Question

A bond currently sells for AED1,040 and has a par value of AED1,000. It pays a AED65 annual coupon and has a 15-year maturity, but it can be called in 5 years at AED1,100. Find the approximate yield to maturity.

Answer 1

Let the Yield to maturity be y. The approximate YTM is given by

y = (C+(M-P)/n) / (0.4*M+0.6*P)

Where:

C    = the annual interest payments

M = the maturity (face) value of the bond

P   = the current market price of the bond

N = the number of years to maturity\

y = (65+(1000-1040)/15)/(0.4*1000+0.6*1040)

=0.060872

Putting this value of y into

65/y*(1-1/(1+y)^15) +1000/(1+y)^15 = 1040

we get LHS =1039.86 which is approximately correct, by hit and trial around this value , we get y =0.06086

So, the value of YTM = 0.06086 o 6.086%

As the bond pays higher coupons, it might be called after 5 years . The approximate Yield to call (YTC) is given by

y = (65+(1100-1040)/5)/(0.4*1100+0.6*1040) =0.072368

As the YTC is significantly higher , the Bond will not be called and its YTM will be 6.086%