Instructions: I need all the steps to be shown and calculated this order: A. For
ID: 2653179 • Letter: I
Question
Instructions: I need all the steps to be shown and calculated this order: A. Formula, then numbers plugged in formula and answer. B. I don’t need graphs and tones of numbers got from finance software programs. Only I need steps and how all the steps are calculated using the formula, plugged numbers and answers. C. Answer exactly what I’m asking on the both questions. D. Follow these instructions. 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. Compute the ytm and the call rate. Comment on their magnitude in comparison to each other.Explanation / Answer
(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.