Question

1. Bonds issued by Fairfax Mechanical were priced at 933.2 dollars six months ago and are priced at 918.89 dollars today. The bonds have a face value of 1,000 dollars, pay semi-annual coupons, and just made a coupon payment. The bonds had a percentage return over the past six months (from 6 months ago to today) of 8.69 percent. What is the coupon rate of the bonds? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

Solution:

Given:

Face Value of Bond = $ 1,000

Price of Bond 6 Months ago = $ 933.20

Price of Bond After 6 Months i.e. Present Day = $ 918.89

Percentage Return After 6 Months i.e. Present Day = 8.69 %

To Calculate:

The Coupon Rate of the Bonds

Formula:

Percentage Return After 6 Months = (Price of Bond After 6 Months - Price of Bond Before 6 Months + Coupon Payment) / Price of Bond Before 6 Months

Note:

Coupon Payment = (Face Value × Coupon Rate) / Number of Times Interest Paid in a Year

Number of Times Interest Paid in a Year = 2 (Semi- Annual Payment n = 2)

So, Coupon Payment = (1000 × CR) / 2

CR = Coupon Rate

Here:

Percentage Return After 6 Months = 8.69 % = 0.0869

Price of Bond After 6 Months = $ 918.89

Price of Bond Before 6 Months = $ 933.20

Coupon Payment = (1000 × CR) / 2

Now we calculate Coupon Rate by putting the above values in the formula,

Percentage Return After 6 Months = (Price of Bond After 6 Months - Price of Bond Before 6 Months + Coupon Payment) / Price of Bond Before 6 Months

0.0869 = (918.89 – 933.20 + (1000 × CR / 2)) / 933.20

0.0869 × 933.20 = (-14.31 + 500 × CR)

81.09508 = -14.31 + 500 × CR

81.09508 + 14.31 = 500 × CR

95.40508 = 500 × CR

CR = 95.40508 / 500

CR = 0.19081016 or 19.081016 %

Coupon Rate = 0.19081016

Ans: Coupon Rate = 0.1908