Question

A 20-year $1000 bond with 8% annual coupons redeems for $1100 and is callable on coupon dates beginning 12 years from today. Find the maximum price the investor should pay in order to guarantee a minimum yield of 7%.

Answer 1

Assume that bond's yield-to-call is 7%; the formula to calculate the bond's maximum price

P = the current market price of bond =?

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

CP = the call price = $1,100 (assumed it as the maturity value if the bond is callable)

t = the number of years remaining until the call date = 12 years

YTC = the yield to call =7%

The complete formula to calculate yield to call is:

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

P = $80 *{(1- 1/ (1+ 7%) ^12)/ (7%)} + ($1,100/ (1+7%) ^12)

= $635.41 + $488.41

= $1,123.83

Therefore the maximum price the investor should pay is $1,123.83 in order to guarantee a minimum yield of 7%.