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Bonds issued by Oxygen Optimization were priced at 1,186.65 dollars 6 months ago. The bonds pay...

Bonds issued by Oxygen Optimization were priced at 1,186.65 dollars 6 months ago. The bonds pay semi-annual coupons, have a coupon rate of 4.66 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 -3.97 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.

Bonds issued by Fairfax Paint have a par value of 1000 dollars, were priced at 1,008.8 dollars six months ago, and are priced at 942.55 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 -1.98 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.

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Expert Solution

Bonds by Oxygen Optimization:

Given,

Price 6 months ago (P₀)=$1,186.65

Face Value FV=$1,000

Coupon rate (R)=4.66% Payable semiannually.

Percentage Return over the past 6 months (Y)= -3.97% Or, -.0397

Semi annual interest payment (I)= FV*R/2= $1,000*0.0466/2= $23.30

Let the price today be P₁

Percentage Yield Y= (Interest +(End price- Begin Price))/Begin price

ie., Y=[I+(P₁-P₀)]/P₀

-0.0397=(23.30 + P₁-1186.65)/1186.65

P₁-1163.35= -0.0397*1186.65= -47.1105

Therefore the price (P₁)= -47.1105+1163.35= $1,116.24

Current yield today=Coupon interest per year/Price today

= ($23.30*2)/$1116.24=0.0417

======

Bonds by Fairfax Paint:

Given,

Price 6 months ago (P₀)=$1,008.80

Face Value FV=$1,000

Percentage Return over the past 6 months (Y)= -1.98% Or, -.0198

Price today (P₁)= $942.55

Interest frequency= Semi annual

Let semiannual interest be (I)

Percentage Yield Y= (Interest +(End price- Begin Price))/Begin price

ie., Y=[I+(P₁-P₀)]/P₀

-0.0198=(I +942.55-1008.80)/1008.80

I -66.25= -0.0198*1008.80= -19.9742

Therefore Coupon payment I= -19.9742+66.25 = $46.2758

Current yield 6 months ago=Coupon interest per year/Price 6 months ago

=$46.2758*2/1008.80=0.0974

=====

jeff jeffy answered 1 year ago

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