Question

B. A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in 5 years at a call price of $1100. The bond currently sells at a yield to maturity (YTM) of 7% (3.5% per half-year). What is the yield to call? How does it relate to the YTM? Why?   

Answer 1

Given,

Interest rate = 8%

Call period = 5 years

YTM = 7%

Yield to Maturity = Interest / Current price

7% = 80 / Current price

Current price = (80 X 100) / 7

Therefore,

Current price = 1142.86

Let us calculate Yield to call if call price is 1100:

So

i = 80

n = 5

Rv (redemption value) = 1100

M_p (current market price ) = 1142.86

Let us say A = (R_v – M_p) / n and B = (R_v – M_p) / 2

So, A = (1100 – 1142.86) / 5 = –42.86 / 5 = –8.572

B = (1100 + 1142.86) / 2 = 1121.43

Therefore,

Yield to call = (i+A) / B

= (80 – 8.572) / 1121.43

= 71.428 / 1121.43

= 0.0637 or 6.37%

= 6.37%

Yield to call is 6.37%

Yield to call(YTC) and Yield to maturity(YTM) relationship:

YTM is the total return that cleared out from the event of a bond's acquisition to its termination date. YTC is the amount that spent if the issuer of a callable bond prefers to pay early. Usually, callable bonds allow an insignificantly higher YTM. A callable bond traded with the view that the issuer may repay before it approaches maturity.

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