Question: We have a semiannual bond selling for $950 and paying an annual coupon

Question

Question:

We have a semiannual bond selling for $950 and paying an annual coupon rate of 10% per annum for a period of 25 years. The issuer has inserted a call feature enabling it to buy back the bond at face value plus 2 semesters’ interest after 5 years.

1) Compute the ytm (yield to maturity)

2) Compute the call rate.

3) Comment on their magnitude in comparison to each other.

Please identify the numbers, such as showing which number is n (Number of Periods), I (coupon rate), Par value, Pb (price of the bond), and et cetera.

Please display the formula that you used and please show work (step by step). The more detailed, clear, organized your work, it will help me understand the problem a lot better.

Explanation / Answer

Ans;

1) YTM

A bond's YTM is calculated as

YTM =

YTC = [C + {(FV - MP) / N}] / [(FV + MP) / 2]

C: Annual coupon payment = $100 ( = Face Value x 10%)

FV: Face Value = $1,000

MP: Market Price = $950

N: Years to Maturity = 25

So, YTM = [$100 + $ {(1,000 - 950) / 25}] / $[(1,000 + 950) / 2]

= $ 101 / $975 = 10.36%

(2) Call rate

Since this bond is callable in 5 years, the YTM we calculate is called the Yield to Call (YTC), or Call Rate.

The YTC formula is as follows:

YTC = [C + {(CP - MP) / N}] / [(CP + MP) / 2]

C: Annual coupon payment

Call Price, CP = Face Value + 2 semi-annual coupons = $1,000 + $100 = $1,100

MP: Current Market Price = $950

N: Number of years till call date = 5

So,

YTC = [$100 + $ {(1,100 - 950) / 5}] / $[(1,100 + 950) / 2]

= $130 / $1,025 = 12.68%

(3) We observe that, bond's YTM is less than the YTC. This is not surprising. Calling a bond is an advantage to the issuer and disadvantage to the bondholder, because a callable bond is called only when the market interest rate falls down below the coupon rate, therefore the issuer can call the issue & refinance it at lower rate. The call feature reduces the obligation of the issuers. To compensate the bondholder for this potential disadvantage, callable bonds carry a higher yield than a non-callable bond.

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