Question

Bonds issued by Oxygen Optimization were priced at 836.64 dollars 6 months ago. The bonds pay semi-annual coupons, have a coupon rate of 5.46 percent, just made a coupon payment, and have a face value of 1,000 dollars. If the bonds had a percentage return over the past 6 months (from 6 months ago to today) of 4.58 percent, then what is the current yield of the bonds today? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098. In another case, bonds issued by Fairfax Paint have a par value of 1000 dollars, were priced at 1,175.23 dollars six months ago, and are priced at 1,097.89 today. The bonds pay semi-annual coupons and just made a coupon payment. If the bonds had a percentage return over the past 6 months (from 6 months ago to today) of -1.61 percent, then what was the current yield of the bonds 6 months ago? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098. Lastly, Bonds issued by Fairfax Mechanical were priced at 1,054.17 dollars six months ago and are priced at 1,038.31 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 7.16 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

Bonds issued by Oxygen Optimization

Coupon paid by the bond = $1000* 5.46%/2 = $27.30

% return over past 6 months = 4.58% * $836.64 = $38.32

So, increase in price = $38.32-$27.30 = $11.02

So, price today = $836.64+$11.02 =$847.66

Current yield today = Annual coupon/current price = $1000*5.46%/$847.66 = 0.0644

Bonds issued by Fairfax paint

Let the coupon rate be c%

Coupon paid by the bond = $1000* c%/2 = $500*c% = 5*c

% return over past 6 months = -1.61%* $1175.23 = -$18.80

So, increase in price = -18.80 - 5c

So, Also increase in price = $1097.89-$1175.23 =-$77.34

So, -18.80 - 5c = -77.34

=> c= 11.71%

Current yield six months ago = Annual coupon/ price six months ago = $1000*11.71%/$1175.23 = 0.0996

Bonds issued by Fairfax Mechanical

Let the coupon rate be c%

Coupon paid by the bond = $1000* c%/2 = $500*c% = 5*c

% return over past 6 months = 7.16%* $1054.17 = $75.48

So, increase in price = $75.48 - 5c

So, Also increase in price = $1038.31-$1054.17 =-$15.86

So, 75.48 - 5c = -15.86

=> c= 18.27%

Coupon rate of the bond is 0.1827