 = $32.5

Price of the bond = $1,127.25

Assuming Par Value of the bond = $1,000

Time to call = 8 years

Call Premium = One year of coupon payments = 6.5% * 1000 = $65

Call Price = Price paid to the bondholder if the bond is called = Par Value + Call Premium = 1000 + 65 = $1,065

Yield to Call (YTC) is simply the yield to maturity of the bond assuming that the bond is called on the call date at the call price. Thus, in this case, the time to maturity becomes the call date = 8 years

So, using the bond pricing formula,

1127.25 = 32.5/[1 + (YTC/2)]1 + 32.5/[1 + (YTC/2)]2 + 32.5/[1 + (YTC/2)]3 + _ _ _ _ _ _ + 32.5/[1 + (YTC/2)]14 +

                 32.5/[1 + (YTC/2)]15 + (32.5 + 1065)/[1 + (YTC/2)}16

Thus, YTC/2 = 2.60%

YTC = 2.60% * 2 = 5.20%

Thus, yield to call of the bond is 5.20%

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