Question

Bond ABC is currently (year 2020) selling at 105% of par value, it matures by the end of 2030 but callable by the end of 2025.

When it is called in 2025, there is 6% call premium. The annual coupon rate is 8%. It is an annual coupon bond, and 2020's coupon has not been distributed to investors yet.

What is Bond ABC’s Yield to Call if you purchase it right now? (Please round up your answers to two decimals and write in percentage points without the sign. e.g. If your answer is 12.859%, type 12.86 without the percentage sign)

Answer 1

The formula to calculate the bond's yield-to-call is

P = C * {(1 – 1/ (1 + YTC) ^ t) / (YTC)} + (CP / (1 + YTC) ^t)

Where,

P = the current market price of bond = $1,000 * 105% = $1050 (selling at 105% of par value)

C = coupon payment = 8% of $1000 = $80

CP = the call price (with 6% call premium) =$1,000 * (1+6%) = $1,060 (assumed it as the maturity value if the bond is callable)

t = the number of coupons remaining until the call = 6

YTC = the yield to call =?

Therefore,

$1,050 = $80 *{(1- 1/ (1+ YTC) ^6)/ (YTC)} + ($1,060/ (1+YTC) ^6)

With the help of above equation and by trial and error method we can calculate the value of YTC = 7.75% per year

[Or you can use excel function for YTC calculation in following manner

“= Rate(N,PMT,PV,FV,0)”

“Rate(6,-80,1050,-1060,0)” = 7.75%]

[Note: If coupon payments are assumed at the beginning of the period (as nothing is written clearly in the question) then YTC will be 8.39% per year; “Rate(6,-80,1050,-1060,1)” = 8.39%]